《微观经济学》清华大学课件 Ch4 Utility.ppt

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1、ChapterFourUtility效用WhatDoWeDoinThisChapter?Wecreateamathematicalmeasureofpreferenceinordertoadvanceouranalysis.UtilityFunctionsApreferencerelationthatiscomplete,reflexive,transitivecanberepresentedbyautilityfunction.UtilityFunctionsAutilityfunctionU(x)

2、representsapreferencerelationifandonlyif:x’x”U(x’)>U(x”)x’x”U(x’)

3、y.UtilityFunctions&Indiff.CurvesAllbundlesinanindifferencecurvehavethesameutilitylevel.U(x1,x2)=Constantistheequationofanindifferencecurve.UtilityFunctions&Indiff.CurvesUº6Uº4(2,3)(2,2)~(4,1)x1x2pUtilityFunctions&Indiff.CurvesThecollectionofallindiffere

4、ncecurvesforagivenpreferencerelationisanindifferencemap.Anindifferencemapisequivalenttoautilityfunction.UtilityFunctionsIfUisautilityfunctionthatrepresentsapreferencerelationandfisastrictlyincreasingfunction,thenV=f(U)isalsoautilityfunctionrepresenting

5、.~f~fGoods,BadsandNeutralsAgoodisacommodityunitwhichincreasesutility(givesamorepreferredbundle).Abadisacommodityunitwhichdecreasesutility(givesalesspreferredbundle).Aneutralisacommodityunitwhichdoesnotchangeutility(givesanequallypreferredbundle).Goods,B

6、adsandNeutralsUtilityWaterx’UnitsofwateraregoodsUnitsofwaterarebadsAroundx’units,alittleextrawaterisaneutral.UtilityfunctionSomeOtherUtilityFunctionsandTheirIndifferenceCurvesConsiderV(x1,x2)=x1+x2.Whatdotheindifferencecurvesforthis“perfectsubs

7、titution”utilityfunctionlooklike?PerfectSubstitutionIndifferenceCurves55991313x1x2x1+x2=5x1+x2=9x1+x2=13V(x1,x2)=x1+x2.PerfectSubstitutionIndifferenceCurves55991313x1x2x1+x2=5x1+x2=9x1+x2=13Allarelinearandparallel.V(x1,x2)=x1+x2.SomeOtherUtilityFunction

8、sandTheirIndifferenceCurvesConsiderW(x1,x2)=min{x1,x2}.Whatdotheindifferencecurvesforthis“perfectcomplementarity”utilityfunctionlooklike?PerfectComplementarityIndifferenceCurvesx2x145omin{x1,x2}=8358358min{x1,x2}=5min{x1,x2}=