消费者最优选择.PPT

ChapterFive,Choice消费者最优选择,,WhereAreWeDoinginThisChapter?,Aftermodelingaconsumer’schoicesetandhispreference(representedbyutilityfunctions),wenowputthemtogetherandmodelhowhe/shemakesoptimalchoice.Inmathematicalterms,thisisaconstrainedmaximizationproblem;Ineconomics,thisisarationalchoiceproblem.,,,RationalConstrainedChoice,,Affordablebundles,,,,,x1,x2,Morepreferredbundles,,RationalConstrainedChoice,Themostpreferredaffordablebundleiscalledtheconsumer’sORDINARYDEMANDatthegivenpricesandbudget.Ordinarydemandswillbedenotedbyx1*(p1,p2,m)andx2*(p1,p2,m).,RationalConstrainedChoice,Whenx1*>0andx2*>0thedemandedbundleisINTERIOR.Ifbuying(x1*,x2*)costs$mthenthebudgetisexhausted.,,RationalConstrainedChoice,,,,,,x1,x2,,,,,,x1*,x2*,(x1*,x2*)isinterior.(a)(x1*,x2*)exhauststhebudget;p1x1*+p2x2*=m.,,RationalConstrainedChoice,,,,,,x1,x2,,,,,,x1*,x2*,(x1*,x2*)isinterior.(b)Theslopeoftheindiff.curveat(x1*,x2*)equalstheslopeofthebudgetconstraint.,RationalConstrainedChoice,(x1*,x2*)satisfiestwoconditions:(a)thebudgetisexhausted;p1x1*+p2x2*=m(b)theslopeofthebudgetconstraint,-p1/p2,andtheslopeoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).,ComputingOrdinaryDemands-aCobb-DouglasExample.,SupposethattheconsumerhasCobb-Douglaspreferences.,ComputingOrdinaryDemands-aCobb-DouglasExample.,SupposethattheconsumerhasCobb-Douglaspreferences.Then,ComputingOrdinaryDemands-aCobb-DouglasExample.,SotheMRSis,ComputingOrdinaryDemands-aCobb-DouglasExample.,SotheMRSisAt(x1*,x2*),MRS=-p1/p2so,(A),ComputingOrdinaryDemands-aCobb-DouglasExample.,(x1*,x2*)alsoexhauststhebudgetso,(B),ComputingOrdinaryDemands-aCobb-DouglasExample.,SowehavediscoveredthatthemostpreferredaffordablebundleforaconsumerwithCobb-Douglaspreferences,is,,ComputingOrdinaryDemands-aCobb-DouglasExample.,,,,,,x1,x2,,,,,,RationalConstrainedChoice,Whenx1*>0andx2*>0and(x1*,x2*)exhauststhebudget,andindifferencecurveshaveno‘kinks’,theordinarydemandsareobtainedbysolving:(a)p1x1*+p2x2*=y(b)theslopesofthebudgetconstraint,-p1/p2,andoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).,RationalConstrainedChoice,Butwhatifx1*=0?Orifx2*=0?Ifeitherx1*=0orx2*=0thentheordinarydemand(x1*,x2*)isatacornersolutiontotheproblemofmaximizingutilitysubjecttoabudgetconstraint.,ExamplesofCornerSolutions--thePerfectSubstitutesCase,x1,x2,,MRS=-1,,Slope=-p1/p2withp1>p2.,,,,,,,,ExamplesofCornerSolutions--thePerfectSubstitutesCase,x1,x2,,,,MRS=-1,,Slope=-p1/p2withp1<p2.,,,,,中国最庞大的数据库下载,ExamplesofCornerSolutions--thePerfectSubstitutesCase,SowhenU(x1,x2)=x1+x2,themostpreferredaffordablebundleis(x1*,x2*)where,and,ifp1p2.,,,ExamplesofCornerSolutions--thePerfectSubstitutesCase,,,x1,x2,,MRS=-1,,Slope=-p1/p2withp1=p2.,,,,ExamplesofCornerSolutions--thePerfectSubstitutesCase,,,x1,x2,,,Allthebundlesintheconstraintareequallythemostpreferredaffordablewhenp1=p2.,ExamplesofCornerSolutions--theNon-ConvexPreferencesCase,,,x1,x2,,,Better,,,ExamplesofCornerSolutions--theNon-ConvexPreferencesCase,,,x1,x2,,,,,,,ExamplesofCornerSolutions--theNon-ConvexPreferencesCase,,,x1,x2,,,,,,,,Whichisthemostpreferredaffordablebundle?,,,,,ExamplesofCornerSolutions--theNon-ConvexPreferencesCase,,,x1,x2,,,,,,Themostpreferredaffordablebundle,,,,,ExamplesofCornerSolutions--theNon-ConvexPreferencesCase,,,x1,x2,,,,,,Themostpreferredaffordablebundle,,,Noticethatthe“tangencysolution”isnotthemostpreferredaffordablebundle.,,Examplesof‘Kinky’Solutions--thePerfectComplementsCase,,,x1,x2,,,,U(x1,x2)=min{ax1,x2},x2=ax1,Examplesof‘Kinky’Solutions--thePerfectComplementsCase,,,x1,x2,,,,MRS=0,,U(x1,x2)=min{ax1,x2},x2=ax1,Examplesof‘Kinky’Solutions--thePerfectComplementsCase,,,x1,x2,MRS=-,,,,,,MRS=0,U(x1,x2)=min{ax1,x2},x2=ax1,,Examplesof‘Kinky’Solutions--thePerfectComplementsCase,,,x1,x2,MRS=-,,,,,,MRS=0,MRSisundefined,,U(x1,x2)=min{ax1,x2},x2=ax1,,Examplesof‘Kinky’Solutions--thePerfectComplementsCase,,,x1,x2,,,,U(x1,x2)=min{ax1,x2},x2=ax1,,Examplesof‘Kinky’Solutions--thePerfectComplementsCase,,,x1,x2,,,,U(x1,x2)=min{ax1,x2},x2=ax1,,,,Themostpreferredaffordablebundle,,,Examplesof‘Kinky’Solutions--thePerfectComplementsCase,,,x1,x2,,U(x1,x2)=min{ax1,x2},x2=ax1,,,,x1*,x2*,(a)p1x1*+p2x2*=m(b)x2*=ax1*,,Summary:ThreeStepstoFindtheOptimalChoiceoftheConsumer,Step1:Drawthebudgetset;Step2:Drawtheindifferencecurves;Step3:Locatethepointofoptimalchoiceandcalculatethesolution.,