微观经济学第6章

ChapterSix Demand需求 PropertiesofDemandFunctions Comparativestaticsanalysis 比较静态分析 ofordinarydemandfunctions thestudyofhowordinarydemandsx1 p1 p2 y andx2 p1 p2 y changeaspricesp1 p2andincomeychange Structure Own pricechangesPriceoffercurve 价格提供曲线 OrdinarydemandcurveInversedemandcurve 反需求函数 IncomechangesIncomeoffercurve 收入提供曲线 Engelcurve 恩格尔曲线 Cross priceeffects 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 x1 p1 Own PriceChanges p1 p1 Fixedp2andy x1 p1 p1 x1 p1 p1 x1 Own PriceChanges Fixedp2andy p1 p1 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 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 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 Thentheordinarydemandfunctionsforcommodities1and2are Take 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 Thentheordinarydemandfunctionsforcommodities1and2are 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 p1 p1 p2 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 MeaningoftheInverseDemandFunction AtoptimalchoiceOrIftakinggood2asmoneyonothergoods thenp2 1andp1 MRS Thisisthemarginalwillingnesstopay 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 Engelcurve good1 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 Supposep1 p2 Then and and IncomeChangesandPerfectly SubstitutablePreferences y y x1 x2 0 Engelcurveforgood1 Engelcurveforgood2 IncomeChanges IneveryexamplesofartheEngelcurveshaveallbeenstraightlines Q Isthistrueingeneral A No Engelcurvesarestraightlinesiftheconsumer spreferencesarehomothetic Homotheticity 位似偏好 Aconsumer spreferencesarehomotheticifandonlyifforeveryk 0 Thatis theconsumer sMRSisthesameanywhereonastraightlinedrawnfromtheorigin x1 x2 y1 y2 kx1 kx2 ky1 ky2 p p IncomeEffects ANonhomotheticExample Quasilinearpreferencesarenothomothetic Forexample Optimalinteriorconsumption 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 正常品 Thereforeanormalgood sEngelcurveispositivelysloped IncomeEffects Agoodforwhichquantitydemandedfallsasincomeincreasesiscalledincomeinferior 劣质品 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 Incomeoffercurve IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 x1 y Engelcurveforgood1 IncomeChanges Good2IsNormal Good1BecomesIncomeInferior x2 x1 x1 x2 y y Engelcurveforgood2 Engelcurveforgood1 OrdinaryGoods 一般商品 Agoodiscalledordinaryifthequantitydemandedofitalwaysincreasesasitsownpricedecreases OrdinaryGoods Fixedp2andy x1 x2 p1priceoffercurve OrdinaryGoods Fixedp2andy x1 x2 p1priceoffercurve x1 Downward slopingdem