Equipe Universitaire de Recherche en Economie Quantitative - UMR Health effects and optimal environmental taxes in welfare state countries

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1 Equipe Universitaire e Reherhe en Eonomie uantitative - UR 8594 eath effets an optima environmenta taxes in wefare state ountries hashs version - 7 e 2007 Jean-Christophe CAFFET EUREua aison es ienes Éonomiques 06-2 bouevar e 'ôpita Paris Ceex 3 N :

2 eath Effets an Optima Environmenta Taxes in Wefare tate Countries hashs version - 7 e 2007 Jean-Christophe Caffet Université Paris Panthéon-orbonne am gratefu to ireie Chiroeu-Assouine for hepfu omments an suggestions an partiuary thank Geri an Naja Bresous-ehigan for their transation assist.

3 Résumé: hashs version - 7 e 2007 es étues onsarées à hypothèse e oube iviene sont traitionneement menées en équiibre généra afin e mettre en éviene es effets interation fisae entre a taxe environnementae et es taxes pré-existantes. Pour a pupart ees onuent que es effets interation (négatifs) annuent effet (positif) e reyage u revenu fisa environnementa est à ire qu une réforme fisae environnementae aroît e oût soia goba u système fisa onuisant ainsi au rejet e hypothèse e oube iviene. En onséquene e taux optima e taxation e a poution est éga au ratio u taux Pigouvien (ommages marginaux) sur e oût margina es fons pubis. Cet artie revient sur es onusions en souignant es effets positifs sur a santé et offre e travai es ménages que on peut vraisembabement attenre e éaboration une fisaité environnementae. En intégrant existene un système e protetion soiae ans un moèe équiibre généra assique et artie montre que e taux e taxe optimae est supérieur à eui traitionneement mis en éviene. ots-efs : taxe environnementae oube iviene empoi santé séurité soiae. Abstrat: ost stuies on the green tax reform issue point out that environmenta taxes exaerbate pre-existing tax istortions thereby inreasing the wefare osts assoiate with the overa tax oe. As a resut the optima environmenta tax shou ie beow the Pigovian eve (or margina soia amages). This artie haenges this fining by arguing that heath benefits from reue poution may suffiienty affet abor suppy to reate benefit-sie tax interations whih in turn may be of the same magnitue as ost-sie ones. Using a simpe genera equiibrium moe that assumes the existene of a soia seurity system this paper shows that the optima environmenta tax rate ou be greater than traitionay thought. Key-Wors : environmenta tax oube ivien empoyment heath soia seurity. JE Cassifiation: J

4 ntroution ine the Rio Conferene took pae in 992 an espite the faiure of Kyoto ummit (997) there has been a very extensive iterature on the environmenta tax reforms issue. f it is ommony aepte that government must intervene in reguating environmenta externaities it atuay remains an open question to know what forms this intervention shou rather take (taxes or quotas) an what we shou expet from it in terms of eonomi effiieny. This ast notion now wiey referre as to the oube ivien hypothesis is the key-point of the ebate. hashs version - 7 e 2007 Tuok (967) an Terka (984) were the first to suggest that revenues from environmenta taxation ou be use to finane reutions in preexisting taxes. This fun reying proess wou signifianty reue the wefare osts assoiate with the overa tax oe ompare to the ase where environmenta revenues are returne ump-sum. The oube ivien hypothesis in its strong form aims that suh a swap ou generate a wefare gain in other wors that a we-aibrate environmenta tax reform ou have negative gross osts. The argument requires that the environmenta tax raises revenue in a ess istortionary way than the tax it repaes so that there is a wefare gain assoiate with the tax swap even if we ignore the environmenta improvement. n partiuar if the revenue obtaine from environmenta taxation were use to reue taxation of abor it wou reue the istortion in the abor market thereby reuing the eaweight oss assoiate with inome taxes. As a resut the oube ivien hypothesis impies that the optima environmenta tax generay exees margina amages when revenues are use in this way. espite the intuitive appea of this notion a iterature eveope in the 990s whih suggeste that the abiity to simutaneousy urb poution an tax istortions is muh more imite than previousy thought. Athough the authors of this iterature aknowege the positive wefare effet of reying environmenta revenues through tax uts they aso emphasize seon-best negative impats of poution taxes. Arme with generaequiibrium moes they highight previousy unreognize wefare osts reate to interations between the new tax an preexisting taxes : in a seon-best wor where abor is areay taxe environmenta taxation by riving up the prie of (pouting) goos reative to eisure tens to ompoun the istortions ause by taxes in abor markets an onsequenty 3

5 inues a wefare oss. This effet has beome known as the tax-interation effet an has been promote by authors ike Bovenberg an e ooij (994) Bovenberg an Van er Poeg (994) Parry (996) Gouer (995) or Gouer Parry Burtraw (997) who furthermore aime that this tax-interation effet typiay ominates the revenue-reying effet. The main reason is that the environmenta tax eroes the tax base (first ivien) an therefore requires a ompensative inrease in the abor tax rate thus reating an effiieny oss : whereas environmenta taxes were suppose to orret istortions in the abor market they finay exaerbate them As a resut the optima rate of poution taxation ies beow margina environmenta amages in these BPG (Bovenberg e ooij Parry Gouer) moes more preisey it is the ratio of the Pigovian rate ivie by the argina Cost of Pubi Funs (CPF). hashs version - 7 e 2007 n the ate 990s authors ike Kahn an Farmer (999) or hwartz an Repetto (2000) suggeste that BPG onusions were essentiay ue to the unerying assumptions of their moes 2. Reaxing the hypothesis of weak separabiity 3 of environmenta quaity in the utiity funtion or introuing the environment as a fator of proution in BPG moes they show that the tax interation effet is reue in magnitue an may even be offset if the improve environmenta quaity inues peope to inrease their abor suppy by a suffiient amount. Regaring heath impats of air poution 4 hwartz an Repetto (2000) finay assert that prospets for a oube ivien are magnifie as soon as separabiity assumptions are roppe. n other wors : «there are more ways to esape paying the (environmenta) tax beause there are more things to substitute away to the abor tax istorts the onsumption/eisure eision but the tax on the irty goo istorts the onsumption/eisure eision an the hoie between the ean an the irty onsumption goo. Beause the irty goo tax is more istorting than the wage tax oeting an equivaent amount of revenue using the tax on the irty goo auses a higher eaweight oss an reue the rea output of the eonomy more than using the abor tax. n the ontext of a revenue-neutra swap between two taxes the wage tax annot be reue enough to ompensate for the effet on the rea wage of the inrease tax on the irty goo. ene the rea wage an thus non-environmenta wefare eines». Empoyment Environmenta Taxes an nome Taxes N. Eissa R. Bune. Bow Reefining Progress (ay 2000). 2 «We strongy beieve these onusions to be an artifat of the struture of the moes whih have been use to examine the oube ivien ( ). Athough these assumptions make the moes tratabe they o ontribute to the primary finings of these papers» hwartz an Repetto (2000). 3 Weak separabiity impies that environmenta quaity oes not affet onsumers trae-off between onsumption an eisure. 4 tuies by Ostro (994) Zuinema an Nentjes (997) iniate that «ereasing eves of major air poutants by about 30% wi resut in about three ess work-oss ays per worker». 4

6 hashs version - 7 e 2007 Expiity moeing heath impats of air poution in the utiity funtion Wiiams (2003) ontraits hwartz an Repetto s intuitions an onfirms that environmenta taxation tens to exaerbate the istortions of the overa tax system. norporating both meia expenitures an time ost to sik-ays in the respetive househo buget an time onstraints he emonstrates that there is atuay a potentia benefit-sie tax-interation effet from a green tax reform but that this kin of positive interations wou ertainy not offset negative ones so that the oube ivien hypothesis finay fais. is resut is mainy ue to the presene of an inome effet reate to the erease of meia expenitures. This inome effet eas househos to aoate a arge fration of the aitiona time (ess sik-ays) to eisure thus reating an effiieny oss. Furthermore benefit-sie tax interation effets turn out to be negative with typia parameters an what was initiay thought to be a gain is finay osty t seems that we may ritiize Wiiams (2003) onusions the same way he himsef ritiize hwartz an Repetto s (2000) anaysis 5. f Wiiams (2003) sharpy fouses on heath effets an abor suppy eisions it nevertheess seems that he forgot a ruia variabe to orrety examine the oube ivien hypothesis. nee Parry an Bento (2000) have showe that aowing tax eutibe expenitures substantiay reues the osts of revenue-neutra environmenta taxes. ine meia expenitures are at east partiay returne to househos in most eveope ountries it seems that we shou inorporate this kin of subsiies to better examine the oube ivien hypothesis. This paper is organize as foows. etion presents a moe whih is somewhat an extension of Wiiams (2003) to the extent that it eveops a simpe genera-equiibrium moe that inorporates a househo abor-eisure eision aong with a poution externaity. Foowing Parry an Bento (2000) intuitions an in orer to estimate oube ivien prospets within a more reaisti framework our moe inorporates in aition subsiies to meia expenitures. ore generay a soia seurity system is assume whih onsists in subsiies to meia expenitures an soia transfers uring sik-ays. For simpiity we wi suppose that househos sti get their gross wage uring these work-oss ays. etion 5 n his abstrat Wiiams (2003) reproahes hwartz an Repetto (2000) for not having expiity moee heath impats of air poution. ore preisey he ritiizes the fat that their fixe househo time onstraint oes not take work-oss ays into aount. As a resut any erease in what they a enfore eisure eas to an inrease in abor suppy. 5

7 examines the wefare effets of a green tax reform in other wors the wefare impats of a revenue neutra swap between abor an environmenta taxation. Then etion highights the eve of the optima environmenta tax in a seon-best setting where benefit-sie tax interation effets are effetivey taken into aount. Finay etion V presents onusions.. oe We assume a representative agent maximizing his ontinuous an quasi-onave utiity funtion given by : hashs version - 7 e 2007 ( C G ) U U () where C an respetivey represent the (aggregate) onsumptions of ean an irty goos the hours of eisure or non-market time G the quantity of a pubi goo an the heath onition of the agent. As efine by Wiiams (2003) heath onition is a funtion of both environmenta quaity an meia expenitures : ( ) (2) 2 with > 0 > 0 an < 0 2 We then hoose the same inear poution funtion where is an exogenous baseine eve of environmenta quaity : (3) The poution externaity assoiate with the onsumption of the irty goo has two effets : first it iminishes the onsumer wefare by eteriorating his heath onition. eon it auses househos to ose some time to sikness thus reuing their time 6

8 enowment. As oppose to Wiiams (2003) these sik-ays are not exusivey a funtion of environmenta quaity but more generay of the agent s genera heath onition : [ ( ) ] with < 0 (4) This new hypothesis is introue not ony beause it seems more reaisti but aso beause it wi aow us to better approah interations between subsiies to meia expenitures an environmenta taxation. Uner this hypothesis the househo time onstraint beomes : [ ( ) ] T (5) hashs version - 7 e 2007 where T represents househo s time enowment an is time eiate to abor unique proution fator in our moe. We assume that the tehnoogy use exhibits onstant returns to sae an units are normaize so that one unit of abor an proue one unit of any of the four goos : ( ) C G F (6) The initia tax oe inues a tax on abor inome a tax on the onsumption of the pouting goo an a soia seurity system. This soia seurity system both preserves the gross wage uring sik-ays an grants subsiies to meia expenitures; for simpiity we assume a goba subvention rate the foowing onsumer buget onstraint :. We aso normaize the gross wage to equa one yieing ( ) [ ( )] C ( ) ( ) (7) where is ump-sum inome whih is assume to be zero. Government inome is the sum of abor an poution tax revenues. Therefore government buget baane requires : [ ( )] G ( ) (8) 7

9 8 ousehos maximize utiity subjet to their time an buget onstraints taking the quantity of the pubi goo the tax rates an the eve of environmenta quaity as given. This yies the foowing first-orer onitions an then efines the unompensate eman equations for the four goos : ( ) ( ) ( ) U U U C U λ λ λ λ ( ) ( ) ( ) ( ) C where λ is the margina utiity of inome. 2. Wefare effets of a green tax reform. This setion examines impats on wefare of a hange in the environmenta tax rate. To obtain the same kin of reation BPG moes usuay ahieve we introue the foowing key-parameter : ( ) η (9) This is the margina ost of pubi funs (CPF) the ost to the househo of raising a margina oar of government revenue through the abor tax. The numerator of the first term is the wefare oss from an inrementa inrease in ; it is the wege between the gross wage (equa to the vaue margina prout of abor) an the net wage (equa to the margina soia ost of abor in terms of foregone eisure) mutipie by the reution in abor suppy 6. The enominator is margina tax revenue (from ifferentiating ( ) [ ] ). o this first term is the margina eaweight oss per oar of revenue an the CPF inues both the 6 We wi assume that abor suppy is not bakwar-bening. hashs version - 7 e 2007

10 iret ost (equa to unity) of removing revenue from the private setor an the aitiona eaweight oss reate by the istortionary tax 7. n referene to arrington an Portney (987) Wiiams (2003) efines environmenta amages as the sum of two terms the respetive vaues of the iret utiity oss from reue heath an the time ost to iness 8 : W P λ U hashs version - 7 e 2007 ine the representative agent sti earns his wage uring sik-ays it seems that we shou orret the seon term in our moe. Whereas these sik-ays were an equivaent oss of purhasing power in Wiiams (2003) this oss is partiay offset by the soia seurity system we have efine. n fat househos ony bear the istortionary ost introue by the government transfers that is the margina eaweight oss of the abor tax reative to the wagekeeping evie. n this way the Pigovian rate is given by : U P ( η ) (0) λ Arme with these two efinitions we an now approah the wefare effet of a hange in the government buget onstraint being ajuste by. Anaogous to the proeure in BPG (see Appenix for erivation) the wefare effet of the environmenta tax an then be expresse as : U λ ( P ) ( η) η η P R B W W W W () 7 This is a partia equiibrium efinition of the CPF sine it ignores a effets outsie the abor market. niret effets of this tax on goos market espeiay on subsiize onsumptions are atuay not taken into aount with this efinition neither are the hanges in revenues from the orretive tax an environmenta quaity. 8 The gross wage has been normaize to equa one. 9

11 Expression () eomposes the wefare impat of the poiy hange into four omponents. The first is the primary or Pigovian effet W P that is the effet of the tax on the poution externaity. This is the partia equiibrium reution in from a margina inrease in the environmenta tax mutipie by the wege between margina soia ost an the eman prie or margina soia benefit. n a first-best wor without preexisting istortions the optimum is reahe for Pigovian rate. P meaning that the optima environmenta tax must equa the The seon term is the gain from the margina revenue-reying effet R W. This is the hashs version - 7 e 2007 wefare gain from using the poution tax revenues to reue the abor tax reative to when they are returne ump-sum an have no effiieny onsequenes. o R W is the prout of the effiieny vaue per oar of revenue (the margina exess buren of taxation) an the inrementa poution tax revenue (from ifferentiating ). The thir an fourth terms W an W B are respetivey what Wiiams (2003) as ost-sie an benefit-sie tax interation effets. They resut when hanges in househos abor suppy eisions interat with the abor market istortion. For the first one the poution tax rives up the prie of onsumer (pouting) goos owering the rea wage an onsequenty isouraging abor suppy. As we have seen this fa in abor suppy exaerbates the private soia ost of the abor tax by. This aso reues abor tax revenues by thus requiring a ompensating inrease in the abor tax rate an reating an effiieny oss equa to the amount that the government has to refun mutipie by the effiieny ost per oar of abor tax revenue (i.e. the margina exess buren of abor taxation). The tax interation effet ientifie by prior iterature on the oube ivien hypothesis is exusivey the wefare oss from these two impats that is η ost-sie tax interation expression.. n our anaysis there is however a seon term in the This term whih symboizes interations between meia expenitures an environmenta taxation an be expaine with a simiar approah. First any fa in meia 0

12 expenitures generates an effiieny gain ( η ) reate to the ontration of subsiies amount. eon subventions ause this onsumption to be unerprie reative to its soia ost. As a resut any erease in meia expenitures wi ea to a genera-equiibrium wefare gain. This gain equas the wege between suppy an eman pries (respetivey margina soia ost an benefit) mutipie by the reution of subsiize onsumption that is. umming these two eements for the effet of the poution tax on meiines onsumption give the seon term in square brakets 9. Finay benefit-sie tax interation effet W B expresses the impat of improve hashs version - 7 e 2007 environmenta quaity on abor suppy eisions. n opposition to Wiiams (2003) a rise in sik-ays o not impy a erease in government revenues. This ifferene is ue to the wagekeeping hypothesis whih has for impiit onsequene to enarge the tax base of the abor tax : more onretey is evie on ( ) instea of effetive abor inome 0. As a resut wefare impats of sik-ays reution an be resume by the prout of that erease an the sum of the effiieny gain an the private soia benefit reative to that erease (equa to the wege between abor margina soia benefit an the prie of sik-ays i.e. the ost of the transfer ( ). A simiar sum as for ost-sie tax interation effet term of benefit-sie tax interation expression η. η gives the ast 9 n our moe a erease in meia expenitures may eteriorate the heath onition of the representative agent an therefore inrease sik-ays. n that ase the positive effet of the erease in meia expenitures on government buget wou be partiay offset by the wage-keeping system. 0 n Wiiams anaysis an inrease in sik-ays reues abor tax revenues by effiieny ost equa to ( η ) i.e. : [ ( η ) [ ( η ) ].. Refuning it yies an

13 2 3. Optima Tax Foowing Wiiams (2003) we now fous on the two opposite tax interation effets B W W an. We aso onsier the neutra assumption that goos C an are equa substitutes for eisure aowing equation () to be rewritten as (see Appenix for erivation): ( ) ( ) ( ) ( ) P U ε ε η η η λ (2) The first term ombines the primary wefare effet with the revenue-reying effet an the first omponent of ost-sie tax interation effet. Without the other terms on the right-han sie it onfirms that the optima environmenta tax is equa to the Pigovian rate ivie by the CPF. The seon term symboizes the interations we have areay ientifie between subsiies to meia expenitures an environmenta taxation. Finay the ast term shows that benefit-sie tax interation effets improve heath onitions may signifianty reue the gross ost of an environmenta tax reform ontraiting Wiiams onusions. n the introution we have seen that Wiiams respone to hwartz an Repetto s intuitions by insisting on an inome effet reate to the erease of meia expenitures 2. Aoring to him this inome effet wou impy that the inrease time avaiabe for abor an eisure (sik-ays reution) is rather aoate to the seon one. For typia parameters a abor tax rate of 04 an unompensate abor suppy eastiity of 05 an an 2 To make the omparison a itte bit easier Wiiams onusions are given by : ( ) ( ) ( ) P U ε ε η η λ ( ) ( ) P η η with 5 0 ε 5 0 ε an 4 0 hashs version - 7 e 2007

14 inome eastiity of abor suppy of -05 the ast term of Wiiams equation () (see footnotes) is atuay negative : interations that were presume positive in fat introue an aitiona istortion. t seems that we annot raw the same onusions in this paper. For the same typia parameters the sign of benefit-sie tax interation effets stays unetermine 3 beause is positive.. As we have seen this term represents the wefare gain ue to the hashs version - 7 e 2007 reution of soia transfers reative to the wage-keeping evie. Finay the better the goba heath onition of the agent is the more he works : the improvement of his heath onition wou impy the homogenization of his revenue substituting () by. oreover we an notie that the inome effet highighte by Wiiams (2003) is somewhat inferior in our moe; for 00% this inome effet isappears an benefit-sie tax interation effets are unquestionaby positive. t shou be furthermore notie that these onusions have a muh arger sope than Wiiams as they are inepenent of the eve of abor taxation. To onue it appears that Wiiams resuts an be reverse. nee if the negative inome effet ue to the reution of transfers () is superior to the positive inome effet ue to the reution of meia expenitures then the substitution of () by impies that the optima environmenta tax rate is greater than traitionay highighte by BPG moes. V. Conusions This paper has empoye the same methooogy as in BPG anaysis to examine the oube ivien hypothesis. Using a very ose moe to Wiiams (2003) it however shows that there may be an effiieny gain reate to poution taxation in most eveope 4 ountries so that the optima environmenta tax rate might exee margina amages (or Pigovian rate). This ontraiting resut is mainy ue to both hypothesis that have been introue that is the existene of subsiies to meia expenitures an the wage-keeping 3 as sum of two opposite terms. 4 or maybe Wefare tate ountries. 3

15 evie. As expaine above this (simpifie) soia seurity system tens to magnify benefitsie tax interations whih ou finay offset ost-sie ones. hashs version - 7 e 2007 Prior researh has inee essentiay fouse on ost-sie tax interation effets to isquaify the oube ivien hypothesis thus negeting the ifferent hannes through whih an environmenta tax reform may yie a oube-ivien 5. Even if it ony eas with an aitiona hypothesis this paper has trie to show that it is a ruia point in the oube ivien ebate a fortiori in stuies moeing heath effets in the agent s utiity funtion. As we as introuing abor market imperfetions in moes that ea with the possibiity of obtaining a seon ivien in the form of a reue unempoyment eve 6 assuming the existene of a soia seurity system seems aso neessary to orrety estimate oube ivien prospets in expiity moeing heath stuies. 5 This is the sense to give to Wiiams (2002) onusion : future stuies shou onsier the benefit-sie tax interations as we as the ost-sie tax interations in estimating the optima eve of reguation an the potentia gains from suh reguation. tuies that fai to onsier these seon-best effets ou prove to be substantiay miseaing. 6 ee for exampe Bovenberg an Van er Poeg (996) or Chiroeu-Assouine an emiae (200). 4

16 5 Appenix erivation of equation () Taking a tota erivative of utiity with respet to the orretive tax substituting in onsumer first-orer onitions an for onstant pubi spening (G 0) we obtain the foowing reation : ( ) ( ) ( ) U C U λ λ (A.) umming tota erivatives with respet to of the proution funtion (6) an househo time onstraint (5) an using T 0 gives the equation : 0 C (A.2) ubstituting A.2 into A. an eriving equation (3) with respet to we fin with the hep of efinitions (9) an (0) : ( ) ( ) P U η λ 2 (A.3) We then try to make the term more expiit. This term symboizes interations between the environmenta tax an househo abor suppy eisions. Aoring to the unompensate eman equations an sine the government ajusts its buget onstraint with (i.e. ) 0 we an write : (A.4) Taking a tota erivative with respet to of the government buget onstraint (8) an with the hep of (5) we fin for G T 0 : ( ) (A.5) hashs version - 7 e 2007

17 This expression gives the reution in abor tax that an be finane by a margina inrease in the environmenta tax whie maintaining buget baane. Repaing it in A.4 gives: [ ( )] [ ( ) ] (A.6) ( ) Finay substituting A.6 into A.3 gives equation (). erivation of equation (2) hashs version - 7 e 2007 Taking a tota erivative of utiity with respet to hoing the eves of pubi spening utiity an environmenta quaity onstant an substituting in the onsumer firstorer onitions yies : C ( ) ( ) ( ) ( ) where the supersript enotes a ompensate erivative. ( ) (A.7) The assumption that the ross eastiity of an eisure is equa to the average (weighte by onsumption shares) over a goos is given by : ε ε C ε C ε (A.8) where ε i an i (i C ) respetivey represent the ompensate eastiity of eman for goo i with respet to the prie of eisure an the share of that goo i in tota onsumption 7. ubstituting A.8 an the househo buget onstraint (7) into A.7 yies after some manipuations : [ ( )] ( ) (A.9) 7 Formay : ε i i ( ) i an i pi i ( pi i) 6

18 7 As hanges in the prie of eisure an pouting goos are equa to hanges in their respetive tax rates the utsky equations give : (.) ( ) [ ] (.2) Aoring to () an (.) we have : W η Using the utsky symmetry property ( ) reations.2 an A.9 we an rewrite ost-sie tax interation effets in a simiar fashion than Wiiams (2003) : ( ) W η η (A.0) As we have seen the expression for benefit-sie tax interation effets B W is : B W η (A.) Aoring to the househo buget onstraint (7) the hange in spening on C an for a hange in wi equa : ( ) ( ) ( ) C (A.2) imiary for a hange in : ( ) ( ) ( ) C (A.3) Weak separabiity of heath in the utiity funtion impies that eisure eman is etermine ony by the reative pries of C an an by tota spening on those goos. Those reative pries are not affete by hanges in or hanges in. As a resut the hashs version - 7 e 2007

19 erivative of with respet to wi equa the erivative of with respet to times the ratio of the erivative of spening on those goos with respet to (A.2) to the erivative of spening on those goos with respet to (A.3) : ( ) ( ) (A.4) Repaing by its vaue in A. an observing that η ( η ) ε ε we obtain : W B ε ε ( η ) ( ) ( ) (A.5) hashs version - 7 e 2007 where ε is the unompensate abor suppy eastiity an abor suppy 8. ubstituting in expression () the vaues of A.5 gives equation (2). W an ε is the inome eastiity of B W given by A.0 an 8 That is : an ε ε [ ( )] ( ) ( ) [ ( )] ( ) [ ( )] ( ) [ ( )] [ ( )] ( ) 8

20 Referenes A.. Bovenberg R.A. e ooij (994) Environmenta evies an istortionary Taxation Amerian Eonomi Review 84 n 4 pp A.. Bovenberg F. van er Poeg (994) Environmenta Poiy Pubi Finane an the abour arket in a eon-best Wor Journa of Pubi Eonomis 55 n 3 pp hashs version - 7 e 2007 A.. Bovenberg.. Gouer (996) Optima Environmenta Taxation in the Presene of Other Taxes : Genera-Equiibrium Anaysis Amerian Eonomi Review 86 n 4 pp A.. Bovenberg F. Van er Poeg (996) Optima Taxation Pubi Goos an Environmenta Poiy with Unvountary Unempoyment Journa of Pubi Eonomis 62 pp A.. Bovenberg.. Gouer (997) Costs of Environmentay otivate Taxes in the Presene of Other Taxes : Genera Equiibrium Anaysis Nationa Tax Journa 50 n pp A.. Bovenberg (999) Green Tax Reforms an the oube ivien : an Upate Reaer s Guie nternationa Tax an Pubi Finane 6 pp N. Eissa R. Bune. Bow (2000) Empoyment Environmenta Taxes an nome Taxes Reefining Progress (ay 2000)... Gouer (994) Environmenta Taxation an the oube ivien : a Reaer s Guie NBER Working Paper n

21 .. Gouer.W.. Parry. Burtraw (997) Revenue-Raising versus Other Approahes to Environmenta Protetion : The Critia ignifiane of Preexisting Tax istortions RAN Journa of Eonomis 28 n 4 pp Gouer.W.. Parry R.C. Wiiams. Burtraw (999) The Cost-Effetiveness of Aternative nstruments for Environmenta Protetion in a eon-best etting Journa of Pubi Eonomis 72 pp J.R. Kahn A. Farmer (999) The oube ivien eon-best Wors an Rea- Wor Environmenta Poiy Eoogia Eonomis 30 pp hashs version - 7 e 2007.W.. Parry (995) Poution taxes an revenue reying Journa of Environmenta Eonomis an anagement 29 n 3 pp W.. Parry (997) Environmenta Taxes an uotas in the Presene of istortionary Taxes in Fator arkets Resoure an Energy Eonomis 9 pp W.. Parry (997) Revenue Reying an the Costs of Reuing Carbon Emissions RFF Cimate ssues Brief n 2..W.. Parry (998) A eon-best Anaysis of Environmenta ubsiies nternationa Tax an Pubi Finane 5 pp W.. Parry R.C. Wiiams.. Gouer (999) When Carbon Abatement Poiies nrease Wefare? The Funamenta Roe of istorte Fator arkets Journa of Environmenta Eonomis an anagement 37 pp W.. Parry A. Bento (999) Tax eutibe pening Environmenta Poiy an the oube ivien ypothesis RFF isussion Paper n Resoures For the Future Washington C..W. Peare (99) The Roe of Carbon Taxes in Ajusting to Goba Warming The Eonomi Journa 0 pp

22 P.R. Portney W. arrington (987) Vauing the Benefits of eath an afety Reguation Journa of Urban Eonomis 22 pp A.. ansta G. Woff (2000) Tax hifting an the ikeihoo of oube iviens : Theoretia an Computationa ssues Reefining Progress (January 2000). R. hoeb (2003) The oube ivien ypothesis of Environmenta Taxes : A urvey CEifo Working Paper n 946. hashs version - 7 e 2007 J. hwartz R. Repetto (2000) Nonseparabe Utiity an the oube ivien ebate: Reonsiering the Tax-nteration Effet Environmenta an Resoure Eonomis 5 n 2 pp Terka (984) The Effiieny Vaue of Effuent Tax Revenues Journa of Environmenta Eonomis an anagement pp G. Tuok (967) Exess benefit Water Resoures Researh 3(2) pp R.C. Wiiams (2002) Environmenta Tax nterations when Poution Affets eath or Proutivity Journa of Environmenta Eonomis an anagement 44 pp R.C. Wiiams (2003) eath effets an optima environmenta taxes Journa of Pubi Eonomis n 87(2) pp R.C. Wiiams. West (2003) Empiria Estimates for Environmenta Poiy aking in a eon-best etting NBER Working Paper n