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Tax Policy Under Keeping Up with the Joneses and Imperfect

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Tax Policy Under Keeping Up with the Joneses and ImperfectUp,up,Tax,Under,with,the,and,AND,tax

ANNALSOFECONOMICSANDFINANCE6,2536(2005)TaxPolicyUnderKeepingUpwi

    ththeJonesesandImperfectCompetition*Jang-TingGuoDepartmentofEconomics,UniversityofCalifornia,Riverside,U.S.A.E-mail:guojt@ucr.eduThispaperexaminestheoptimal(first-best)fiscalpolicyinastochastic,infinite-horizonrepresentativeagentmodelthatexhibitsa“kee

    pingupwiththeJoneses”utilityfunctionandimperfectlycompetitiveproductmarkets.Wefindthattheoptimallabortaxisaconstant,whosesignisdeterminedbytherelativestrengthofconsumptionexternalityandmonopolypower.Moreover,theoptimalcapitaltaxisunambiguouslynegativeandaffectstheeconomycountercyclically.Ouranalysisshowsthatmodelswithcapitalaccumulation,imperfectcompetition,and“keepingupwiththeJoneses”preferencescallfortraditionalKeynesiandemand-managementpoliciesthataredesignedtomitigatebusinesscyclefluctuations.??c2005PekingUniversityPressKeyWords:FiscalPolicy;KeepingUpwiththeJoneses;ImperfectCompetition.JELClassificationNumbers:E21,E63,H21.1.INTRODUCTIONRecently,LjungqvistandUhlig(2000)haveexaminedtheoptimal(first-best)taxpolicyinastochastic,infinite-horizonrepresentativeagentmodelwithoutcapitalaccumulationandwitha“keepingupwiththeJoneses”utilityfunction1.Inparticular,thehouseholdutilitydependsonthediffer-encebet

    weenanindividual’sownconsumptionandafractionofthecurrent*IthankDanielHenderson,SharonHarrison,KenJudd,KevinLansing,MikkoPuhakka,RobertRussellandseminarparticipantsatAcademiaSinica,Taipei,Taiwan,UCRiverside,2003MidwestMacroeconomicsConference,and2004WinterMeetingsoftheEconometricSocietyforhelpfuldiscussionsandcomments.Allremainingerrorsaremyown.1“KeepingupwiththeJoneses”wasfirstintroducedinDuesenberry’s(1952)relativeconsumptionmodel.Inrecentyears,ithasbeenincorporatedintoassetpricingmodelsasonewaytopartiallyresolvetheequitypremiumpuzzleofMehraandPrescott(1985).See,forexample,Abel(1990,1999),Gal????(1994),Kocherlakota(1996),amongothers.251529-7373/2005Copyright??c2005byPekingUniversityPressAllrightsofreproductioninanyformreserved.;;26JANG-TINGGUOlevelofaggregateconsumptionintheeconomy2.Thisutilityspecificationpostulatesanegativeconsumptionexternalitythatcanbecorrectedbyataxpolicy,governedbythesocialplanner’smarginalrateofsubstitutionbetweenconsumptionandlaborhours,toachievetheParetooptimalal-locations.Itturnsoutthatinthisno-capitalsetting,thefirst-besttaxon(labor)incomeisaconstantthatequalsthestrengthofconsumptionexternality,andisindependentofthetechnologyshock.3Thispaperincorporatescapitalaccumulationandimperfectlycompeti-tiveproductmarketsintotheLjungqvist-Uhligframework.Theseexten-sionsallowustoidentifysomeadditionalmodelfeaturesandparametersthatgoverntheoptimalfiscalpolicy.Specifically,capitalaccumulationintroducesdynamicinterdependencebetweenmacroeconomicaggregates,andimperfectcompetitionaddsasecondmarketfailuretotheanalysis.Ourproductionenvironment,drawnfromtheworkofDixitandStiglitz(1977)andappliedrecentlybyGuoandLansing(1999),consistsoftwosectors:intermediateandfinalgoods.Producersofintermediategoodspossessadegreeofmonopolypower,whereasauniquefinalgoodispro-ducedinaperfectlycompetitivemarket.Asownersofallfirms,householdsreceiveprofitsintheformofdividendsthataretaxedatthesamerateascapitalincome.4Under“keepingupwiththeJoneses”andimperfectcompetition,wefindthatasinLjungqvistandUhlig(2000),thefirst-besttaxonlaborin-comeisaconstantthatisindependentofproductivitydisturbances.Sincecontemporaneousaggregateconsumptionthatentersthehouseholdutilitywillaffecttheintratemporaltrade-offbetweenconsumptionandleisure,thebenevolentsocialplannercanchoosetheoptimallabortaxperiodbyperiod.Moreover,therearetwoopposingfactorsthatinteracttodeter-minethesignoftheoptimaltaxonlaborincome.First,households’hoursworkedarelowerthanthesociallyoptimallevelbecausethewageratethatgovernstheirlaborsupplydecisionislessthanthesocialmarginalproductoflabor.Aneg

    ativetaxrateonlaborincomecanhelpeliminatethismonopolyinefficiency.Second,thelevelofconsumptioninequilibriumishighercomparedtothatattheParetooptimumbecausehouseholdsat-2Sincethereisnocapitalaccumulationandgiventhecontemporaneousnatureofconsumptionspillovers,LjungqvistandUhligonlyneedtoanalyzeasimpleone-periodmodel.3LjungqvistandUhligalsoderivethefirst-besttaxpolicyunder“catchingupwiththeJoneses”wherebypastaggregateconsumptionenterstherepresentativehousehold’sutilityfunction.Underthisformulationofconsumptionexternality,theseauthorsshowthattheoptimallabortaxvariesprocyclicallywithproductivitydisturbances.4BysolvingthedynamicversionofthedeterministicRamseyproblem,GuoandLans-ing(1999)aremainlyconcernedwiththesteady-stateoptimal(second-best)capitaltaxinanotherwisestandardneoclassicalgrowthmodelwithimperfectlycompetitiveprod-uctmarkets.Thefirst-besttaxpolicyisalsoderivedtheretoprovideausefulbenchmark.;;TAXPOLICYUNDERKEEPINGUP27tempttokeepupwiththeJoneses.Apositivetaxrateonlaborincomecanhelpcorrectthisconsumptionexternality.Asaresult,theoptimallabortaxcanbepositive,negativeorzero,dependingonthedifferencebetweenthestrengthofconsumptionexternalityandthedegreeofintermediatefirms’monopolypower.Wealsoshowthatthefirst-besttaxoncapita

    lincomeisunambiguouslynegative,thatis,theoptimalcapitalsubsidyissettoencourageinvestmentbyremovingthewedgebetweentheprivateandsocialmarginalproductsofcapital(seeJudd[1997],[2002]).Inaddition,thefirst-bestcapitalsubsidydoesnotdependonconsumptionspillovers.Theintuitionforthisresultisstraightforward.Thecapitalsubsidyaffectstheintertemporaltrade-offbe-tweenconsumptionatdifferentdates,whereasconsumptionspilloversarecontemporaneousinnature.Itfollowsthattheconsumptionexternalitycanbecorrectedbytheoptimallabortaxwithoutanyintertemporalcon-siderations.Ontheotherhand,wefindthattheoptimalcapitalsubsidyoperateslikeaclassicautomaticstabilizerwhichmovespositivelywiththetechnologyshockbecausethesocialplannernowneedstoaddressthedy-namiclinkagebetweenmacroeconomicaggregates.Therefore,thefirst-bestpolicyinvolvesacountercyclicalcapitalsubsidy,e.g.,“cool

    ingdown”theeconomywithalowersubsidyoncapitalincomewhenitis“overheating”duetoapositiveproductivitydisturbance.Finally,whentheintermediatesectorisperfectlycompetitive,theopti-malcapitaltax/subsidyturnsouttobezerosincemonopolyinefficiencynolongerexists.Inthiscase,thefirst-bestpolicyonlyconsistsofatime-invariantlabortaxthatcorrectstheconsumptionexternality.ThisimpliesthataddingcapitalaccumulationalonetotheLjungqvist-Uhligmodeldoesnotaltertheirmainresult.Insum,ouranalysisshowsthatmodelswithcapitalaccumulation,imperfectcompetition,anda“keepingupwiththeJoneses”utilityfunctioncreateanopportunityforKeynesian-typestabi-lizationpoliciesthataredesignedtomitigatebusinesscyclefluctuations.ThispaperisrelatedtorecentworkofAlonso-Carrera,Caballe??andRaurich(2004)whoalsostudythefirst-besttaxpolicyintheLjungqvist-Uhligeconomywithcapitalaccumulation.Ouranalysisdiffersfromtheirsinthreeimportantaspects.First,intheirmodel,laborsupplyisfixedandhouseholdsderiveutilityfromtheirownconsumptionincomparisonwithareferencelevel.Thisreferencelevelisdeterminedbytherepre-sentativehousehold’spastconsumption(“habitformation”)

    ,togetherwiththecurrentandlaggedlevelsofaggregateconsumption(“keepingup”and“catchingup”preferences,respectively).Bycontrast,variablelaborsup-plyisallowedinourmodel,andth

    ehouseholdutilityisonlysubjecttospilloversgeneratedbycontemporaneousaggregateconsumption.Second,intheirmodel,thereisoneproductionsectorunderperfectcompetition,whereasourmodelincludestwoproductionsectors,oneisperfectlycompet-;;28JANG-TINGGUOitiveandtheotherismonopolisticallycompetitive.Third,Alonso-Carreraet.al.consideradeterministicmodelwithconsumptionandcapitaltaxes,whereasouranalysisisconductedwithinastochasticframeworkwithtaxesonlaborandcapitalincome.5Theremainderofthispaperisorganizedasf

    ollows.Section2presentsthemodelandtheconditionsthatcharacterizeacompetitiveequilibriumandtheParetooptimum.Section3derivesanddiscussesthefirst-bestfiscalpolicy.Section4concludes.2.THEMODELThemodeliscomprisedofthreetypesofagents:households,firmsandthegovernment.Households’preferencesaredefinedovertheirowncon-sumptionandleisure,as

    wellasthecurrentlevelofaggregateconsumptionintheeconomy.Theproductionsideoftheeconomyconsistsoftwosectors:intermediateandfinalgoods.Intheintermediate-goodsector,monopolis-ticallycompetitivefirmsoperatewithaCobb-Douglastechnologythatusescapitalandlaborasfactorsofproduction,subjecttoanaggregateproduc-tivityshock.Ahomogeneousfinalgood(GDP)isproducedfromthesetofintermediateinputsinaperfectlycompetitiveenvironment.Thegov-ernmentbalancesitsbudgeteachperiodandchoosesthefirst-bestfiscalpolicy.2.1.FirmsTherearetwoproductionsectorsintheeconomy.Auniquefinalgoodytisproducedfromacontinuumofintermediateinputsyit,i?

    [0,1],usingthefollowingDixit-Stiglitztechnologythatexhibitsconstantreturns-to-scale:(?1)??

    11ηyt=y1??ηitdi,η?

    [0,1).(1)0Weassumethatthefinal-goodsectorisperfectlycompetitive,thusfinal-goodproducersmakezeroprofitsinequilibrium.Thefirst-orderconditionforthefinal-goodproducer’sprofit

    maximizationproblemisyit=??1pηityt,(2)wherepitdenotestherelativepriceoftheithintermedi

    ategood,andthepriceelasticityofdemandforyitisgivenby??1η.Noticethatwhenη=0,intermediategoodsareperfectsubstitutesinproducingthefinalgood,5Alonso-Carrera,Caballe??andRaurich(2003)examinethefirst-bestincometaxationpolicyinadeterministicAKmodelofendogenousgrowthwherethehouseholdutilityfunctionexhibitshabitformationand“keepingupwiththeJoneses”.;;TAXPOLICYUNDERKEEPINGUP29andtheintermediatesectorisalsoperfec

    tlycompetitive.Whenη>0,intermediate-goodproducersfaceadownwardslopingdemandc

    urvethatcanbeexploitedtomanipulateprices.Inthiscase,intermediatefirmsearnaneconomicprofitthatisdistributedtohouseholdsintheformofdividends.Eachintermediategoodisproducedbythesametechnologygivenbyyit=ztkθith1??θit,0<θ<1,(3)whereztisanaggregatetechnologyshock.Inaddition,kitandhitarecapitalandlaborinputsemployedbytheithintermediate-goodproducer.Undertheassumptionthatfactormarketsareperfectlycompetitive,thefirst-orderconditionsfortheintermediate-goodproducer’sprofitmaximiza-tionproblemarert=θ(1??η)pit

    yit,(4)kitwt=(1??θ)(1??η)pityit,(5)hitwherertisthecapitalrentalrateandwtistherealwagerate.Inwhatfollows,werestricttheanalysistoasymmetricequilibriuminwhichpit=pt,kit=ktandhit=ht,foralli.Itfollowsfrom(1)and(3)thattheaggregateproductionfunctionisyt=ztkθth1??θt.(6)Moreover,substituting(2)intothefinal-goodproducer’szero-profitcondi-tionandimposingsy

    mmetryyieldspit=pt=1,foralli.(7)Usingequations(4)-(7),weobtainthefollowingexpressionsforequilibriumrentalrateandrealwage:rt=θ(1??η)yt,(8)ktwt=(1??θ)(1??η)yt.(9)htNoticethat

    whenη>0,theequilibriumfactorpricesrtandwtarelowerthanthecorrespondingsocialmarginalproductsθytkand(1??θ)ytthimpliedtbythesocialtechnology(6).Finally,profitspitintheintermediatesectoraregivenbypit=ηyt.(10);;30JANG-TINGGUOTherefore,theparameterηn

    otonlyindexesthedegreeofmonopolypower,butalsorepresentstheequilibriumprofitshareofnationalincome.2.2.HouseholdsTheeconomyispopulatedbyaunitmeasureofidentical,infinitely-livedhouseholds.Eachhouseholdisendowedwithoneunitoftimeandmaximizes??[]1??σE(ct??αCt)h1+γtoβt,(11)1????Aσ1+γt=00<β<1,0?α<1,σ>0,σ6=1,A>0,γ?0,wherectandhtaretheindividualhousehold’sconsumptionandhoursworked,andCtisthecontemporaneousaggregateconsumptionthatistakenasgivenbytherepresentativehousehold.Inaddition,theparametersα,β,γandσgoverntherelativeimportanceofaggregateconsumption,thediscou

    ntfactor,theintertemporalelasticityofsubstitutioninlaborsupply,andthecurvatureoftheutility

    function,respectively6.Noticethatthestandardpreferencescorrespondtothecaseofα=0wherebyhouseholdsderiveutilityfromtheirownconsumption.Whenα>0,themarginalutilityofan

    individualhousehold’sownconsumptionincreaseswiththeaggregateconsumption.Inthiscase,thehouseholdutil-ityissaidtoexhibitthe“keepingupwiththeJoneses”featuresinceotherhouseholds’consumptionbehavesasacomplementtotherepresentativehousehold’sconsumption.Thisfeaturealsoimpliesjealousyoranegativeconsumptionexternalitybecauseindividualhouseholdsfailtointernalizethattheirconsumptionreducetheutilityofeveryoneelse(seeDuporandLiu[2003]).7Thebudgetconstraintfacedbytherepresentativehouseholdisgivenbyct+kt+1??(1??δ)

    kt=(1??τht)wtht+(1??τkt)(rtkt+pit)+τktδkt+Tt,(12)wherektisthehousehold’scapitalstock,andδ?

    (0,1)denotesthecapitaldepreciationrate.Householdsderivetheirincomefromsupplyinglaborandcapitalservicestointermediatefirmsatrateswtandrt,andpaytaxesonlaborandcapitalincomeatratesτhtandτkt,respectively.Threeaddi-tionalsourcesofhouseholdincomeareintermediatef

    irms’after-taxprofits(1??τkt)pit,thedepreciationallowanceτktδktthatisbuiltintotheU.S.tax6Fortheconvenienceofanalyticaltractability,LjungqvistandUhlig(2000)examinethemodelwithindivisiblelaborasdescribedbyHansen(1985)andRogerson(1988).Inthisformulation,thehouseholdutilityislinearinhoursworked,i.e.,γ=0.7LahiriandPuhakka(1998)usesimilarpreferencestoanalyzetheeffectsofhabitpersistenceonsavingsandequilibriumdynamicsinoverlappinggenerationsmodels.;;TAXPOLICYUNDERKEEPINGUP31code,andalump-sumtransferTt.Thegovernmentsetsτht,τktandTt,subjecttothefollowingconstraintthatbalancesitsbudgeteachperiod:Tt=τhtwtht+τkt(rtkt+pit??δkt).(13)Combining(8)-(10),(12)and(13)yieldsthea

    ggregateresourceconstraintfortheeconomy8ct+kt+1??(1??δ)kt=yt.(14)2.3.CompetitiveEquilibriumInacompetitiveequilibrium,eachhouseholdmaximizes(11)subjecttoitsbudgetconstraint(12),whiletakingfactorprices,taxratesandconsumptionspillovers(oraggregateconsumption)asgiven.Thefirst-orderconditionsforthehousehold’soptimizationproblemare(ct??αC??σt)=λt,(15)Ahγt=(1??τλht)wt,(16)tλt=βEt{λt+1[1+(1??τkt+1)(rt+1??δ)]},(17)limt??βtλtkt+1=0,(18)whereλtdenotestheLagrangianmultiplierassociatedwiththehousehold’sbudgetconstraint(12),(16)equatestheslopeofthehousehold’sindiffer-encecurvetotheafter-taxwagerat

    e,(17)isthestandardEulerequationforintertemporalconsumptionchoices,and(18)isthetransversalitycon-dition.Substitutingtheaggregateconsistencyconditionct=Ctinto(15)yieldsthefollowingexpressionforλtinequilibrium:λ??σt=[(1??α)ct].(19)2.4.ParetoOptimumAttheParetooptimum,thesocialplannerinternalizestheconsumptionexternalitybysettingct=Ctintheutilityfunction(11),subjecttothesocialtechnology(6)andtheaggregateresourceconstraint(14).Thefirst-orderconditionsfortheplanner’soptimizationproblemare(1??α)[(1??α??σ)ct]=??t,(20)8AsinLjungqvistandUhlig(2000),governmentspendingongoodsandservicesdoesnotentertheanalysisbecausewefocusonthefirst-bestfiscalpolicyinthispaper.;;32JANG-TINGGUOAhγt=t(1??yθ),(21)??tht[()]??1t=βEt??t+11??δ+yt+θ,(22)kt+1limt??βt??tkt+1=0,(23)where??tdenotestheLagrangianmultiplierassociatedwiththeaggregateresourceconstraint(14),and(21)equatestheslopeoftheplanner’sindiffer-encecurvetothesocialmarginalproductoflab

    or,(22)istheconsumptionEulerequation,and(23)isthetransversalitycondition.Noticethatsincetheutilityfunction(11)withct=Ctandtheaggregateproductionfunction(6)botharestrictlyconcave,equations(20)-(23)arenecessaryandsufficientconditionsforcharacterizingtheuniqueParetooptimalallocations.3.FIRST-BESTFISCALPOLICYTherearetwokindsofmarketimperfectionsinourmodeleconomy.First,whenα>0,theconsumptionexternalitygeneratesahigherlevelofcon-sumptioninequilibriumcomparedtothatattheParetooptimum.Second,whenη&gt;0,thepresenceofmonopolypowerleadstolowerlevelsofequi-libriumhoursworkedandinvest

    mentincomparisontothoseinaperfectlycompetitiveeconomy.Therefore,theseenvironmentscreateanincentiveforgovernmentinterventiontoaddressthesourcesofmarketfailuresbecausecompetitiveequilibriumdoesnotyieldanefficient(first-best)allocationofresources.Proposition1.Thefirst-bestfiscalpolicythatimplementstheplanner’sallocationsasadecentralizedequilibriumisτ??ht=α??η24)1??,(η()rtτ??kt=??η(25){1??ηrt??,δ[()]}rT??tt=α(1??θ)??η1+η1??ηrt??yt,(26)δforallt,wherertisgivenby(8)andytisgivenby(6).Proof.Wenotethatequations(15)-(1

    9)arenecessaryandsufficientconditionsforacompetitiveequilibrium.Ontheotherhand,asmentioned;;TAXPOLICYUNDERKEEPINGUP33earlier,equations(20)-(23)arenecessaryandsufficientconditionsfortheParetooptimum.Toderivethefirst-bestfiscalpolicy,weneedtoshowthatwhenthepolicyrules(24)and(25)areimplemented,theresultingequilib-riumallocations,characterizedby(15)-(19),satisfytheParetooptimalityconditionsasin(20)-(23).Bycomparing(19)and(20),wefindthatthemarginalutilityofcon-sumptioninequilibriumisproportionaltoitsefficientcounterpartwhere??t=(1??α)λt.(27)Substitutingthiscondition,togetherwiththeequilibriumwagerate(9)andtheproposedτ??ht=α??η1??ηinto(16)showsthatthesocialplanner’sfirst-orderconditionforlaborhours(21)issatisfied.Similarly,substituting(27),to-getherwiththeperiod-t+1equilibriumcapitalrentalrater()t+1=θ(1??η)yt+1kt+1andrt+1theproposedτ??kt+1=??η1??ηrt+1??δinto(17)provesthatthesocialplanner’sconsumptionEulerequation(22)issatisfied.Finally,theoptimallump-sumtransferT??tisobtainedbysubstituting(8)-(10),(24)and(25)intothegovernmentbudgetconstraint(13).Equation(24)showsthat,asinLjungqvistandUhlig(2000),thefirst-besttaxonlaborincomeisaconstantthatisindependentofthepro-ductivityshock.9Theintuitionforthisfindingisstraightforward.Thefirst-orderconditionforlaborsupplygovernstheintratemporaltrade-offbetweenconsumptionandleisure,alongwiththecontemporaneousnatureofconsumptionspilloversimplythatthebenevolentsocialplannercanchoosetheoptimallabortaxperiodbyperiod.Moreover,thesignofτ??htisdeterminedbytherelativemagnitudeoftwoopposingforces.Eliminatingthewedgebetweenthesocialandprivatemarginalproductsoflaborhoursrequiresanincomesubsidy(τ??ht<0),whereascorrectingthepositivecon-sum

    ptionexternalitycallsfortaxinglaborincome(τ??ht>0).Asaresult,τ??htcanbepositive,negativeorzero,dependingonthedifferencebetweenthestrengthofconsumptionexternalityαandthedegreeofmonopolypowerη.Ontheotherhand,sincethenetrateofreturnfrominvestmentrt??δispositivesothathouseholdshaveanincentivetoinvest,theoptimaltaxoncapitalincomeunderthefirst-bestpolicy,givenby(25),isunambiguouslynegative(τ??kt<0).Thatis,τ??ktissettoachievetheParetooptimallevelofinvestmentbyremovingthemonopolyinefficiencythatdrivesawedgebetweentheprivateandsocialmarginalproductsofcapital.Moreover,thefirst-bestcapitalsubsidydoesnotdependontheconsumptionexternality9Bycontrast,LiuandTurnovsky(2002)showthatinastationaryorgrowingecon-omywithelasticlaborsupply,theinteractionbetweenconsumptionandproductionexternalitieshasanimportantimpactontheoptimal(first-best)taxpolicy.;;34JANG-TINGGUOthatisrepresentedbytheparameterα.Intuitively,thecapitalsubsidyaffectstheintertemporaltrade-offbetweenconsumptiongoodsatdiffer-entdates,whereasthecurrentlevelofaggregateconsumptionentersthehouseholdutility.Therefore,consumptionspilloverscanbecorrectedbytheoptimallabortax(24)withoutanyintertemporalconsiderations.Next,usingthechainruleleadstothefollowingrelationshipbetweentheoptimalsubsidyoncapitalincomeandthetechnologyshock:()??τ????rtkt=??τ??r(kt)t??δ??rt????>0,(28)??zt??rt??r??zrt??δ?;;t??;;t??;;?

    negativepositivenegativewhichindicatesthatτ??ktoperateslikeanautomaticstabilizerwhichmovespositivelywiththemacroeconomicconditions.Withcapitalaccumulation,thesocialplannerneedstoaddresstheinterrelationsbetweenmacroeco-nomicaggregatesofdifferenttimeperi

    ods.Asaresult,thefirst-bestpolicyinvolvesacapitalsubsidythataffectstheeconomycountercyclically,e.g.,“stimulating”theeconomywithahighersubsidyoncapitalincomeinre-cessionscau

    sedbyadverseproductivitydisturbances.Finally,whentheintermediatesectorisperfectlycompetitive(η=0),werecoverLjungqvistandUhlig’sresultofτ??ht=αwherebyαpercentofthelaborincomeistaxedaway.Underthispolicy,thehouseholdfacesthecorrectLagrangianmultiplier(seeequation27)sothattheresultinglevelofequilibriumconsumptionisParetooptimal.Moreover,intheabsenceofmonopolyinefficiency,thereisnoneedtotax/subsidizecapitalincomeatall,thusτ??kt=0.ThisimpliesthataddingcapitalaccumulationalonetotheLjungqvist-Uhligmodeldoesnotchangetheirmainfindingwherethefirst-bestpolicyonlyconsistsofatime-invariantlabortaxthatcorrectstheconsumptionexternality.Insum,ouranalysisillustratesthatmodelswithcapitalaccumulation,imperfectcompetition,anda“keepingupwiththeJoneses”utilityfunc-tioncreatean

    opportunityforKeynesian-typestabilizationpoliciesthataredesignedtomitigatebusinesscyclefluctuations.Bycontrast,LjungqvistandUhlig(2000)showthatmodelswithoutcapitalaccumulationandwith“catchingupwiththeJoneses”preferencesalsocallfortraditionalKeyne-siandem

    and-managementpoliciestocorrectexternalitiesthatarisefrompastaggregateconsumptionintheeconomy.4.CONCLUSIONBuildingonLjungqvistandUhlig’swork,wehaveshownthattoachieveParetooptimalityinastochasticrepresentativeagentmodelwithcontem-;;TAXPOLICYUNDERKEEPINGUP35poraneousconsumptionspilloversandimperfectcompetition,thefirst-besttaxonlaborincomeisaconstantthatisindependentofproductivitydis-turbances.Inaddition,thesignoftheoptimallabortaxistheoreticallyambiguous,determinedbytherelativestrengthofconsumptionexternal-ityandmonopolypower.Ontheotherhand,thefirst-besttaxoncapitalincomeisunambiguouslynegativeanddoesnotdependontheconsump-tionexternality.Finally,thefirst-bestfiscalpolicystabilizesbusinesscyclefluctuationsviacountercyclicalcapitalsubsidy,e.g.,“coolingdown”theeconomywithalowersubsidyoncapitalincomewhenitis“overheating”duetoapositivetechnologyshock.Thispapercanbeextendedinseveraldirections.Forexample,wecanconsiderotherkindsofmarketimperfectionsthathavebeeninvestigatedintheoptimaltaxationliterature,suchasincompletemarkets(Aiyagari,1995),untaxedfactorsofproduction(Correia,1996)andlackofcommit-ment(BenhabibandRustichini,1997),amongmanyothers.Moreover,itwouldbeworthwhiletoincorporateproductiveand/orutility-generatingpublicexpendituresintoourmodeleconomy,andthenanalyzethesecond-best(Ramsey)fiscalpolicy.Thiswillallowustocompareandcontrasttheresultsundersecond-besttaxationwiththosereportedinthispaper.Weplantopursuetheseprojectsinthenearfuture.REFERENCESAiyagari,S.Rao,1995,Optimalcapitalincometaxationwithincompletemarkets,borrowingconstraints,andconstantdiscounting.JournalofPoliticalEconomy103,1158-1175.Abel,Andrew,1990,AssetpricesunderhabitformationandcatchingupwiththeJoneses.AmericanEconomicReviewPapersandProceeding80,38-42.Abel,Andrew,1999,Riskpremiaandtermpremiaingeneralequilibrium.JournalofMonetaryEconomics43,3-33.Alonso-Carrera,Jaime,JordiCaballe??,andXavierRaurich,2003,Incometaxationwithhabitformationandconsumptionexternalities.Unpublishedmanuscript.Alonso-Carrera,Jaime,JordiCaballe??,andXavierRaurich,2004,Consumptionex-ternalities,habitformation,andequilibriumefficiency.ScandinavianJournalofEco-nomics106,231-251.Benhabib,Jess,andAldoRustichini,1997,Optimaltaxeswithoutcommitment.Jour-nalofEconomicTheory77,231-259.Correia,Isabel,1996,Shouldcapitalincomebetaxedinthesteadystate?JournalofPublicEconomics60,147-151.Dixit,Avinash,andJosephStiglitz,1977,Monopolisticcompetitionandoptimumproductdiversity.AmericanEconomicReview67,297-308.Duesenberry,James,1952,Income,Saving,andtheTheoryofConsumerBehavior.Cambridge:HarvardUniversityPress.Dupor,Bill,andWen-FangLiu,2003,Jealousyandequilibriumoverco

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