中级微观经济学课件尼科尔森

柯孔林浙江工商大学金融学院1Chapter3PREFERENCESANDUTILITY柯孔林浙江工商大学金融学院2AxiomsofRationalChoiceCompletenessifAandBareanytwosituations,anindividualcanalwaysspecifyexactlyoneofthesepossibilities:AispreferredtoBBispreferredtoAAandBareequallyattractive柯孔林浙江工商大学金融学院3AxiomsofRationalChoiceTransitivityifAispreferredtoB,andBispreferredtoC,thenAispreferredtoCassumesthattheindividual’schoicesareinternallyconsistent柯孔林浙江工商大学金融学院4AxiomsofRationalChoiceContinuityifAispreferredtoB,thensituationssuitably“closeto”AmustalsobepreferredtoBusedtoanalyzeindividuals’responsestorelativelysmallchangesineandprices柯孔林浙江工商大学金融学院5UtilityGiventheseassumptions,itispossibletoshowthatpeopleareabletorankinorderallpossiblesituationsfromleastdesirabletomostEconomistscallthisrankingutilityifAispreferredtoB,thentheutilityassignedtoAexceedstheutilityassignedtoBU(A)>U(B)柯孔林浙江工商大学金融学院6UtilityUtilityrankingsareordinalinnaturetheyrecordtherelativedesirabilityofcommoditybundlesBecauseutilitymeasuresarenotunique,itmakesnosensetoconsiderhowmuchmoreutilityisgainedfromAthanfromBItisalsoimpossibletocompareutilitiesbetweenpeople柯孔林浙江工商大学金融学院7UtilityUtilityisaffectedbytheconsumptionofphysicalcommodities,psychologicalattitudes,peergrouppressures,personalexperiences,andthegeneralculturalenvironmentEconomistsgenerallydevoteattentiontoquantifiableoptionswhileholdingconstanttheotherthingsthataffectutilityceterisparibusassumption柯孔林浙江工商大学金融学院8UtilityAssumethatanindividualmustchooseamongconsumptiongoodsx1,x2,…,xnTheindividual’srankingscanbeshownbyautilityfunctionoftheform:utility=U(x1,x2,…,xn;otherthings)thisfunctionisuniqueuptoanorder-preservingtransformation柯孔林浙江工商大学金融学院9EconomicGoodsIntheutilityfunction,thex’sareassumedtobe“goods”moreispreferredtolessQuantityofxQuantityofyx*y*Preferredtox*,y*??Worsethanx*,y*柯孔林浙江工商大学金融学院10IndifferenceCurvesAnindifferencecurveshowsasetofconsumptionbundlesamongwhichtheindividualisindifferentQuantityofxQuantityofyx1y1y2x2U1Combinations(x1,y1)and(x2,y2)providethesamelevelofutility柯孔林浙江工商大学金融学院11MarginalRateofSubstitutionThenegativeoftheslopeoftheindifferencecurveatanypointiscalledthemarginalrateofsubstitution(MRS)QuantityofxQuantityofyx1y1y2x2U1柯孔林浙江工商大学金融学院12MarginalRateofSubstitutionMRSchangesasxandychangereflectstheindividual’swillingnesstotradeyforxQuantityofxQuantityofyx1y1y2x2U1At(x1,y1),theindifferencecurveissteeper.ThepersonwouldbewillingtogiveupmoreytogainadditionalunitsofxAt(x2,y2),theindifferencecurveisflatter.Thepersonwouldbewillingtogiveuplessytogainadditionalunitsofx柯孔林浙江工商大学金融学院13IndifferenceCurveMapEachpointmusthaveanindifferencecurvethroughitQuantityofxQuantityofyU1<U2<U3U1U2U3Increasingutility柯孔林浙江工商大学金融学院14TransitivityCananytwoofanindividual’sindifferencecurvesintersect?QuantityofxQuantityofyU1U2ABCTheindividualisindifferentbetweenAandC.TheindividualisindifferentbetweenBandC.TransitivitysuggeststhattheindividualshouldbeindifferentbetweenAandBButBispreferredtoAbecauseBcontainsmorexandythanA柯孔林浙江工商大学金融学院15ConvexityAsetofpointsisconvexifanytwopointscanbejoinedbyastraightlinethatiscontainedcompletelywithinthesetQuantityofxQuantityofyU1TheassumptionofadiminishingMRSisequivalenttotheassumptionthatallcombinationsofxandywhicharepreferredtox*andy*formaconvexsetx*y*柯孔林浙江工商大学金融学院16ConvexityIftheindifferencecurveisconvex,thenthecombination(x1+x2)/2,(y1+y2)/2willbepreferredtoeither(x1,y1)or(x2,y2)QuantityofxQuantityofyU1x2y1y2x1Thisimpliesthat“well-balanced”bundlesarepreferredtobundlesthatareheavilyweightedtowardonecommodity(x1+x2)/2(y1+y2)/2柯孔林浙江工商大学金融学院17UtilityandtheMRSSupposeanindividual’spreferencesforhamburgers(y)andsoftdrinks(x)canberepresentedbySolvingfory,wegety=100/x

SolvingforMRS=-dy/dx:MRS=-dy/dx=100/x2柯孔林浙江工商大学金融学院18UtilityandtheMRSMRS=-dy/dx=100/x2Notethatasxrises,MRSfallswhenx=5,MRS=4whenx=20,MRS=0.25柯孔林浙江工商大学金融学院19MarginalUtilitySupposethatanindividualhasautilityfunctionoftheformutility=U(x,y)ThetotaldifferentialofUisAlonganyindifferencecurve,utilityisconstant(dU=0)柯孔林浙江工商大学金融学院20DerivingtheMRSTherefore,weget:MRSistheratioofthemarginalutilityofxtothemarginalutilityofy柯孔林浙江工商大学金融学院21DiminishingMarginalUtilityandtheMRSIntuitively,itseemsthattheassumptionofdecreasingmarginalutilityisrelatedtotheconceptofadiminishingMRSdiminishingMRSrequiresthattheutilityfunctionbequasi-concavethisisindependentofhowutilityismeasureddiminishingmarginalutilitydependsonhowutilityismeasuredThus,thesetwoconceptsaredifferent柯孔林浙江工商大学金融学院22ConvexityofIndifferenceCurvesSupposethattheutilityfunctionisWecansimplifythealgebrabytakingthelogarithmofthisfunctionU*(x,y)=ln[U(x,y)]=0.5lnx+0.5lny柯孔林浙江工商大学金融学院23ConvexityofIndifferenceCurvesThus,柯孔林浙江工商大学金融学院24ConvexityofIndifferenceCurvesIftheutilityfunctionisU(x,y)=x+xy+yThereisnoadvantagetotransformingthisutilityfunction,so柯孔林浙江工商大学金融学院25ConvexityofIndifferenceCurvesSupposethattheutilityfunctionisForthisexample,itiseasiertousethetransformationU*(x,y)=[U(x,y)]2=x2+y2柯孔林浙江工商大学金融学院26ConvexityofIndifferenceCurvesThus,柯孔林浙江工商大学金融学院27ExamplesofUtilityFunctionsCobb-DouglasUtilityutility=U(x,y)=xywhereandarepositiveconstantsTherelativesizesofandindicatetherelativeimportanceofthegoods柯孔林浙江工商大学金融学院28ExamplesofUtilityFunctionsPerfectSubstitutesutility=U(x,y)=x+yQuantityofxQuantityofyU1U2U3Theindifferencecurveswillbelinear.TheMRSwillbeconstantalongtheindifferencecurve.柯孔林浙江工商大学金融学院29ExamplesofUtilityFunctionsPerfectComplementsutility=U(x,y)=min(x,y)QuantityofxQuantityofyTheindifferencecurveswillbeL-shaped.Onlybychoosingmoreofthetwogoodstogethercanutilitybeincreased.U1U2U3柯孔林浙江工商大学金融学院30ExamplesofUtilityFunctionsCESUtility(Constantelasticityofsubstitution)utility=U(x,y)=x/+y/

when0andutility=U(x,y)=lnx+lny

when=0Perfectsubstitutes=1Cobb-Douglas=0Perfectcomplements=-柯孔林浙江工商大学金融学院31ExamplesofUtilityFunctions证：utility=U(x,y)=x/+y/

当

0,

当和都为1时，上式即为Cobb-Douglas效用函数的MRS。柯孔林浙江工商大学金融学院32ExamplesofUtilityFunctions证：显然，当时，

这是一个完全互补效用函数的无差异曲线。柯孔林浙江工商大学金融学院33ExamplesofUtilityFunctionsCESUtility(Constantelasticityofsubstitution)Theelasticityofsubstitution()isequalto1/(1-)Perfectsubstitutes=Fixedproportions=0柯孔林浙江工商大学金融学院34ExamplesofUtilityFunctions证明：柯孔林浙江工商大学金融学院35HomotheticPreferencesIftheMRSdependsonlyontheratiooftheamountsofthetwogoods,notonthequantitiesofthegoods,theutilityfunctionishomotheticPerfectsubstitutesMRSisthesameateverypointPerfectcomplementsMRS=ify/x>/,undefinedify/x=/,andMRS=0ify/x</柯孔林浙江工商大学金融学院36HomotheticPreferencesForthegeneralCobb-Douglasfunction,theMRScanbefoundas柯孔林浙江工商大学金融学院37NonhomotheticPreferencesSomeutilityfunctionsdonotexhibithomotheticpreferencesuti