《微观经济学》清华大学教学课件Ch5Choice消费者最优选择

《微观经济学》清华大学课件Ch5Choice消费者最优选择26、机遇对于有准备的头脑有特别的亲和力。27、自信是人格的核心。28、目标的坚定是性格中最必要的力量泉源之一，也是成功的利器之一。没有它，天才也会在矛盾无定的迷径中，徒劳无功。--查士德斐尔爵士。29、困难就是机遇。--温斯顿．丘吉尔。30、我奋斗，所以我快乐。--格林斯潘。《微观经济学》清华大学课件Ch5Choice消费者最优选择《微观经济学》清华大学课件Ch5Choice消费者最优选择26、机遇对于有准备的头脑有特别的亲和力。27、自信是人格的核心。28、目标的坚定是性格中最必要的力量泉源之一，也是成功的利器之一。没有它，天才也会在矛盾无定的迷径中，徒劳无功。--查士德斐尔爵士。29、困难就是机遇。--温斯顿．丘吉尔。30、我奋斗，所以我快乐。--格林斯潘。ChapterFiveChoice消费者最优选择WhereAreWeDoinginThisChapter?Aftermodelingaconsumer’schoicesetandhispreference(representedbyutilityfunctions),wenowputthemtogetherandmodelhowhe/shemakesoptimalchoice.Inmathematicalterms,thisisaconstrainedmaximizationproblem;Ineconomics,thisisarationalchoiceproblem.RationalConstrainedChoiceWhenx1*>0andx2*>0thedemandedbundleisINTERIOR.Ifbuying(x1*,x2*)costs$mthenthebudgetisexhausted.RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.

(a)(x1*,x2*)exhauststhe

budget;p1x1*+p2x2*=m.RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.

(b)Theslopeoftheindiff.

curveat(x1*,x2*)equals

theslopeofthebudget

constraint.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.

ThenComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSisComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSis

At(x1*,x2*),MRS=-p1/p2so(A)ComputingOrdinaryDemands-aCobb-DouglasExample.(x1*,x2*)alsoexhauststhebudgetso(B)ComputingOrdinaryDemands-aCobb-DouglasExample.Sowehavediscoveredthatthemost

preferredaffordablebundleforaconsumer

withCobb-Douglaspreferences

isComputingOrdinaryDemands-aCobb-DouglasExample.x1x2RationalConstrainedChoiceWhenx1*>0andx2*>0

and(x1*,x2*)exhauststhebudget,

andindifferencecurveshaveno

‘kinks’,theordinarydemandsareobtainedbysolving:(a)p1x1*+p2x2*=y(b)theslopesofthebudgetconstraint,-p1/p2,andoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).RationalConstrainedChoiceButwhatifx1*=0?Orifx2*=0?Ifeitherx1*=0orx2*=0thentheordinarydemand(x1*,x2*)isatacornersolutiontotheproblemofmaximizingutilitysubjecttoabudgetconstraint.ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1>p2.ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1<p2.ExamplesofCornerSolutions--thePerfectSubstitutesCaseSowhenU(x1,x2)=x1+x2,themost

preferredaffordablebundleis(x1*,x2*)

whereandifp1<p2ifp1>p2.ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1=p2.ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2Allthebundlesinthe

constraintareequallythe

mostpreferredaffordable

whenp1=p2.ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2BetterExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Whichisthemostpreferred

affordablebundle?ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Themostpreferred

affordablebundleExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Themostpreferred

affordablebundleNoticethatthe“tangencysolution”

isnotthemostpreferredaffordable

bundle.Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=0U(x1,x2)=min{ax1,x2}x2=ax1Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=-¥MRS=0U(x1,x2)=min{ax1,x2}x2=ax1Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=-¥MRS=0MRSisundefinedU(x1,x2)=min{ax1,x2}x2=ax1Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1ThemostpreferredaffordablebundleExamplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1x1*x2*(a)p1x1*+p2x2*=m

(b)x2*=ax1*Summary:

ThreeStepstoFindtheOptimalChoiceoftheConsumerStep1:Drawthebudgetset;Step2:Drawtheindifferencecurves;Step3:Locatethepointofop