ch11_补偿性需求曲线

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1、Chapter11Appendix1DerivationoftheFormulaforExcessBurdenofaUnitTaxW=1/2T×DQWhere:W=excessburden(Deadweightloss)T=taxDQ=changeinequilibriumquantityasaresultofthetax2SolvingforDQStep1:SomeDefinitionsT=PG–PNDPG=PG–P*DPN=PN–P*3SolvingforDQStep2:ElasticitycomesintoplayED=(DQ/Q*)/(DPG/P*)=(DQ/Q*)×(P*/DPG

2、)=(DQ/Q*)×[P*/(PG–P*)]ES=(DQ/Q*)/(DPN/P*)=(DQ/Q*)×(P*/DPN)=(DQ/Q*)×[P*/(PN–P*)]4SolvingforDQStep3:SolvingforPGED=(DQ/Q*)×[P*/(PG–P*)](PG–P*)=(DQ/Q*)×(P*/ED)PG=(DQ/Q*)×(P*/ED)+P*5SolvingforDQStep4:SolvingforPNES=(DQ/Q*)×(P*/(PN–P*)(PN–P*)=(DQ/Q*)×(P*/ES)PN=(DQ/Q*)×(P*/ES)+P*6SolvingforDQStep5:Usingt

3、heT=PG–PNdefinitionT=PG–PN=(DQ/Q*)×(P*/ED)+P*–[(DQ/Q*)×(P*/ES)+P*]=(DQ/Q*)×(P*/ED)–(DQ/Q*)×(P*/ES)=(DQ/Q*)×(P*)×[(1/ED)–(1/ES)]=(DQ/Q*)×(P*)×[(ES–ED)/(EDES)]7SolvingforDQStep6:SolvingT=(DQ/Q*)×(P*)[(ES–ED)/(EDES)]forDQT=(DQ/Q*)×(P*)[(ES–ED)/(EDES)]SoDQ=T(P*/Q*)×[(EDES)/(ES–ED)]PluggingbackintoW=1/2

4、TDQW=1/2T2(P*/Q*)×[(EDES)/(ES–ED)]8DerivationfortheAd-ValoremTaxIfthepre-andpost-taxpricesareclosetooneanother,thenW=1/2t2(P*Q*)×[(EDES)/(ES–ED)]IfLRACisperfectlyinelastic,thenW=1/2t2(P*Q*)×(ED)×[(ES)/(ES–ED)]=1/2t2(P*Q*)×(ED)because[(ES)/(ES–ED)]approaches1.9IndividualLossesinWelfareUnderPerfectCo

5、mpetitionIfthereisperfectcompetition,thenEDisinfinitefromthefirmowner’sperspective.ThisimpliesthatDWL=1/2t2(P*Q*)ES10CompensatedDemandCurvesRecallthatcompensateddemandcurvesshowtherelationshipbetweenpriceandquantitydemanded,excludingtheincomeeffect.Itonlylooksatthesubstitutionawayfromthetaxedgood.1

6、1Figure11A.1RegularandCompensatedDemandCurvesForaNormalGoodPriceGasolineperYear0CurveRegularDemandQ1P1CompensatedDemandCurve12CompensatedSupplyCurvesRecallthatcompensatedsupplycurvesshowtherelationshipbetweenpriceandquantitysuppliedexcludingtheincomeeffect.Itonlylooksatthesubstitutionawayfromthetax

7、edgood.13Figure11A.2UsingACompensatedDemandCurvetoIsolateTheSubstitutionEffectofaTax-InducedPriceIncreaseDCSTPrice(Dollars)GasolineperYear(Gallons)0Q11.00DRSE1DQSPGPNQ2DQAE214Figure11A.3ACompensatedSupplyCu