范里安现代观点课件——南开大学中级微观经济学.ppt

ChapterSix Demand PropertiesofDemandFunctions Comparativestaticsanalysisofordinarydemandfunctions thestudyofhowordinarydemandsx1 p1 p2 y andx2 p1 p2 y changeaspricesp1 p2andincomeychange Own PriceChanges Howdoesx1 p1 p2 y changeasp1changes holdingp2andyconstant Supposeonlyp1increases fromp1 top1 andthentop1 x1 x2 p1 p1 Fixedp2andy p1x1 p2x2 y Own PriceChanges Own PriceChanges x1 x2 p1 p1 p1 p1 Fixedp2andy p1x1 p2x2 y Own PriceChanges x1 x2 p1 p1 p1 p1 Fixedp2andy p1 p1 p1x1 p2x2 y p1 p1 Own PriceChanges Fixedp2andy x1 p1 Own PriceChanges p1 p1 Fixedp2andy x1 p1 p1 x1 p1 p1 x1 Own PriceChanges Fixedp2andy p1 p1 x1 p1 p1 x1 p1 p1 p1 p1 x1 Own PriceChanges Fixedp2andy x1 p1 x1 p1 p1 x1 p1 p1 p1 p1 x1 Own PriceChanges Fixedp2andy x1 p1 x1 p1 p1 x1 p1 x1 p1 p1 p1 x1 Own PriceChanges Fixedp2andy x1 p1 x1 p1 p1 x1 p1 x1 p1 p1 p1 p1 p1 x1 Own PriceChanges Fixedp2andy x1 p1 x1 p1 x1 p1 p1 x1 p1 x1 p1 p1 p1 p1 p1 x1 Own PriceChanges Fixedp2andy x1 p1 x1 p1 x1 p1 p1 x1 p1 x1 p1 x1 p1 p1 p1 p1 x1 Own PriceChanges Fixedp2andy x1 p1 x1 p1 x1 p1 p1 x1 p1 x1 p1 x1 p1 p1 p1 p1 x1 Own PriceChanges Ordinarydemandcurveforcommodity1 Fixedp2andy x1 p1 x1 p1 x1 p1 p1 x1 p1 x1 p1 x1 p1 p1 p1 p1 x1 Own PriceChanges Ordinarydemandcurveforcommodity1 Fixedp2andy x1 p1 x1 p1 x1 p1 p1 x1 p1 x1 p1 x1 p1 p1 p1 p1 x1 Own PriceChanges Ordinarydemandcurveforcommodity1 p1priceoffercurve Fixedp2andy Own PriceChanges Thecurvecontainingalltheutility maximizingbundlestracedoutasp1changes withp2andyconstant isthep1 priceoffercurve Theplotofthex1 coordinateofthep1 priceoffercurveagainstp1istheordinarydemandcurveforcommodity1 Own PriceChanges Whatdoesap1price offercurvelooklikeforCobb Douglaspreferences Own PriceChanges Whatdoesap1price offercurvelooklikeforCobb Douglaspreferences TakeThentheordinarydemandfunctionsforcommodities1and2are Own PriceChanges and Noticethatx2 doesnotvarywithp1sothep1priceoffercurveis Own PriceChanges and Noticethatx2 doesnotvarywithp1sothep1priceoffercurveisflat Own PriceChanges and Noticethatx2 doesnotvarywithp1sothep1priceoffercurveisflatandtheordinarydemandcurveforcommodity1isa Own PriceChanges and Noticethatx2 doesnotvarywithp1sothep1priceoffercurveisflatandtheordinarydemandcurveforcommodity1isarectangularhyperbola x1 p1 x1 p1 x1 p1 Own PriceChanges Fixedp2andy x1 p1 x1 p1 x1 p1 p1 x1 Own PriceChanges Ordinarydemandcurveforcommodity1is Fixedp2andy Own PriceChanges Whatdoesap1price offercurvelooklikeforaperfect complementsutilityfunction Own PriceChanges Whatdoesap1price offercurvelooklikeforaperfect complementsutilityfunction Thentheordinarydemandfunctionsforcommodities1and2are Own PriceChanges Own PriceChanges Withp2andyfixed higherp1causessmallerx1 andx2 Own PriceChanges Withp2andyfixed higherp1causessmallerx1 andx2 As Own PriceChanges Withp2andyfixed higherp1causessmallerx1 andx2 As As Fixedp2andy Own PriceChanges x1 x2 p1 x1 Fixedp2andy Own PriceChanges x1 x2 p1 p1 p1 y p2 p1 x1 Fixedp2andy Own PriceChanges x1 x2 p1 p1 p1 p1 y p2 p1 x1 Fixedp2andy Own PriceChanges x1 x2 p1 p1 p1 p1 p1 y p2 p1 x1 Ordinarydemandcurveforcommodity1is Fixedp2andy Own PriceChanges x1 x2 p1 p1 p1 y p2 Own PriceChanges Whatdoesap1price offercurvelooklikeforaperfect substitutesutilityfunction Thentheordinarydemandfunctionsforcommodities1and2are Own PriceChanges and Fixedp2andy Own PriceChanges x2 x1 Fixedp2andy p1 p1 p2 Fixedp2andy Own PriceChanges x2 x1 p1 x1 Fixedp2andy p1 p1 p1 p2 Fixedp2andy Own PriceChanges x2 x1 p1 x1 Fixedp2andy p1 p1 p1 p2 Fixedp2andy Own PriceChanges x2 x1 p1 x1 Fixedp2andy p1 p1 p1 p2 Fixedp2andy Own PriceChanges x2 x1 p1 x1 Fixedp2andy p1 p1 p1 p2 Fixedp2andy Own PriceChanges x2 x1 p1 x1 Fixedp2andy p1 p1 p1 p2 p2 p1 Fixedp2andy Own PriceChanges x2 x1 p1 x1 Fixedp2andy p1 p1 p2 p1 Fixedp2andy Own PriceChanges x2 x1 p1 x1 Fixedp2andy p1 p2 p1 p1 p1priceoffercurve Ordinarydemandcurveforcommodity1 Own PriceChanges Usuallyweask Giventhepriceforcommodity1whatisthequantitydemandedofcommodity1 Butwecouldalsoasktheinversequestion Atwhatpriceforcommodity1wouldagivenquantityofcommodity1bedemanded Own PriceChanges p1 x1 p1 Givenp1 whatquantityisdemandedofcommodity1 Own PriceChanges p1 x1 p1 Givenp1 whatquantityisdemandedofcommodity1 Answer x1 units x1 Own PriceChanges p1 x1 x1 Givenp1 whatquantityisdemandedofcommodity1 Answer x1 units Theinversequestionis Givenx1 unitsaredemanded whatisthepriceofcommodity1 Own PriceChanges p1 x1 p1 x1 Givenp1 whatquantityisdemandedofcommodity1 Answer x1 units Theinversequestionis Givenx1 unitsaredemanded whatisthepriceofcommodity1 Answer p1 Own PriceChanges Takingquantitydemandedasgivenandthenaskingwhatmustbepricedescribestheinversedemandfunctionofacommodity Own PriceChanges ACobb Douglasexample istheordinarydemandfunctionand istheinversedemandfunction Own PriceChanges Aperfect complementsexample istheordinarydemandfunctionand istheinversedemandfunction IncomeChanges Howdoesthevalueofx1 p1 p2 y changeasychanges holdingbothp1andp2constant IncomeChanges Fixedp1andp2 y y y IncomeChanges Fixedp1andp2 y y y IncomeChanges Fixedp1andp2 y y y x1 x1 x1 x2 x2 x2 IncomeChanges Fixedp1andp2 y y y x1 x1 x1 x2 x2 x2 Incomeoffercurve IncomeChanges AplotofquantitydemandedagainstincomeiscalledanEngelcurve IncomeChanges Fixedp1andp2 y y y x1 x1 x1 x2 x2 x2 Incomeoffercurve IncomeChanges Fixedp1andp2 y y y x1 x1 x1 x2 x2 x2 Incomeoffercurve x1 y x1 x1 x1 y y y IncomeChanges Fixedp1andp2 y y y x1 x1 x1 x2 x2 x2 Incomeoffercurve x1 y x1 x1 x1 y y y Engelcurve good1 IncomeChanges Fixedp1andp2 y y y x1 x1 x1 x2 x2 x2 Incomeoffercurve x2 y x2 x2 x2 y y y IncomeChanges Fixedp1andp2 y y y x1 x1 x1 x2 x2 x2 Incomeoffercurve x2 y x2 x2 x2 y y y Engelcurve good2 IncomeChanges Fixedp1andp2 y y y x1 x1 x1 x2 x2 x2 Incomeoffercurve x1 x2 y y x1 x1 x1 x2 x2 x2 y y y y y y Engelcurve good2 Engelcurve good1 IncomeChangesandCobb DouglasPreferences AnexampleofcomputingtheequationsofEngelcurves theCobb Douglascase Theordinarydemandequationsare IncomeChangesandCobb DouglasPreferences Rearrangedtoisolatey theseare Engelcurveforgood1 Engelcurveforgood2 IncomeChangesandCobb DouglasPreferences y y x1 x2 Engelcurveforgood1 Engelcurveforgood2 IncomeChangesandPerfectly ComplementaryPreferences AnotherexampleofcomputingtheequationsofEngelcurves theperfectly complementarycase Theordinarydemandequationsare IncomeChangesandPerfectly ComplementaryPreferences Rearrangedtoisolatey theseare Engelcurveforgood1 Engelcurveforgood2 Fixedp1andp2 IncomeChanges x1 x2 IncomeChanges x1 x2 y y y Fixedp1andp2 IncomeChanges x1 x2 y y y Fixedp1andp2 IncomeChanges x1 x2 y y y x1 x1 x2 x2 x2 x1 Fixedp1andp2 IncomeChanges x1 x2 y y y x1 x1 x2 x2 x2 x1 x1 y y y y Engelcurve good1 x1 x1 x1 Fixedp1andp2 IncomeChanges x1 x2 y y y x1 x1 x2 x2 x2 x1 x2 y x2 x2 x2 y y y Engelcurve good2 Fixedp1andp2 IncomeChanges x1 x2 y y y x1 x1 x2 x2 x2 x1 x1 x2 y y x2 x2 x2 y y y y y y Engelcurve good2 Engelcurve good1 x1 x1 x1 Fixedp1andp2 IncomeChanges x1 x2 y y x2 x2 x2 y y y y y y x1 x1 x1 Engelcurve good2 Engelcurve good1 Fixedp1andp2 IncomeChangesandPerfectly SubstitutablePreferences AnotherexampleofcomputingtheequationsofEngelcurves theperfectly substitutioncase Theordinarydemandequationsare IncomeChangesandPerfectly SubstitutablePreferences IncomeChangesandPerfectly SubstitutablePreferences Supposep1 p2 Then IncomeChangesandPerfectly SubstitutablePreferences Supposep1 p2 Then and IncomeChangesandPerfectly SubstitutablePreferences Supposep1 p2 Then and and IncomeChangesandPerfectly SubstitutablePreferences y y x1 x2 0 Engelcurveforgood1 Engelcurveforgood2 IncomeChanges IneveryexamplesofartheEngelcurveshaveallbeenstraightlines Q Isthistrueingeneral A No Engelcurvesarestraightlinesiftheconsumer spreferencesarehomothetic Homotheticity Aconsumer spreferencesarehomotheticifandonlyifforeveryk 0 Thatis theconsumer sMRSisthesameanywhereonastraightlinedrawnfromtheorigin x1 x2 y1 y2 kx1 kx2 ky1 ky2 p p IncomeEffects ANonhomotheticExample Quasilinearpreferencesarenothomothetic Forexample Quasi linearIndifferenceCurves x2 x1 Eachcurveisaverticallyshiftedcopyoftheothers Eachcurveintersectsbothaxes IncomeChanges QuasilinearUtility x2 x1 IncomeChanges QuasilinearUtility x2 x1 x1 y x1 Engelcurveforgood1 IncomeChanges QuasilinearUtility x2 x1 x2 y Engelcurveforgood2 IncomeChanges QuasilinearUtility x2 x1 x1 x2 y y x1 Engelcurveforgood2 Engelcurveforgood1 IncomeEffects Agoodforwhichquantitydemandedriseswithincomeiscallednormal Thereforeanormalgood sEngelcurveispositivelysloped IncomeEffects Agoodforwhichquantitydemandedfallsasincomeincreasesiscalledincomeinferior Thereforeanincomeinferiorgood sEngelcurveisnegativelysloped IncomeChanges Goods1 2Normal x1 x1 x1 x2 x2 x2 Incomeoffercurve x1 x2 y y x1 x1 x1 x2 x2 x2 y y y y y y Engelcurve good2 Engelcurve good1 IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 Incomeoffercurve IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 x1 y Engelcurveforgood1 IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 x1 x2 y y Engelcurveforgood2 Engelcurveforgood1 OrdinaryGoods Agoodiscalledordinaryifthequantitydemandedofitalwaysincreasesasitsownpricedecreases OrdinaryGoods Fixedp2andy x1 x2 OrdinaryGoods Fixedp2andy x1 x2 p1priceoffercurve Ordina