消費(fèi)者最優(yōu)選擇英文

ChapterFiveChoice消費(fèi)者最優(yōu)選擇第一頁，共三十七頁。WhereAreWeDoinginThisChapter?Aftermodelingaconsumer’schoicesetandhispreference(representedbyutilityfunctions),wenowputthemtogetherandmodelhowhe/shemakesoptimalchoice.Inmathematicalterms,thisisaconstrainedmaximizationproblem;Ineconomics,thisisarationalchoiceproblem.第二頁，共三十七頁。RationalConstrainedChoiceAffordable

bundlesx1x2Morepreferred

bundles第三頁，共三十七頁。RationalConstrainedChoiceThemostpreferredaffordablebundleiscalledtheconsumer’sORDINARYDEMANDatthegivenpricesandbudget.Ordinarydemandswillbedenotedby

x1*(p1,p2,m)andx2*(p1,p2,m).第四頁，共三十七頁。RationalConstrainedChoiceWhenx1*>0andx2*>0thedemandedbundleisINTERIOR.Ifbuying(x1*,x2*)costs$mthenthebudgetisexhausted.第五頁，共三十七頁。RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.

(a)(x1*,x2*)exhauststhe

budget;p1x1*+p2x2*=m.第六頁，共三十七頁。RationalConstrainedChoicex1x2x1*x2*(x1*,x2*)isinterior.

(b)Theslopeoftheindiff.

curveat(x1*,x2*)equals

theslopeofthebudget

constraint.第七頁，共三十七頁。RationalConstrainedChoice(x1*,x2*)satisfiestwoconditions:(a)thebudgetisexhausted;

p1x1*+p2x2*=m(b)theslopeofthebudgetconstraint,-p1/p2,andtheslopeoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).第八頁，共三十七頁。ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.第九頁，共三十七頁。ComputingOrdinaryDemands-aCobb-DouglasExample.SupposethattheconsumerhasCobb-Douglaspreferences.

Then第十頁，共三十七頁。ComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSis第十一頁，共三十七頁。ComputingOrdinaryDemands-aCobb-DouglasExample.SotheMRSis

At(x1*,x2*),MRS=-p1/p2so(A)第十二頁，共三十七頁。ComputingOrdinaryDemands-aCobb-DouglasExample.(x1*,x2*)alsoexhauststhebudgetso(B)第十三頁，共三十七頁。ComputingOrdinaryDemands-aCobb-DouglasExample.Sowehavediscoveredthatthemost

preferredaffordablebundleforaconsumer

withCobb-Douglaspreferences

is第十四頁，共三十七頁。ComputingOrdinaryDemands-aCobb-DouglasExample.x1x2第十五頁，共三十七頁。RationalConstrainedChoiceWhenx1*>0andx2*>0

and(x1*,x2*)exhauststhebudget,

andindifferencecurveshaveno

‘kinks’,theordinarydemandsareobtainedbysolving:(a)p1x1*+p2x2*=y(b)theslopesofthebudgetconstraint,-p1/p2,andoftheindifferencecurvecontaining(x1*,x2*)areequalat(x1*,x2*).第十六頁，共三十七頁。RationalConstrainedChoiceButwhatifx1*=0?Orifx2*=0?Ifeitherx1*=0orx2*=0thentheordinarydemand(x1*,x2*)isatacornersolutiontotheproblemofmaximizingutilitysubjecttoabudgetconstraint.第十七頁，共三十七頁。ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1>p2.第十八頁，共三十七頁。ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1<p2.第十九頁，共三十七頁。ExamplesofCornerSolutions--thePerfectSubstitutesCaseSowhenU(x1,x2)=x1+x2,themost

preferredaffordablebundleis(x1*,x2*)

whereandifp1<p2ifp1>p2.第二十頁，共三十七頁。ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2MRS=-1Slope=-p1/p2withp1=p2.第二十一頁，共三十七頁。ExamplesofCornerSolutions--thePerfectSubstitutesCasex1x2Allthebundlesinthe

constraintareequallythe

mostpreferredaffordable

whenp1=p2.第二十二頁，共三十七頁。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Better第二十三頁，共三十七頁。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2第二十四頁，共三十七頁。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Whichisthemostpreferred

affordablebundle?第二十五頁，共三十七頁。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Themostpreferred

affordablebundle第二十六頁，共三十七頁。ExamplesofCornerSolutions--theNon-ConvexPreferencesCasex1x2Themostpreferred

affordablebundleNoticethatthe“tangencysolution”

isnotthemostpreferredaffordable

bundle.第二十七頁，共三十七頁。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1第二十八頁，共三十七頁。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=0U(x1,x2)=min{ax1,x2}x2=ax1第二十九頁，共三十七頁。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=-￥MRS=0U(x1,x2)=min{ax1,x2}x2=ax1第三十頁，共三十七頁。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2MRS=-￥MRS=0MRSisundefinedU(x1,x2)=min{ax1,x2}x2=ax1第三十一頁，共三十七頁。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1第三十二頁，共三十七頁。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1Themostpreferredaffordablebundle第三十三頁，共三十七頁。Examplesof‘Kinky’Solutions--thePerfectComplementsCasex1x2U(x1,x2)=min{ax1,x2}x2=ax1x1*x2*(a)p1x1*+p2x2*=m

(b)x2*=ax1*第三十四頁，共三十七頁。Summary:

ThreeStepstoFindtheOptimalChoiceoftheConsumerStep1:Drawthebud