文档介绍：1DerivationoftheFormulaforExcessBurdenofaUnitTaxW=1/2T×DQWhere:W=excessburden(Deadweightloss)T=taxDQ=changeinequilibriumquantityasaresultofthetax文档分享2SolvingforDQStep1:SomeDefinitionsT=PG–PNDPG=PG–P*DPN=PN–P*文档分享3SolvingforDQStep2:esintoplayED =(DQ/Q*)/(DPG/P*) =(DQ/Q*)×(P*/DPG) =(DQ/Q*)×[P*/(PG–P*)]  ES =(DQ/Q*)/(DPN/P*) =(DQ/Q*)×(P*/DPN) =(DQ/Q*)×[P*/(PN–P*)]文档分享4SolvingforDQStep3:SolvingforPGED =(DQ/Q*)×[P*/(PG–P*)] (PG–P*) =(DQ/Q*)×(P*/ED) PG =(DQ/Q*)×(P*/ED)+P*文档分享5SolvingforDQStep4:SolvingforPNES =(DQ/Q*)×(P*/(PN–P*) (PN–P*) =(DQ/Q*)×(P*/ES)PN =(DQ/Q*)×(P*/ES)+P*文档分享6SolvingforDQStep5:UsingtheT=PG–PNdefinition T =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)]文档分享7SolvingforDQStep6:SolvingT=(DQ/Q*)×(P*)[(ES–ED)/(EDES)]forDQ T=(DQ/Q*)×(P*)[(ES–ED)/(EDES)] So  DQ=T(P*/Q*)×[(EDES)/(ES–ED)] PluggingbackintoW=1/2TDQW=1/2T2(P*/Q*)×[(EDES)/(ES–ED)]文档分享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)],thenEDisinfinitefromthefirmowner’=1/2t2(P*Q*)pensateddemandcurvesshowtherelationshipbetweenpriceandquantitydemanded,