Tradable pollution permits in dynamic general equilibrium: can optimality and acceptability be reconciled?

Transcription

1 Tradable polluion permis in dynamic general equilibrium: can opimaliy and accepabiliy be reconciled? Thierry Bréche, Pierre-André Jouve, Philippe Michel, Gilles Roillon February 24, 2009 Draf version Absrac In his paper we sudy opimal growh and is decenralizaion in a wo-secor overlapping generaions model wih polluion. One secor is polluing (power generaion) and he oher no (final good). Polluion is regulaed by radable emission permis. The issue is wheher he opimal growh pah can be replicaed in equilibrium wih polluion permis, given ha permis mus be issued for free for he sake of poliical accepabiliy. We provide a policy rule ha allows o reconcile opimaliy and accepabiliy. JEL Classificaion: D61,D9,Q28 Key words: Opimal growh, environmen, radable emission permis. Cener for Operaions Research and Economerics (CORE) and Louvain School of Managemen, Chair Lhois Berghmans in Environmenal Economics and Managemen, Universié caholique de Louvain, Voie du Roman Pays 34, B-1348 Louvain-la-Neuve, Belgium, hierry.breche@uclouvain.be. EconomiX, Univ. Paris X-Nanerre. Philippe Michel passed away on July 22, EconomiX, Univ. Paris X-Nanerre. 1

2 1 Inroducion Since Mongomery (1972) i is well esablished in he economic lieraure, and widely claimed in he policy debae, ha he way permis are issued does no maer for efficiency. This resuls holds only o a saic seing and in parial equilibrium. Acually, very few papers scruinize he properies of a marke for radable permis in general equilibrium. The excepion is he sream led by Bovenberg, Goulder and Parry and relaed co-auhors on he double dividend issue (see e.g. Bovenberg and de Mooij, 1994, Parry e al. 1999, Goulder, 2002). In an overlapping generaion framework (OLG), Jouve, Michel and Roillon (2005) showed ha decenralizaion of he opimal pah can be obained wih lump-sum ransfers only if radable permis are no given for free o he polluing firms. This resul conrass he sandard OLG model (Allais, 1947, Diamond, 1965) wihou environmenal consrain, where he opimal policy is decenralized wih lump-sum ransfers wihou any oher condiion (see de la Croix and Michel, 2003, on ha issue). Wih an environmenal exernaliy, free permis ac as a subsidy ha raises he reurn o he owners of he firm s capial, hus generaing a disorion in he economy. Despie he fac ha he papers menioned above, by using general equilibrium models, sugges ha aucioned permis or emission fees dominae radable permis wih free endowmen in erms of welfare, free allocaion (via grandfahering) remains he main opion in pracice. This holds for he US marke on SO 2, for he EU-ETS marke on CO 2, and also under he Kyoo proocol. Savins (1998) popularized he moives why policy makers favor free allocaion insead of aucion, wha we shall call accepabiliy. Following Savins (1998) and Goulder (2002) we define accepabiliy by he fac ha he environmenal regulaion does no reduce firm s profi. Clearly, if such a policy is possible, boh he polluers (he firms) and pollues (he consumer) will agree on he proposed policy. As explained by Savins, exising firms favor freely allocaed radable permis because hey convey rens o hem, wha is called windfall profis in he lieraure. Emission permis also creae enry barriers since new comers have o purchase permis o he exising firms 2

3 (Kousaal, 1997). Unforunaly, i comes ou from he lieraure ha opimaliy canno be reached because i will be rejeced by he polluers, here he firms. To sum up, accepabiliy suggess giving polluion permis for free while opimaliy requires o fully aucion hem, or o se an emission ax. According o he lieraure, hese wo objecives canno be reconciled. Opimaliy and accepabiliy remain conflicing issues. In his paper we quesion his resul. By developing a wo-secor OLG model we show ha he opimal pah can be decenralized while saisfying he accepabiliy condiion ha firm s profi is no reduced. We provide a policy rule for ha. The paper is organized as follows. In Secion 2 he seing is presened. The opimal growh problem is saed in Secion 3, and we explicily idenify he condiions for an opimal growh. Then, in Secion 4, we define he dynamic general equilibrium wih polluion permis and we show why giving permis for free o he polluers canno lead o opimal growh. In Secion 5 we explore alernaive policy soluions and we provide a rule such ha opimal growh and accepabiliy can be reconciled. 2 The model We consider an economy wih wo secors. The firs secor produces an inermediae good by using capial and labor, and by emiing some global polluan. The second secor produces a final good by using capial, labor and he inermediae good. I does no pollue. One may see he firs secor as he power generaion secor, and he polluan as carbon dioxide. The final good secor uses he energy supplied by he power secor, and hus does no emi carbon dioxide emissions. Sill, i has an indirec effec of polluion hrough is energy demand o he power secor. The power secor is indexed by e, and he final good secor by g. Households consume he final good and power, and heir uiliy level is impaced by he qualiy of he environmen. 3

4 2.1 Technologies The oupu Y g of he final good secor occurs in each period according o a producion funcion F g (.) of capial, K g, labor, L g and power Z, Y g = F g (K g, L g, Z ) (1) The power generaion secor produces an oupu Y e wih a producion funcion F e (.) by using capial, K e, labor, L e and emissions E, Y e = F e (K e, L e, E ) (2) Boh producion funcions are homogenous of degree one and differeniable. The power supply Y e will be used boh as an inermediary inpu for he final good secor and as a final good for consumers. 2.2 Polluion and abaemen Le us consider a sock polluan which dynamics a ime, P, are given by P = (1 h)p 1 + m(e, X ) (3) where h is he naural level of polluion absorpion, 0 h 1, and m(.) is he polluion flow ne of abaemen, wih E he emissions flow coming from he power secor and X he spending in polluion abaemen. We assume ha m E 0 and m X Households We consider an overlapping generaion model wih wo consumpion goods, he final good and power, and he polluion level. Individuals live wo periods. The number of agen born a dae, N, is exogenous. Each agen young a period, supplies inelasically one uni of labor in period. She derives uiliy from he consumpion of he wo goods during he wo periods - i.e. c g and c e in period and d g +1 and d e +1 when old. The polluion sock negaively affecs uiliy during he wo periods of life - i.e. P and P +1. 4

5 Households preferences are hus represened by a general uiliy funcion of he form U = U(c g, c e, P, d g +1, d e +1, P +1 ) (4) The funcion U(.) is sricly concave, increasing wih respec he wo consumpion goods, decreasing wih respec polluion, wice coninuously differeniable and i saisfies he Inada condiions. 3 Opimal growh 3.1 The resource consrains The final good secor uses capial K g, labor L g and energy Z as producive inpus and delivers is oupu owards he households (young and old) capial accumulaion and polluion abaemen expendiures. Is resource consrain is hus he following, Y g = F g (K g, L g, Z ) = N c g + N 1 d g + K +1 + X (5) where K +1 is he oal capial sock in he economy in he nex period. In he power secor, capial K e, labor L e and emissions E are he inpus and he oupu is used for final consumpion (young and old ages) and inermediae consumpion in he final good secor. The resource consrain is, Y e = F e (K e, L e, E ) = N c e + N 1 d e + Z (6) We assume oal depreciaion of he capial sock a each period of ime. Thus, he capial resource consrain implies ha, K = K g + K e (7) Finally, he resource consrain for labor is a follows, N = L g + L e (8) The objecive of he cenral planner is o maximize he welfare of all 5

6 agens over all generaions, wih a discoun facor γ, 0 < γ < 1, ha is, + = 1 γ N U given he iniial value of he capial sock K 0 and he polluion sock P 1, given he pas values of consumpion for he firs old, and subjec o he resource consrains (5) - (8) and o he dynamics of polluion accumulaion (3) 3.2 Opimaliy condiions The cenral planner chooses he level of consumpions, c g, c e, d g +1 and d e +1, capial K g, K e, emission E, polluion abaemen X and he inermediae consumpion Z. Since K and N are given a period we can use K e = K K g and L e = N L g. Denoing by λ g and λ e respecively he Lagrangian mulipliers of he resources consrains (5) and (6) and by µ he Lagrangian mulipliers of he dynamic of he sock of polluion (3), he Lagrangian is defined by + γ 1 N 1 U 1 + =0 γ [ ] N U + λ g F g (K g, L g, Z ) N c g N 1 d g K +1 X [ ] F e (K K g, N L g, E ) N c e N 1 d e Z +λ e +µ [P (1 h)p 1 m(e, X )] One obains hereby he firs-order condiions, 1. for he final consumpion in he firs period U c g = λg and U c e = λ e 2. for final consumpion in he second period 1 γ U d g = λg and 1 γ U d e = λe 6

7 3. for energy use, Z, emissions level E and abaemen X, λ g F g Z = λ e, λ e F e E = µ m E, λ g = µ m X where F g Z represens he derivaive of F g (K g, L g, Z ) wih respec o he hird argumen, and similarly for FE e, m E and m X. The arbirage condiions for capial and labor among he wo producive secors of he economy are as follows, λ g F g K g = λ e F e K e and λ g F g L g = λ e F e L e The dynamics of he shadow prices are obained by differeniaing he Lagrangian wih respec o K +1 and P, 0, and λ g = γλ e +1F e K e +1 (K +1 K g +1, N +1 L g +1, E +1 ) U µ = γµ +1 (1 h) + N + N 1 U 1 P γ P The ranversaliy condiion is (Michel, 1990), lim + γ ( λ g K +1 + µ P ) = Opimal arbirage condiions From he firs-order condiions one can eliminae he shadow prices relaed o he physical capial socks and he polluion sock. By rearranging he erms, he rade-offs faced by he cenral planner a he opimal soluion can be explicily wrie down. The hree following condiions, C.1, C.2 and C.3, represen he necessary condiions for opimal growh: Condiion C.1 - Opimal producion facors allocaion: he raio λ g /λ e is equal o: 1 F g Z = F e Ke F g K g = F e L e F g L g (9) 7

8 Condiion C.2 - Trade-offs beween consumpions over he life cycle (using he dynamic equaion of λ g ): U c g = F g U K g d g and U c e = F g Z FK e U +1 e d e = F g Z +1 F g F g U K g d e (10) Z +1 Condiion C.3 - Trade-offs beween he consumpions of he wo goods: U c e = F g Z U c g and U d e = F g Z U d g (11) The condiion C.1 corresponds o he opimal capial and labor allocaion beween he wo secors. If his condiion does no hold hen an equilibrium wih wo secors is sub opimal. By combining condiions C.1, C.2 and C.3 we obain he following, 1 F g Z = F e Ke F g K g = F e L e F g L g = U c g U c e = U g d = F g Z +1 U d g +1 U d e F g (12) Z U d e +1 4 Equilibrium wih polluion permis Le us know consider he dynamic general equilibrium of he economy. All markes are assumed o be perfecly compeiive. We ake he oupu of he final good secor as numeraire and he energy price is denoed by p e. 4.1 Governmen The governmen is endowed wih hree policy insrumens. I can regulae polluion wih a marke for radable permis, i can organize ransfers among households, and i can improve he environmenal qualiy by financing polluion abaemen. Le us deail hese hree insrumens. Polluion is regulaed by he means of a marke for radable emission permis à la Mongomery (1972). A given amoun of emission permis is issued o he firms by he regulaor, each permi allowing for a uniary emission level. Then, firms are allowed o rade hese permis among hemselves on a marke. I is assumed hroughou he paper ha he governmen issues 8

9 an amoun of permis E ha coincides wih he opimal polluion level, E = E. In order o be as general as possible we consider ha wo issuing mehods may be implemened by he governmen: free endowmen, or aucioning. The amoun E e (0 E e E ) is given for free o he polluing firms, and he remaining par E E e is aucioned. The price on he polluion permis is denoed by q. As in any OLG model he governmen can also organize lump-sum ransfers o he households, wih τ being associaed o he young agen and θ o he old agen. These ransfers allow he governmen o modify he households ineremporal rade-offs. Finally, he governmen can improve he environmenal qualiy by financing polluion abaemen, X. This spending can be financed eiher by aucioning (some) emission permis and/or by axing he households. The governmen budge consrain is he following, X + N τ + N 1 θ = q (E E e ) (13) 4.2 Households Households ake he environmen as given. A he firs period of life, he young agen earns he wage w and receives a ransfer τ which may be posiive or negaive. She consumes he final good and energy, c g and c e, and saves s. Thus, he firs period budge consrain is, w + τ = c g + p e c e + s (14) When old, she is reired and receives a ransfer θ +1 in addiion o he reurn of her savings, Ω +1 s, wih Ω +1 he gross ineres rae. The old agen consumes d g +1 and d e +1 wih all her income. The second period budge consrain is hus, d g +1 + p e +1d e +1 = Ω +1 s + θ +1 (15) The represenaive household maximizes is uiliy (4) by choosing consumpions subjec o he budge consrains (14) and (15). Given prices and 9

10 polluion levels, P and P +1, he firs-order condiions of arbirage beween he wo goods are, p e U c g = U c e (16) p e +1U d g +1 = U d e +1 (17) and he ineremporal arbirage beween young and old age leads o, U c g = Ω +1U d g and U c +1 e = pe Ω p e +1 U d e +1 (18) +1 Relaions (16) and (17) give he rade-offs beween final good consumpion and energy. The relaion (18) gives he rade-off beween consumpions over he agen s life cycle. 4.3 Firms In each secor we consider a represenaive firm operaing under perfec compeiion. A ime he capial socks of he wo secors, K g and K e, are given (hey are given by 1 savings decision). The firms ake prices w, p e and q as given and maximize heir ne revenue. In he final good secor, he represenaive firm maximizes F g (K g, L g, Z ) w L g p e Z wih respec o L g and Z and he firs-order condiions are, F g L g (K g, L g, Z ) = w (19) F g Z (K g, L g, Z ) = p e (20) The capial reurn is given by Ω g = π g /K g. From he Euler equaion, i is equal o he marginal produciviy of capial i.e. Ω g = F g K (K g, L g, Z ). In he power secor, by aking K e and E e as given he represenaive firm maximizes p e F e (K e, L e, E ) w L e q (E E e ). The firs-order condiions are hus, FL e e(ke, L e, E ) = w (21) p e F e E (K e, L e, E ) = q p e (22) 10

11 Consequenly, he capial reurn in he power secor Ω e = π e /K e is equal o, Ω e = p e F e K e + q E e. (23) K e Profis per uni of capial represen he reurn on invesmen ha is given o he shareholder, i.e. he owner of he capial sock. In our model, he owner of he capial sock is he household when old. One can see from hese firs-order condiions ha he capial reurn in he power secor is deermined no only by he capial marginal produciviy, bu also by he marke value of he free endowmen of polluion permis given o he firm. The laer represens wha is called windfall profi in he lieraure. This also characerizes an equilibrium à la Hahn and Solow (1995) in erms of gross operaing surplus, as presened in he following secion. 4.4 Ineremporal general equilibrium The ineremporal equilibrium is defined for a given sequence of governmen decisions {τ, θ, X, E, E e } saisfying he governmen budge consrain, given by equaion (13). I is a sequence of prices {p e, w, q }, individual variables {c g, c e, s, d g +1, d e +1} and aggregae variables {K g, L g, Z, Y g }, {K e, L e, E, Y e }, P and K +1, saisfying all he equilibrium condiions. Households maximize heir uiliy and each firm maximizes is profi. A necessary condiion for equilibrium in he capial marke is he equaliy of capial reurns beween he wo secors, Ω g = Ω e = Ω. The oal capial sock is equal o savings i.e. K g + K e = K = N 1 s 1. All markes clear (labor, capial, polluion permis, energy and final good). The dynamical equaion for he environmen holds. The firs old agen, born a ime 1, saisfies her budge consrain and he opimal rade-off condiions, p e 0d e 0 + d g 0 = Ω 0 s 1 + θ 0 and U d g 0 = pe 0U d e 0 (24) and he iniial capial sock K 0 = Ns 1 is given. 11

12 We explicily define he equilibrium of he economy as follows. Definiion 1 Ineremporal general equilibrium For a given policy {E, E e, X, τ, θ } 0 an equilibrium is defined by a sequence of prices {q, p e, w } 0 and capial reurns {Ω } 0, a sequence of individuals variables {c g, c e, s, d g +1, d e +1} 0 saisfying relaions (14) o (18), and d g 0 and d e 0 saisfying (24), a sequence of aggregae variables {K g, L g, Z, Y g } 0, *{K e, L e, E, Y e } 0, {P } 0 and {K +1 } 0 saisfying (19) o (23), such ha, 0, he following equilibrium condiions hold: i/ he governmen budge (13) is balanced, ii/ he capial sock K = K g + K e and K e saisfying Ω g = Ω e, is equal o savings N 1 s 1, wih K g iii/ markes for labor, final good, power, and radable permis clear, i.e.: L g + L e = N, Y g = F g (K g, L g, Z ) = N c g + N 1 d g + K +1 + X, Y e = F e (K e, L e, E ) = N c e + N 1 d e + Z, E = E = E, iv/ he dynamics of polluion follow relaion (3). Now we are equipped o sae he firs resul of he paper. I shows ha giving emission permis for free o he polluing firms prevens he economy from following an opimal growh pah. Proposiion 1 For any policy {E, E e, X, τ, θ } 0 such ha E = E, E e > 0, and q > 0, 0, opimaliy condiion C.1 is no saisfied in equilibrium. 12

13 Proof. In equilibrium he condiion of equal capial reurn in boh secors is π g K g = πe K e F g K g This, along wih equaion (20), implies ha (K g, LK g, Z ) = p e F e K + q E e K e π g K g = πe K e F g K g (K g, LK g, Z ) = F g Z F e K + q E e K e which depars from he opimaliy condiion C.1. I clearly appears ha giving permis for free boils down o increase he capial reurn in he polluing secor. This secor hen becomes arificially more producive han he final good secor, hus aracing oo much capial han i should from a social opimum sandpoin. Le us noe ha, in his equilibrium, however, he polluion level coincides wih he opimal one, for he amoun of permis issued by he governmen is opimal. I is ineresing o noice ha in ha equilibrium, he wo oher opimaliy condiions are me. Firsly, for he rade-off beween consumpions over he life cycle (condiion C.2), i can be checked by combining relaion (18), firms opimizaion condiions and he equilibrium condiion on capial allocaion, i.e. he equaliy of capial reurns beween he wo secors. This yields, U c g = F g U K g d g and U c e = F g Z F g F g K g Z +1 +1U d e +1 which corresponds o he opimaliy condiion. Secondly, abou he rade-offs beween he consumpions of he wo goods (condiion C.3), i is sraighforward o see ha i is also saisfied. Naurally, relaion (12) canno be saisfied since, F e K e F g K g = F e L e F g L g Hence, proposiion 1 shows ha giving permis for free o he polluers does no allow o regulae polluion opimally. Even hough his idea is well-esablished in he lieraure (see inroducion), he heoreical raional q F g K g E e F g L g 13

14 for i is far from being commonly assessed. In our seing i clearly appears ha free permis endowmen generaes some windfall profis o polluers ha disor he capial marke, yielding o oo much capial accumulaion in he polluing secor. This resul generalizes Jouve e al. (2005) in wo ways. Firs, we do no make use of he Sokey (1998) specificaion o inroduce polluion in producion. Second, i is esablished for a wo-secor economy. The following proposiion is required before proceeding on how o resore opimaliy. I shows ha he opimal pah is an equilibrium, provided an adequae public policy. Proposiion 2 The opimal pah {c g, c e, d g, d e, K g, L g, Z, X, E, P, K +1 } 0 is an equilibrium wih public decisions X, E = E, τ = c g + p e c e + s w and θ = d g +p e d e Ω s, where p e = 1/F g Z, w = F g, Ω L g = F g, q K g = FE e F g Z and s = K +1 /N. Proving his proposiion is sraighforward. I is sufficien o verify ha all ineremporal equilibrium condiions are saisfied. Acually, any pah saisfying he resource consrains of he economy and he opimaliy condiions C.1, C.2 and C.3 is an equilibrium. 5 How o resore opimaliy condiions? The quesion raised in his secion is he following. Le us consider ha, for some reasons (ha will be quesioned below) he governmen decides o regulae polluing emissions wih radable polluion permis, and ha he permis mus be issued for free. Two soluions will be presened. 5.1 No free endowmen A firs soluion o resore opimaliy condiions C.1, C.2 and C.3 appears naurally from Proposiion 1. I simply consiss in giving no permis for free o he polluers. This is wha he following Proposiion saes. Proposiion 3 A policy (E, E e, X, τ, θ ) 0 such ha E = E and q > 0 replicaes he opimal soluion in ineremporal equilibrium if E e = 0, 0. 14

15 Proof. The equilibrium condiion π g K g = πe K e F K (K, L, Z ) = F Z F e K + q E e K e coincides wih he opimaliy condiion C.1 if E e = 0. Pu differenly, permis should be fully aucioned, and no given for free. As soon as some are given for free, even if i for a small fracion, he whole economy depars from he opimum. This resul confirms, in he more general seing of a wo-secor economy, he resul of Jouve e al. (2005). The fac ha he marke of permis have impacs in he whole economy hrough inermediae consumpion in he final good secor does no aler ha conclusion. 5.2 Polluion permis for all The secoral dimension of our model allows us o invesigae anoher and original soluion for resoring opimaliy condiion in capial allocaion. If one seeks a resoring equal capial reurn in boh producive secors, hen i immediaely follows ha giving permis o boh secors would solve he problem. Le us denoe by E g he amoun of permis ha is given for free o he firms belonging o he final good secor. We assume ha oal permis endowmen in he economy E fis he opimal one and ha a fracion is given for free, E g + E g E = E, 0. This second soluion flows direcly from he proof of Proposiion 1 and i is expressed in he following proposiion. Proposiion 4 Under a policy (E, E e, E g, X, τ, θ ) 0 such ha E = E, E e > 0, E g > 0, and q > 0, 0, he opimaliy condiion C.1 is saisfied if E e K e = Eg K g 15

16 Proof. The general equilibrium wih free permis endowmens E g > 0 and E e > 0 allocaed o boh secor resuls in he following propery F g K g + q E g K g = FK e + q E e e K e F g K g = F e K e + q ( Ee K e Eg K g ) Thus, he opimaliy condiion C.1 is fulfilled if Ee K e = Eg, q K g. This resul shows ha, by giving adequaely permis for free o all firms, dynamics condiions on capial allocaion among secors can be resored. Because he final good secor does no pollue, giving i some polluion permis is equivalen o give i some lump sum ransfer. Imporanly, his ransfer is valued a he marke price of radable permis in equilibrium, which coincides wih he opimal price since he emission cap is equal o he socially opimal emission level. I can be noed ha equilibrium does no depend on he proporion of permis ha are given for free. This sharing rule is a dynamic one. Each ime period he balance mus be me beween he wo secors, such ha he lump sum ransfer is similar among he secors in erms of capial unis. Proposiion 3 can hus be seen as a special case of proposiion 4. One may be puzzled by he fac ha emission permis are given o firms which do no pollue. Two argumens can be provided as a jusificaion: 1. cos passhrough: he final good secor bears a cos because he power secor increases is oupu price when he price of carbon increases in he marke for radable permis; so some compensaion should be given o hese firms; 2. fairness: if a lump sum is o be given o some firms which increases heir marke value (he power secor), hen i should also be given o all oher firms in he economy. A sriking poin in Proposiion 4 is ha opimal growh wih wo secors can be resored whaever he share of emissions permis ha are given for free, as long as he regulaor applies he sharing rule given in he proposiion. This has o do wih a key issue in he poliical implemenaion of markes 16

17 for emission permis. I is well-esablished ha an emission fee is far more expensive for firms han a marke for radable emission permis wih free endowmen. In he former case, firms have o pay for every uni of polluion while, in he laer case, hey only bear he opporuniy cos of polluion, which is valued a he marke price of emission permis. On he ground of his argumen (see Savins, 1998), radable emission permis are considered o have a higher poliical accepabiliy han emission axes. Proposiion 3 clearly jusifies such an argumen: giving emission permis for free o he polluers is equivalen o give hem some lump sum ransfers. This ransfer corresponds o he righ o pollue valued a he marke price. I is equivalen o he ax amoun ha would have been paid by hem under a pigouvian ax. I is obvious ha polluers will favor joining a marke for radable permis wih free endowmen, raher han a pigouvian ax, and i is possible o ensure ha firms are no worse-off by his means. The windfall profi can be designed (hrough he free endowmen rae) such ha i exacly offses he abaemen cos borne by he firm. 5.3 A closer look o accepabiliy Proposiion 4 saes ha opimaliy condiion C1 can be resored, which was no he case when permis were given only o polluing firms. I also shows ha accepabiliy can be fulfilled. Does i means ha opimaliy and accepabiliy could be reconciled? The following Corollary answers ha quesion. Corollary Under Proposiion 4, opimal growh can be replicaed in equilibrium, provided adequae ransfers τ and θ. Proof. Under he allocaion rule given in Proposiion 4, considering he equaliy of capial reurns, relaion (18) corresponds now o, U c g = (F g K g +1 E g +1 + q +1 K g )U d g and U c +1 e = pe (F g E g +1 + q +1 p e K g K g )U d e wih he households rade-off beween he wo goods (16) and (17) and firms opimizaion condiions (19), (21) and (20), condiion C.3 is also verified. 17

18 This allows ha he relaion (12) is also verified. Then, we obain opimal proporion of consumpions and we only have o resor he opimal level of consumpions wih can be done wih adequae ransfers beween young and old a each ime. Because Proposiion 4 holds for any share of he emission o be given for free, i may be possible o combine poliical accepabiliy (defined as a non negaive impac of profi level for he firms considered) and opimaliy (defined following Proposiion 2). All firms belonging o he final good secor will be willing o join he sysem, since hey receive a lump sum ransfer (hey jus have o sell heir endowmen o he polluing firms, valued a he marke price). Firms belonging o he polluing secor can receive an amoun of permis such ha heir willingness is non negaive, hus ensuring poliical accepabiliy. Sill, behind his resul is hidden an opimal fiscal policy which chooses inergeneraional ransfers such ha opimal growh can be resored. Giving some permis for free such ha no firm is worse-off increases capial reurn. In urn, i increases he revenue of capial owners. In our seing, capial owners are he old, and hen free endowmen increases consumpion in he old age beyond wha is socially opimal. To resore he opimal life-cycle arbirage condiion he governmen mus levy a ax on savings and redisribue ha receip o he young. In a more realisic poin of view, i means ha he capial reurn associaed o he windfall profis are redisribued opimally among he households. This also means ha, depending on he opimaliy crieria considered, he redisribuion rule, leading o opimal value for τ and θ, may be differen. A direc and imporan policy implicaion of his resul is ha radable permis issued for free should no be considered as subsiues o fiscal policies anymore, as i is he case in he lieraure oday. 1 Permis migh be given for free on he ground of he accepabiliy argumen ha firms should no be worse-off, bu permis should also be accompanied wih an adequae fiscal policy on facor income. In oher words, quaniy-based regulaion and 1 We refer o he plehoric debae in environmenal economics on quaniy vs. price regulaion iniiaed by Weizman (1974). 18

19 price-base should be combined in order o reach opimal growh and poliical accepabiliy. They are complemenary, no subsiues. Finally, our resul quesions he very concep of accepabiliy as inroduced in he beginning of he aricle in accordance wih Savins (1998) and Goulder (2002). Is no-profi loss he adequae rule for accepabiliy? No necessarily, because his does necessarily imply ha he capial owners are beer-off, especially if he fiscal policy is such ha capial reurn is axed such ha he windfall profis associaed o he free endowmen of permis is capured and redisribued. Imporanly, i is no he windfall profi iself ha is axed, bu he excess in capial reurn, wo hings ha may be quie differen in general equilibrium. As a consequence, accepabiliy should be judged on he ground of capial owners welfare, no firm s profi. And his is all he more rue as capial owners, like any people, may suffer from polluion. This means ha in some sense, hey are also eager o improve he environmenal qualiy. In a general equilibrium seing, he usual conflic beween polluers and polluees is no more ha clear. References [1] Allais M., 1947, Economie e Inérê, Imprimerie Naionale. [2] Bovenberg A.L. and R.A. de Mooij, 1994, Environmenal levies and disorionary axaion, American Economic Review 84(4), [3] Coase M.A. 1960, The Problem of Social Cos, Journal of Law and Economics, 3, [4] de la Croix, D. and Ph. Michel, 2002, A Theory of Economic Growh: Dynamics and Policy in Overlapping Generaions, Cambridge Universiy Press. [5] Diamond P.A. 1965, Naional Deb in a Neoclassical Growh Model, American Economic Review, 30, [6] Goulder L.H Miigaing he Adverse Impacs of CO 2 Abaemen Policies on Energy-Inensive Indusries, RFF Discussion Paper

20 [7] Jouve P.A., Ph. Michel and G. Roillon, 2005, Opimal Growh wih Polluion : How o Use Polluion Permis, Journal of Economic Dynimics and Conrol, 29, [8] Kousaal P., 1997, Economic Policy and Climae Change: Tradeable Permis for Reducing Carbon Emissions, Edward Elgar Publishing Limied, UK. [9] Michel Ph., 1990, Some Clarificaions on Traversaliy Condiions, Economerica, 58, [10] Mongomery D.W., 1972, Markes in Licenses and Efficien Polluion Conrol Programs, Journal of Economic Theory, 5, [11] Parry I.W.H., R.C. Williams, and L.H. Goulder, 1999, When Can Carbon Abaemen Policies Increase Welfare? The Fundamenal Role of Disored Facor Markes Journal of Environmenal Economics and Managemen, 37, [12] Savins R.N., 1998, Wha Can We Learn from he Grand Policy Experimen? Lessons from SO 2 Allowance Trading, Journal of Economic Perspecives, 12(3), [13] Weizman R., Prices vs. quaniies, Review of Economic Sudies, 41,