Preferences消费者偏好(2)

ChapterThreePreferences消费者偏好WhereAreWeintheCourse?Wearestudyingthe1stofthethreeblocksofmicroeconomics:Consumerbehavior,productiontheory,andmarketequilibriumWithinthe1stblock,weareworkingonthe2ndofthethreecomponents:choiceset,preference,andconsumerdemandWhatDoWeMeanbyPreference?(偏好)Itreferstotheorderedrelationshipamongalternativechoicesgivenbyaneconomicagent.Inmosteconomicliterature,consumerpreferenceistreatedastheultimateexogenouselement.PreferenceRelationsComparingtwodifferentconsumptionbundles,xandy:–strictpreference:xismorepreferredthanisy.–weakpreference:xisasatleastaspreferredasisy.–Indifference:xisexactlyaspreferredasisy.Notationsdenotesstrictpreference;~denotesindifference;denotesweakpreference;p~fPreferenceRelationsxyandyximplyx~y.xyand(notyx)implyxy.~f~f~f~fpAssumptionsaboutPreferenceRelationsCompleteness:Foranytwobundlesxandyitisalwayspossibletomakethestatementthateitherxyoryx.~f~fAssumptionsaboutPreferenceRelationsReflexivity:Anybundlexisalwaysatleastaspreferredasitself;i.e.xx.~fAssumptionsaboutPreferenceRelationsTransitivity:Ifxisatleastaspreferredasy,andyisatleastaspreferredasz,thenxisatleastaspreferredasz;i.e.xyandyzxz.~f~f~fIndifferenceCurves无差异曲线(或,无差异集)Takeareferencebundlex’.Thesetofallbundlesequallypreferredtox’istheindifferencecurvecontainingx’;thesetofallbundlesy~x’.Sinceanindifference“curve”isnotalwaysacurveabetternamemightbeanindifference“set”.IndifferenceCurvesx2x1x”x”’x’~x”~x”’x’IndifferenceCurvesx2x1zxyppxyzIndifferenceCurvesx2x1xAllbundlesinI1arestrictlypreferredtoallinI2.yzAllbundlesinI2arestrictlypreferredtoallinI3.I1I2I3IndifferenceCurvesx2x1WP(x),thesetofbundlesweaklypreferredtox.WP(x)includesI(x).xI(x)IndifferenceCurvesx2x1SP(x),thesetofbundlesstrictlypreferredtox,doesnotincludeI(x).xI(x)IndifferenceCurvesCannotIntersect!(不相交!)x2x1xyzI1I2FromI1,x~y.FromI2,x~z.Thereforey~z.IndifferenceCurvesCannotIntersectx2x1xyzI1I2FromI1,x~y.FromI2,x~z.Thereforey~z.ButfromI1andI2weseeyz,acontradiction.pSlopesofIndifferenceCurvesWhenmoreofacommodityisalwayspreferred,thecommodityisagood.Ifeverycommodityisagoodthenindifferencecurvesarenegativelysloped.SlopesofIndifferenceCurvesGood2Good1Twogoodsanegativelyslopedindifferencecurve.SlopesofIndifferenceCurvesIflessofacommodityisalwayspreferredthenthecommodityisabad.SlopesofIndifferenceCurvesGood2Bad1Onegoodandonebadapositivelyslopedindifferencecurve.ExtremeCasesofIndifferenceCurves;PerfectSubstitutesIfaconsumeralwaysregardsunitsofcommodities1and2asequivalent,thenthecommoditiesareperfectsubstitutesandonlythesumofthetwocommoditiesinbundlesdeterminestheirpreferencerank-order.ExtremeCasesofIndifferenceCurves;PerfectSubstitutesx2x1881515Slopesareconstantat-1.I2I1BundlesinI2allhaveatotalof15unitsandarestrictlypreferredtoallbundlesinI1,whichhaveatotalofonly8unitsinthem.ExtremeCasesofIndifferenceCurves;PerfectComplementsIfaconsumeralwaysconsumescommodities1and2infixedproportion(e.g.one-to-one),thenthecommoditiesareperfectcomplementsandonlythenumberofpairsofunitsofthetwocommoditiesdeterminesthepreferencerank-orderofbundles.ExtremeCasesofIndifferenceCurves;PerfectComplementsx2x1I2I145o5959Sinceeachof(5,5),(5,9)and(9,5)contains5pairs,eachislesspreferredthanthebundle(9,9)whichcontains9pairs.PreferencesExhibitingSatiationAbundlestrictlypreferredtoanyotherisasatiationpointorablisspoint.Whatdoindifferencecurveslooklikeforpreferencesexhibitingsatiation?IndifferenceCurvesExhibitingSatiationx2x1BetterSatiation(bliss)pointIndifferenceCurvesforDiscreteCommoditiesAcommodityisinfinitelydivisibleifitcanbeacquiredinanyquantity;e.g.waterorcheese.Acommodityisdiscreteifitcomesinunitlumpsof1,2,3,…andsoon;e.g.aircraft,shipsandrefrigerators.IndifferenceCurvesforDiscreteCommodities(studythisyourself)Supposecommodity2isaninfinitelydivisiblegood(gasoline)whilecommodity1isadiscretegood(aircraft).Whatdoindifference“curves”looklike?IndifferenceCurvesWithaDiscreteGood(studythisyourself)Gas-olineAircraft01234Indifference“curves”arecollectionsofdiscretepoints.Well-BehavedPreferencesApreferencerelationis“well-behaved”ifitis–monotonicandconvex.Monotonicity:Moreofanycommodityisalwayspreferred(i.e.nosatiationandeverycommodityisagood).Well-BehavedPreferencesConvexity(凸性):Mixturesofbundlesare(atleastweakly)preferredtothebundlesthemselves.E.g.,the50-50mixtureofthebundlesxandyisz=(0.5)x+(0.5)y.zisatleastaspreferredasxory.Well-BehavedPreferences--Convexity.x2y2x1y1xyz=(tx1+(1-t)y1,tx2+(1-t)y2)ispreferredtoxandyforall0t1.Well-BehavedPreferences--Convexity.x2y2x1y1xyPreferencesarestrictlyconvexwhenallmixtureszarestrictlypreferredtotheircomponentbundlesxandy.zWell-BehavedPreferences--WeakConvexity.x’y’z’Preferencesareweaklyconvexifatleastonemixturezisequallypreferredtoacomponentbundle.xzyNon-ConvexPreferencesx2y2x1y1zThemixturezislesspreferredthanxory.MoreNon-ConvexPreferencesx2y2x1y1zThemixturezislesspreferredthanxory.MarginalRate-of-Substitution(边际替代率)Theslopeofanindifferencecurveisitsmarginalrate-of-substitution(MRS)(边际替代率)HowcanaMRSbecalculated?MarginalRateofSubst