Chapter13–TaxationandEfficiency1IntroductionArepeopleunaffectedbyataxincreaseiftheypayzerointaxesafterwards?No,consumptionmayhavechangedinresponsetothetaxincreaseBundleconsumedislessdesirableExcessburdenisalossofwelfareaboveandbeyondthetaxrevenuescollected.2ExcessBurdenDefinedTwocommoditiesBarleyandcornFixedincomePbandPcarepricesofgoodsNodistortionssuchasexternalities,imperfectcompetition,publicgoods,etc.3ExcessBurdenDefinedFigure13.1showsthebudgetconstraint(AD),withutilitymaximizedatbundleE1.Ad-valoremtaxleviedonbarleyatratetbraisesthepriceto(1+tb)Pb,androtatesthebudgetconstraintalongthex-axis.ThenewbudgetconstraintisAF.4Figure13.15ExcessBurdenDefinedAteachconsumptionlevelofbarley,theverticaldistancebetweenADandAFshowstaxpaymentsintermsofforgonecorn.NormalizePc=$1sothatverticaldistancecanbemeasuredineitherquantityofcornordollars.6ExcessBurdenDefinedFigure13.2showsnewoptimizingchoicewiththehigherpricesalongbudgetconstraintAF.UtilitymaximizedatbundleE2.Verticaldistancebetweenold&newbudgetconstraintsisGE2isthe“taxbill.〞7ExcessBurdenDefinedAnytaxwilllowerutility,butisthereanalternativetaxthatraisesthesamerevenue,GE2,butentailsasmallerutilityloss?Orgreaterrevenuewiththesameutilityloss?Ifso,thetaxonbarleyleadstoexcessburden.8Figure13.29ExcessBurdenDefinedEquivalentvariationistheamountofincomewewouldhavetotakeaway(beforeanytaxwasimposed)toinduceamovetothelowerindifferencecurve.Takingawayincomeisequivalenttoaparallelmovementinwardonthebudgetconstraint.BudgetconstraintHIinFigure13.3showsthis.10Figure13.311ExcessBurdenDefinedNotethatME3=GN>GE2,butbothgivetheconsumerthesameutility.Thus,thedifferenceE2Nistheexcessburdenofthebarleytax.Thebarleytaxmakesthepersonworseoffbyanamountthatexceedstherevenueitgenerates.12ExcessBurdenDefinedLumpsumtaxisataxthatmustbepaidregardlessofthetaxpayer’sbehavior.BudgetconstraintHIsatisfiesthis.Revenueyieldexactlyequalstheequivalentvariation.Conclusion:Lumpsumtaxhasnoexcessburden.13QuestionsandAnswersWhyaren’tlumpsumtaxeswidelyused?Construedasunfairbecausepeople’sabilitiestopayvaryHowdolumpsumtaxesrelatetowelfareeconomics?Theequilibriumconditionsbecome:14QuestionsandAnswersIntuitively,whenMRS>MRTthemarginalutilityofsubstitutingbarleyconsumptionforcornconsumptionexceedsthechangeinproductioncostsfromdoingso.Inthepresenceofthetax,thereisnofinancialincentivetodoso.15QuestionsandAnswersIntuitively,whenMRS>MRTthemarginalutilityofsubstitutingbarleyconsumptionforcornconsumptionexceedsthechangeinproductioncostsfromdoingso.Inthepresenceofthetax,thereisnofinancialincentivetodoso.16QuestionsandAnswersDoesanincometaxentailexcessburden?Itusuallydoesentailexcessburden,ifathirdcommodity,leisure,exists.Ifdemandforacommodityisperfectlyinelastic,isthereexcessburden?Yes,seeFigure13.417Figure13.418QuestionsandAnswersInFigure13.4,theordinary(uncompensated)demandcurveisinelastic–B1=B2whenthepriceincreases.Butthisisbecausetheincomeeffectoffsetsthesubstitutioneffect.Thesubstitutioneffectisthepartnecessarytocomputeexcessburden.Thecompensateddemandcurve(whichholdsutilityconstantaspriceschange)istherelevantone,andtheelasticityforitisnon-zero.19ExcessBurdenMeasurementwithDemandCurvesConsideracompensateddemandcurve,suchastheoneinFigure13.5.Imposeanad-valoremtaxonbarley,sothatitspriceincreasesto(1+tb)Pb.Equivalenttothesupplycurveshiftingupward.20Figure13.521ExcessBurdenMeasurementwithDemandCurvesExcessburdenequaltotrianglefid.Throughsomemathematicalmanipulation,thiscanbeexpressedas:22ExcessBurdenMeasurementwithDemandCurvesImplicationsofformula:Higher(compensated)elasticitiesleadtolargerexcessburdenExcessburdenincreaseswiththesquareofthetaxrateThegreatertheinitialexpenditureonthetaxedcommodity,thelargertheexcessburden23DifferentialTaxationofInputsSomeinputsaretaxeddifferentlydependingonwheretheyareused:Capitalusedinthecorporatesectorissubjecttoahighertaxratethancapitalusedinthenoncorporatesector.LaborusedinthehouseholdisuntaxedFigure13.8measurestheefficiencycost24Figure13.825DifferentialTaxationofInputsInthisfigure,totalamountoflaborisfixedatOO’.Movingalongthex-axissimplyshiftslaborfromthelabormarkettothehouseholdsector.VMPisthevalueofmarginalproduct,orthedollarvalueoftheadditionalinputproducedfromanhourofwork.VMPdeclineswithhoursworkedinasector.Optimalallocationofhoursequatesmargins,suchthatOH*isspentinhouseholdproduction,andO’H*isspentinthemarket.26DifferentialTaxationofInputsIfataxisleviedonmarketwork,butnothouseholdproduction,thenthe“effective〞VMPcurveformarketworkrotatesdownward.Figure13.9showstheeffects.27Figure13.928DifferentialTaxationofInputsPeopleshifthoursintonon-marketwork.Ho