消费者最优选择(3)培训资料

ChapterFiveChoice消费者最优选择(xuǎnzé)第一页，共35页。WhereAreWeDoinginThisChapter?Aftermodelingaconsumer’schoicesetandhispreference(representedbyutilityfunctions),wenowputthemtogetherandmodelhowhe/shemakesoptimalchoice.Inmathematicalterms,thisisaconstrainedmaximizationproblem;Ineconomics,thisisarationalchoiceproblem.第二页，共35页。RationalConstrainedChoiceAffordable

bundlesx1x2Morepreferred

bundles第三页，共35页。RationalConstrainedChoiceThemostpreferredaffordablebundleiscalledtheconsumer’sORDINARYDEMANDatthegivenpricesandbudget.Ordinarydemandswillbedenotedby

x1*(p1,p2,m)andx2*(p1,p2,m).第四页，共35页。RationalConstrainedChoiceWhenx1*>0andx2*>0thedemandedbundleisINTERIOR.Ifbuying(x1*,x2*)costs$mthenthebudgetisexhausted.第五页，共35页。RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.

(a)(x1*,x2*)exhauststhe

budget;p1x1*+p2x2*=m.第六页，共35页。RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.

(b)Theslopeoftheindiff.

curveat(x1*,x2*)equals

theslopeofthebudget

constraint.第七页，共35页。RationalConstrainedChoice(x1*,x2*)satisfiestwoconditions:(a)thebudgetisexhausted;

p1x1*+p2x2*=m(b)theslopeofthebudgetconstraint,-p1/p2,andtheslopeoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).第八页，共35页。ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.第九页，共35页。ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.

Then第十页，共35页。ComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSis第十一页，共35页。ComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSis

At(x1*,x2*),MRS=-p1/p2so(A)第十二页，共35页。ComputingOrdinaryDemands-aCobb-DouglasExample.(x1*,x2*)alsoexhauststhebudgetso(B)第十三页，共35页。ComputingOrdinaryDemands-aCobb-DouglasExample.Sowehavediscoveredthatthemost

preferredaffordablebundleforaconsumer

withCobb-Douglaspreferences

is第十四页，共35页。ComputingOrdinaryDemands-aCobb-DouglasExample.x1x2第十五页，共35页。RationalConstrainedChoiceWhenx1*>0andx2*>0

and(x1*,x2*)exhauststhebudget,

andindifferencecurveshaveno

‘kinks’,theordinarydemandsareobtainedbysolving:(a)p1x1*+p2x2*=y(b)theslopesofthebudgetconstraint,-p1/p2,andoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).第十六页，共35页。RationalConstrainedChoiceButwhatifx1*=0?Orifx2*=0?Ifeitherx1*=0orx2*=0thentheordinarydemand(x1*,x2*)isatacornersolutiontotheproblemofmaximizingutilitysubjecttoabudgetconstraint.第十七页，共35页。ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1>p2.第十八页，共35页。ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1<p2.中国最庞大(pángdà)的数据库下载第十九页，共35页。ExamplesofCornerSolutions--thePerfectSubstitutesCaseSowhenU(x1,x2)=x1+x2,themost

preferredaffordablebundleis(x1*,x2*)

whereandifp1<p2ifp1>p2.第二十页，共35页。ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1=p2.第二十一页，共35页。ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2Allthebundlesinthe

constraintareequallythe

mostpreferredaffordable

whenp1=p2.第二十二页，共35页。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Better第二十三页，共35页。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2第二十四页，共35页。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Whichisthemostpreferred

affordablebundle?第二十五页，共35页。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Themostpreferred

affordablebundle第二十六页，共35页。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Themostpreferred

affordablebundleNoticethatthe“tangencysolution”

isnotthemostpreferredaffordable

bundle.第二十七页，共35页。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1第二十八页，共35页。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=0U(x1,x2)=min{ax1,x2}x2=ax1第二十九页，共35页。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=-¥MRS=0U(x1,x2)=min{ax1,x2}x2=ax1第三十页，共35页。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=-¥MRS=0MRSisundefinedU(x1,x2)=min{ax1,x2}x2=ax1第三十一页，共35页。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1第三十二页，共35页。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1Themostpreferredaffordablebundle第三十三页，共35页。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1x1*x2*(a)p