北大微观经济学课件]ch4Utility

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1、ChapterFourUtility效用StructureUtilityfunction(效用函数）DefinitionMonotonictransformation（单调转换）ExamplesofutilityfunctionsandtheirindifferencecurvesMarginalutility（边际效用）Marginalrateofsubstitution边际替代率MRSaftermonotonictransformationUtilityFunctionsAutilityfunctionU(x)representsa

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

3、ff.CurvesConsiderthebundles(4,1),(2,3)and(2,2).Suppose(2,3)(4,1)~(2,2).Assigntothesebundlesanynumbersthatpreservethepreferenceordering;e.g.U(2,3)=6>U(4,1)=U(2,2)=4.Callthesenumbersutilitylevels.pUtilityFunctions&Indiff.CurvesAnindifferencecurvecontainsequallypreferredbun

4、dles.Equalpreferencesameutilitylevel.Therefore,allbundlesinanindifferencecurvehavethesameutilitylevel.UtilityFunctions&Indiff.CurvesSothebundles(4,1)and(2,2)areintheindiff.curvewithutilitylevelUº4Butthebundle(2,3)isintheindiff.curvewithutilitylevelUº6.Onanindifferencecu

5、rvediagram,thispreferenceinformationlooksasfollows:UtilityFunctions&Indiff.CurvesUº6Uº4(2,3)(2,2)~(4,1)x1x2pUtilityFunctions&Indiff.CurvesComparingmorebundleswillcreatealargercollectionofallindifferencecurvesandabetterdescriptionoftheconsumer’spreferences.UtilityFunction

6、s&Indiff.CurvesUº6Uº4Uº2x1x2UtilityFunctions&Indiff.CurvesThecollectionofallindifferencecurvesforagivenpreferencerelationisanindifferencemap.Anindifferencemapisequivalenttoautilityfunction;eachistheother.UtilityFunctionsThereisnouniqueutilityfunctionrepresentationofapref

7、erencerelation.SupposeU(x1,x2)=x1x2representsapreferencerelation.Againconsiderthebundles(4,1),(2,3)and(2,2).UtilityFunctionsU(x1,x2)=x1x2,soU(2,3)=6>U(4,1)=U(2,2)=4;thatis,(2,3)(4,1)~(2,2).pUtilityFunctionsU(x1,x2)=x1x2(2,3)(4,1)~(2,2).DefineV=U2.pUtilityFunctionsU(

8、x1,x2)=x1x2(2,3)(4,1)~(2,2).DefineV=U2.ThenV(x1,x2)=x12x22andV(2,3)=36>V(4,1)=V(2,2)=16soagain(2,3)(