Tradeable Emission Permits Regulations in the Presence of Imperfectly Competitive Product Markets: Welfare Implications

Transcription

1 Environmental and Resource Economics 9: 65 81, c 1997 Kluwer Academic Publishers. Printed in the Netherlands. Tradeable Emission Permits Regulations in the Presence of Imperfectly Competitive Product Markets: Welfare Implications EFTICHIOS SOPHOCLES SARTZETAKIS University College of the Cariboo, Department of Economics, P.O. Box 3010, Kamloops, B.C. Canada V2C 5N3 Accepted 24 April 1996 Abstract. In the present paper, we analyse the interaction of a competitive market for emission permits with an oligopolistic product market. It is well known that a competitive permits market achieves the cost minimizing distribution of abatement effort among the polluting firms for a given reduction in emissions. However, when the product market is oligopolistic, it may redistribute production inefficiently among firms. It has been suggested that this inefficiency can outweigh the gains obtained from using emission permits instead of command and control. Although this argument is clearly correct under full information, it is shown in the present paper that it reverses under incomplete information. In particular, it is shown that when tradeable emission permits are specified according to the standard textbook example, they yield higher social welfare than the command and control regulation. Key words: emission permits, oligopoly, welfare 1. Introduction The efficiency properties of systems of economic incentives have been contrasted to inferior outcomes of bureaucratic mechanisms by economists in various fields. The support for systems of tradeable emission permits and environmental taxes over systems of command and control is particularly strong in the literature of environmental economics. However, while the cost-efficiency 1 of taxes and competitive emission permit markets is independent of the product market structure, the overall efficiency of these systems depends on the assumption of perfectly competitive markets. In the case of imperfectly competitive markets, both tax and permits systems might not lead to the optimization of the resource allocation problem. 2 Thus, systems of economic incentives are not necessarily superior to command and control systems. Assuming policy makers have a genuine interest in promoting economic welfare, under what conditions will systems of economic incentives outperform command and control regulations? The present paper examines the welfare implications of tradeable emission permits regulations 3 in the presence of imperfectly competitive product markets and compares these systems to command and control systems in terms of their

2 66 EFTICHIOS SOPHOCLES SARTZETAKIS welfare performance. We focus on four main features of the two regulatory systems designed to simplify the exposition of our results and isolate the effects of permits trading that we feel are important. First, the command and control regulation takes the form of assigning emission quotas 4 for each firm. In this form, command and control regulation differs from tradeable emission permits regulation in only that, under the latter, emission quotas (permits) are tradeable among firms. Secondly, we assume that policy makers have incomplete information both about the damage cost of emissions and the demand and cost structures. Thus, pollution levels are not optimally chosen; policy makers try to achieve the highest level of social welfare given an emission ceiling. 5 More important, policy makers cannot derive the welfare maximizing allocation of emission quotas among firms. 6 Thirdly, we assume that the pollutant in question is emitted by many industries producing goods with zero cross-price elasticity of demand and that the distribution of abatement costs among firms is similar across industries. Thus, while the industry in question is imperfectly competitive, the permits market is competitive. Finally, we assume that emission quotas are allocated to firms according to their emissions at some historic period; the allocation scheme is the same under both systems. 7 Our results indicate that trading of emission permits has two effects. First, it achieves cost-minimization of emissions control effort by equalizing marginal cost of abatement among firms; a direct consequence of competitive permits market. Second, it redistributes production among firms due to imperfections in product markets and firm-specific differences in emissions control technologies. The first is clearly a welfare increasing effect, while the second might be welfare decreasing if the inefficient firms are the ones that gain market share. As the paper shows, the redistribution of market shares among firms is controlled by the permits market mechanism and the welfare-increasing effect dominates. To show this, we develop a model that has two key features that allow us to focus attention on the two welfare effects of permits trading. First, since our concern is over the output redistribution effect, we adopt a Cournot Nash duopolistic framework with linear demand. This framework of strategic substitutability of firms actions generates large output redistribution effects. Secondly, we assume that emission reduction technologies differ among firms while production technologies are similar. As a result, differences in emission reduction technologies are the sole determinant of both the cost-minimization and the output-redistribution effects. In reality, of course, differences in production technologies influence the magnitude of the output redistribution and its effect on welfare. However, as a first step in understanding the welfare effects of permits trading it is useful to isolate the impact through differences in emissions reduction cost. We briefly discuss in the conclusions the case that production technologies differ between firms. Within this framework, consider the case that emission quotas are tradeable. Trade of emission permits implies that their value is not anymore limited to the value for own use; the link between firms implicit price for own use is established. Since there are many firms participating in the permit market, and the

3 TRADEABLE EMISSION PERMITS REGULATIONS 67 distribution of technologies is similar to that in the duopolistic sector, the permit price will be between the marginal abatement costs of the two Cournot players. At the equilibrium, the implicit prices of emission quotas, i.e. the marginal cost of emissions reduction, are equalized among firms and minimization of aggregate cost of emissions reduction is achieved. As a result, output at the oligopolistic sector increases. This beneficial increase in output is achieved through redistribution of market shares relative to when emission quota are not tradeable. The less efficient in reducing emissions firm becomes more aggressive in the output market as acquisition of permits reduces its marginal cost of emissions control. This redistribution of market shares from the more to the less efficient firm is augmented due to the nature of the Cournot game. However, the excess redistribution of market shares is only a second order effect to the aggregate output increase. Further, the competitive process in the market for emission quota limits the redistribution of market shares. As the less efficient firm increases output, its marginal cost of emissions control increases; the process stops when the two firms marginal costs are equal. At the equilibrium, market shares are determined by the marginal cost of production alone. Overall, we show that the cost-minimization effect dominates the output redistribution effect. Despite the great attention that tradeable emission permits regulations have received recently, the evaluation of their performance in the presence of imperfectly competitive markets has received little attention in the literature. This is despite the fact that most of the regulated industries are imperfectly competitive. Borenstein (1988) has shown that competitive markets for operating licenses do not, in general, lead to social welfare maximization. The reasons for the failure of the competitive process is due to either lumpiness of the licenses, or to imperfections in the product markets. In both cases, trade of licenses leads to redistribution of market share. Malueg (1990) considers the welfare effects of emission permits trading in the case of oligopolistic product markets. He points out the ambiguity of the overall welfare effect of trading due to redistribution of market shares. Malueg (1990) also offers an example in which trading of emission permits is welfare inferior to non-trading. Although, with respect to question and approach there is a lot of similarity to Malueg (1990), our results differ. This is mainly due to differences in the specification of the tradeable emission permits regulation. Malueg (1990) assumes that the policy maker does not assign the emissions ceiling ex-ante and thus, it has no control over the ex-post volume of emissions. Consequently, if the regulation targets a specific reduction of emissions, the policy maker has to impose an additional constraint on permits trading. The imposition of this additional constraint distorts the equilibrium. 8 Therefore, even when the regulated firms are price takers in the permit market, equalization of the marginal cost of emissions reduction is not attained. The results obtained in this paper should not be interpreted as excluding the possibility that social welfare might be lower after the introduction of permits trading. As mentioned above, under complete information a non-trading system

4 68 EFTICHIOS SOPHOCLES SARTZETAKIS dominates a trading system. Even under incomplete information, Malueg (1990) shows that this possibility does exist under certain specifications. In the present paper we emphasize, instead, the importance of designing correctly the tradeable emission permits regulation in the presence of an oligopolistic product market. 9 Further, clarification of the source of the output redistribution effect allow us to suggest some simple modifications of emission permits regulations that can further increase social welfare. In particular, there are ways in which tradeable emission permits regulations can be modified so as to minimize the importance of the output redistribution effect. One such modification would be the allocation of a number of non-tradeable permits to more efficient firms. Such an allocation of permits, when unanticipated, 10 decreases the abatement requirements of the more efficient firms and induces an increase in their outputs, which compresses the output redistribution effect. The fact that under the provisions of the 1990 Clean Air Act Amendments the allocation of a number of additional permits to the low emitting firms is planned for Phase II of the program is consistent with the results of our work. 11 This provision of the Clean Air Act Amendments gives a margin for growth to the low emitters and thus reduces the excess output reshuffling effect. To the extent that low emitting firms are also more efficient in reducing emissions, the present paper provides a rationale for the free distribution of additional permits to these firms. The paper is organized as follows: Section 2 describes the model in the absence of regulation. Sections 3 and 4 characterize the equilibrium under the two regulatory systems, while Section 5 compares the level of social welfare achieved under each system. Section 6 contains the concluding remarks. Most proofs have been relegated to an appendix. 2. The Model Assume a two-sector economy; the first is a numeraire sector; the second is a homogeneous Cournot duopoly. the production process in both sectors generates a negative externality, emissions e of a common pollutant. Assume that consumers preferences are given by a utility function which is separable in the numeraire good and emissions, U = u(q) v(e) +m; (1) where Q is the aggregate output of the duopolistic sector, E is the aggregate level of emissions, and m is expenditure on the competitively supplied numeraire sector. The utility derived from the consumption of Q is assumed strictly concave and quadratic, such that the derived inverse demand is linear, p=a bq. On the production side, we assume that firms face constant, and equal among them, marginal cost of production c. Emissions are assumed to be proportional to the firms output, e i = q i,where istherateofemission,andisassumedto be the same for both firms. The firms can reduce emissions by either reducing

5 TRADEABLE EMISSION PERMITS REGULATIONS 69 output or controlling emissions. Firm i s total cost of controlling emissions is K i = k i (z i,q i )z i q i,whereq i,isfirmi s output, z i is firm i s abatement per unit of output and k i is the average cost of controlling emissions. k i is assumed to be a non-decreasing function of both the output and the abatement per unit of output: k i = k i (q i,z i ), with k q 0, k z 0, and k qz 0. Cost of controlling emissions differs between the two firms. Without any loss of generality assume that firm 1 is more efficient in abatement. Consider now the problem of regulatory intervention for reducing emissions. We assume that the emissions ceiling Ē, is decided through a political process involving consultation with various interest groups and is bound by international agreements. The policy maker chooses the regulatory instrument that implements the given emissions aggregate and yields the highest level of social welfare. Two forms of regulatory intervention are considered; a bureaucratic mechanism, namely a command and control (CC) regulation in the form of non-tradeable emission quotas, and an economic incentives mechanism, namely a tradeable emission permits (TEP) regulation. 3. Command and Control Regulation Under a CC regulation the policy maker specifies an emissions quota for each firm and allows them to choose the means of compliance. Let Ē be the aggregate emissions ceiling, and Ē i, i =1,2,befirmi s emission quota, with 2 i=1ēi = Ē. Note that, q i z i q i = Ē i. Given firm i s emissions ceiling Ē i, its constrained profit maximization problem is, max qi ;z i L i =(a bq)q i cq i k i (q i ;z i )z i q i + i [ E i ( z i )q i ]: (2) Assuming that the regulatory constraint is effective and excluding corner solutions, the first order conditions are a 2bq i bq j c k i (z i ;q i )z i z i q i i ( z i )=0; (3) k i q i z i q i + i q i = 0; (4) and E i ( z i )q i = 0: (5) Optimization implies that firm i reduces its output to the point where the marginal loss in profit from forgone output the implicit price of emissions quota is equal to its marginal cost of abatement, i = k i +[@k i /@z i ]z i. Under a CC regulation that prohibits resale of emission quota, the value of an emission quota is limited to the

6 70 EFTICHIOS SOPHOCLES SARTZETAKIS productive value in own use, not allowing the establishment of links between the marginal opportunity cost, or implicit price, of the two firms. Denote by q =(q/k)(@k/@q) and z =(z/k)(@k/@z) the elasticity of the average abatement cost with respect to output and with respect to abatement per unit of output respectively. With this notation in mind, the above first order conditions yield firm 1 s output reaction function, q 1 ic = 2b [a c 1 ic z ic k ic ( q z ic ic )] 2 q jc; (6) where the subscript C denotes the variables values at the CC equilibrium. Under a CC regulation, given that firm 1 is assumed to be more efficient in abatement, it values emissions quota less relative to firm 2, i.e. 1 < 2, it engages in higher level of abatement which allows it to retain higher level of output relative to firm 2, and, as a result, increases its product market share relative to the preregulation equilibrium. 4. Tradeable Emission Permits Regulation Under the TEP regulation, each permit allows the emission of one unit of pollutant, and is freely transferable. A total of Ē units of emissions are allowed, the same as under the CC regulation, and an equal number of permits are distributed free of charge to each firm. 12 In order to isolate the effect of trading, we assume that the allocation of permits corresponds to the firms emissions quota under the CC regulation. With the introduction of tradeable permits, another market is added to the model. This market can either be perfectly or imperfectly competitive. Since we assume that the pollutant in question is emitted by firms in both sectors of the economy, the two Cournot players are price takers in the permits market. We also assume that the distribution of abatement technologies is similar across industries and the demand parameters are such that the total number of permits in each industry does not change after trading, and thus, equilibrium permit price can be derived by examining the oligopolistic sector alone. Firm i s net demand for permits is ND i = ( z i )q i Ē i. In equilibrium, 2 i=1 ND i =0. Firm i s profit maximization problem is max qi ;z i i =(a bq)q i cq i k i (z i ;q i )z i q i P " [( z i )q i E i ]; (7) where, P " is the equilibrium permit price. The first order conditions are and a 2bq i bq j c k i z i z i q i P " ( z i )=0; (8) k i q i z i q i + P " q i = 0: (9)

7 TRADEABLE EMISSION PERMITS REGULATIONS 71 Firm i sells or buys permits until the opportunity cost of holding an extra permit, P ", is equal to its marginal cost of abatement. Trade of emission permits implies that their value is not anymore limited to the value for own use; the link between the two firms implicit price of emission permits is established. At the equilibrium the two firms marginal cost of abatement is equal to the permits price. Aggregate cost of emission reduction is minimized. Using the definition of the output and abatement per unit of output elasticities of the average abatement cost, the above first order conditions yield firm i s reaction function: q 1 it = 2b [a c P 1 " z it k it ( q z it it )] 2 q jt; (10) where the subscript T denotes the variables values at the TEP equilibrium. Notice first that as long as both firms are price takers in the permits market, the initial endowment of permits does not affect their optimal decisions. The competitive price of permits depends on the aggregate emissions ceiling but not on the allocation of permits among firms. Under the TEP regulation, all uncontrolled emissions are assigned property rights and since they are tradeable, they have an opportunity cost which, at the equilibrium, is equal to the competitive price. Thus, since firm 1 is more efficient in controlling emissions, which yields a lower implicit price in the case that quotas are non-tradeable, 2C > 1C, both firms have an incentive to trade permits at a price P ", such that 2C > P " > 1C. Trading of emission permits induces redistribution of emissions control effort from the less to the more efficient firm. Firm 1 increases its abatement per unit of output, and thus its marginal cost of abatement, in order to free some of its permits and sell them to firm 2. Firm 2 buys permits and reduces its abatement per unit of output, and thus its marginal cost of abatement. The two firms trade permits to the point that marginal costs are equalized. The redistribution of emissions control effort has two effects. First, aggregate cost of abatement for a given level of output decreases. If, however, aggregate output increases as a result of trading, aggregate cost of abatement might also increase. Second, market share is redistributed between firms. Comparison of equations (6) and (10) reveals how trading of emission permits affect firm i s marginal cost and thus its level of output. Since the two firms are Cournot players in the product market, the initial redistribution of output from the more to the less efficient firm induces a second order effect of output redistribution. The effect of permits trading on the Cournot output equilibrium is illustrated in Figure 1 for the case of linear demand. Firm s reaction functions have negative slopes so the outputs are strategic substitutes. The equilibrium under the command and control regulation is depicted by point A. As a result of permits trading, marginal cost of firm 1 increases while for firm 2 it decreases. Firm 1 s reaction function shifts inwards while firm 2 s reaction function shifts outwards. The new equilibrium is at point B. Firm 1 s output decreases while firm 2 s increases.

8 72 EFTICHIOS SOPHOCLES SARTZETAKIS Figure 1. Market share effects of emission permits trading. Redistribution of output from the more to the less efficient firm implies redistribution of profits in the same direction and thus a decrease in aggregate profits for a given level of output. Only when there is no redistribution of profits, permits trading achieves maximization of social welfare. Thus, the cost-minimization property of competitive permits markets does not necessarily imply that these systems are welfare superior to command and control systems. The extend of profits redistribution determines which of the two systems achieves higher welfare. To make inferences about the size of profit redistribution the reader should notice that the process of output redistribution is controlled by the competitive trading process. Trade of permits stops when firms marginal cost of abatement are equalized, putting effectively a limit on output and profits redistribution. In what follows, we show that the redistribution of emissions control effort has an overall positive effect on social welfare. 5. Welfare Comparison of the CC and TEP Regulations In order to facilitate derivation of analytical solutions we assume that abatement cost is quadratic, K i =[d+e i z i q i ]z i q i,whered,e i > 0 represent technological parameters. 13 Abatement technologies differ between firms, with e 2 > e 1 so that firm 1 has a more efficient abatement technology. Using this specification, the

9 TRADEABLE EMISSION PERMITS REGULATIONS 73 two firms reaction functions from equation (6) are solved for firm i s output as a function of the two firm s Lagrange multipliers; industry s output is also derived, q ic = a c (2 ic jc ) 3b ; Q C = 2(a c) ( ic + jc ) : (11) 3b The equilibrium level of firm i s Lagrange multiplier is also derived, ic = 2e i(b + 2e j 2 )[(a c) 3b E i ]+b[3b+2(2e j +e i )r 2 ]d 3b 2 +4b(e i +e j ) 2 +4e i e j 4 (12) The difference between the two firms Lagrange multipliers is ic jc = b(e i e j )[2(a c) 3b E] 2b 2 (e i e j )d 3b 2 + 4b(e i + e j ) 2 + 4e i e j 4 : (13) Rearranging terms, equation (13) can be written as follows, ic jc = 3b2 (e i e j )[2(a c d)=3b E] 3b 2 + 4b(e i + e i ) 2 + 4e i e j 4 : (14) Under the above specification of abatement cost, equation (4) yields, z ic q ic = ( ic d)/2e i. Excluding corner solutions, z ic >0,q ic >0,thisimpliesthat ic > d, i = 1, 2. This inequality along with aggregate output Q C =[2(a c) ( ic + jc )]/3b, implies that ic jc > 3b 2 (e i e j )(Q C E) 3b 2 + 4b(e i + e j ) 2 + 4e i e j 4 : (15) Inspection of equation (15) reveals that e 2 > e 1 implies 2C > 1C,sinceQ C Ē =A ic + A jc >0. In the case of a TEP regulation, firm i s reaction function is given by equation (10). Under the abatement cost s specification made in this section, we solve the two firms reaction functions to obtain firm i s output as function of the permit price; industry s output is also derived, q it = a c P " ; Q T = 3b " 2(a c) 2P : (16) 3b Substituting the two firms output and abatement into the permits market clearing condition, 2 i=1 ND i = 0, the equilibrium permits price is also obtained, P " = 2e ie j [2(a c) 3b E]+3b(e j +e i )d 3b(e i +e j )+4e i e j 2 : (17)

10 74 EFTICHIOS SOPHOCLES SARTZETAKIS By comparison of the values of the competitive permit price, equation (17), and the Lagrange multipliers at the CC equilibrium, equation (12), the following relationship is obtained, P e i(3b " + 2e j 2 ) jc + e j (3b + 2e i 2 ) ic = 3b(e i + e j )+4e i e j 2 : (18) Equation (18) shows that when the TEP market is well specified, the permits price, P ", is a weighted sum of the firms marginal abatement costs under the CC regulation, 1C,and 2C. Setting the right-hand side of equation (18) smaller than the average of s and cross-multiplying, we obtain 3b(e i e j )( j i )<0.We have shown above that e i > e j implies jc > ic. Therefore, the competitive permit price is no greater than the average of the Lagrange multipliers, i.e. e i 6= e j ) P " <( i + j )/2, while e i = e j ) P " =( i + j )/2. Inspection of equations (11) and (16) reveals that permits trading does not increase the industry s marginal cost of abatement. Industry s output increases as a result of permits trading when e i 6= e j, while it remains the same when e i = e j. The latter case, although model-specific, adds to the understanding of the welfare effects of permits trading. If the only difference between the two firms abatement cost is in the intercept of the marginal abatement cost, i.e. d 2 > d 1 and e 1 = e 2, then emission permits are traded and aggregate abatement cost decreases, while marginal abatement cost does not change relative to the non-trade situation, P " = ( i + j )/2, leaving aggregate output unchanged. From equation (21) in Appendix B, the following remark is immediate. REMARK. When firms abatement technologies differ in such a way that emission permits trading yields changes in firms marginal cost of abatement but does not affect the industry s marginal cost of abatement, aggregate abatement cost decreases and social welfare increases relative to the case that emission quotas are non tradeable. The above remark extends the aggregate compliance cost minimization property of competitive permits markets, form the case of a fixed vector of outputs, to the case of a variable vector of outputs as long as aggregate output does not change. Return now to the case that aggregate output increases as a result of permits trading, e i 6= e j. Equation (18) determines the magnitude of the aggregate output increase resulting from trading as well as the extend of the market shares redistribution. Firms trade emission permits to the point that their marginal cost of abatement equals the permits price. The price of permits is a function of the firms marginal abatement cost when emission quota are non-tradeable. Thus, competition in the permits market puts a limit on the amount of permits traded and effectively on output redistribution. This limit to output redistribution relative to the CC regulation ensures that social welfare is higher under a competitive TEP market than under CC. We may then state the following result:

11 TRADEABLE EMISSION PERMITS REGULATIONS 75 PROPOSITION. Social welfare is higher under a tradeable emission permits regulation that allows emissions quota to be traded in a competitive market rather than under a command and control regulation that restricts trade, even when the polluting firms are Cournot players in the product market. The proof of the proposition is relegated to Appendix B. The intuition underlying this result was discussed above. In brief, trading of permits reduces the industry s marginal abatement cost leading to higher aggregate output and thus higher consumer surplus. On the other hand, trading of permits reduces the marginal abatement cost of the high-abatement-cost firm which becomes more aggressive in the product market. The redistribution of market share from the more to the less efficient firm in controlling emissions leads to lower aggregate profits. When the permit market is competitive the positive effect on social welfare dominates. 6. Conclusions It is established in the literature that competitive markets for operating licenses do not necessarily achieve social welfare maximization when the product market is oligopolistic. In the presence of market imperfections, trading of emission permits induces excessive output redistribution from the more to the less efficient firm in controlling emissions. Output redistribution adversely affects industry s profits. Trading of emission permits is optimal only when there is no redistribution of profits among firms in the industry. The extend of profits redistribution determines whether trading of emission permits yields higher social welfare relative to a command and control system that prohibits trading of permits. This paper has presented a simple model to examine the effects of emission permits trading on welfare. We specified the model in such a way as to facilitate, first, the examination of the two conflicting effects of permits trading on social welfare and, second, the derivation of analytical solutions. Our most important results are that redistribution of output is initiated but also controlled by the trading process of emission permits and, moreover, that, in the case of competitive permit markets, trading of emission permits is welfare superior to a non-trading situation. It is important, however, to recognize the limitations of our analysis. The model employed in this paper deals only with interior solutions. Thus, cases of extreme differences between firms abatement technologies are not discussed. It is clear, though, that in the case of extreme differences between firms abatement technologies output redistribution can be more important. Such a case is presented in Malueg (1990) where one of the firms is assumed to have zero cost of abatement in the relevant range. In this example, output redistribution is enhanced and trading of emission permits is inferior. However, in the presence of such differences another policy concern arises. Indeed, the more efficient firm might have a large net supply of emission permits and might exercise price setting power in the permits market, especially when the number of firms participating in the market is small.

12 76 EFTICHIOS SOPHOCLES SARTZETAKIS The existence of market power in the permits market will have a much bigger adverse effect on social welfare than the output redistribution effect. In the case of dominated permits markets, social welfare decreases as a result of emission permits trading in most cases (see Misiolek and Elder 1987; von der Fehr 1993; Sartzetakis 1993). The extent to which market power affects social welfare depends on the initial allocation of emission permits. Thus, when the abatement cost differs substantially among the regulated firms, the allocation of emission permits should be such as to prevent strategic behaviour in the permits market. The result that social welfare is higher when permits trading is allowed is sensitive only to the assumption of constant and equal between firms cost of production. If we assume that marginal costs of production are increasing and different between firms, then even the effect of permits trading on the industry s output is uncertain. Consider for example the case that the more efficient in abatement firm is also more efficient in production. Under the assumption that the firm s technological advantage is stronger in production than in abatement, trading of emission permits leads to a decrease in the industry s output. Although trading of permits leads to minimization of aggregate abatement costs, output redistribution leads to an increase in aggregate production costs. The welfare effect of permits trading is negative, since both consumer surplus and industry s profits decrease. 14 In the present paper we assume, following the literature, that the only technological difference between firms is in abatement and we examine the case that trading of permits leads to an increase in the industry s output. While our model is stylized and some of the results model-specific, the main results spring from the general assumptions about the structure of the product and permits markets: strategic complementarity of firms actions in the product market yields the higher output redistribution effect; competition in the permits market ensures efficiency in the allocation of emissions control effort among firms. The simple structure of our model allows us to derive analytical solutions for the effect of permits trading on welfare and examine the basic relationships driving our results. Acknowledgement I would like to thank Donald McFetridge, Thomas Ross, Keith Acheson and Steven Ferris for their helpful comments and suggestions on earlier versions of this paper. I am also indebted to Christos Constantatos, Benoît Laplante and Mahn Nguyen Hung for many comments and suggestions. I gratefully acknowledge financial support form the Groupe de recherche en économie de l énergie et des ressources naturelles (GREEN), Départementd économique,université Lavalandthe Centre for International Business Studies (CIBS), University of British Columbia.

13 TRADEABLE EMISSION PERMITS REGULATIONS 77 Appendix A (A note on the abatement cost function) In the present paper we assume that firm s emissions are proportional to its output with the factor of proportionality depending on its abatement activities. A firm that emits units of a pollutant per unit of output and engages in z units of abatement per unit of output emits a total of ( z)q units of the pollutant. 15 The firm s abatement is then zq. We further assume that the cost of abatement is quadratic on abatement, i.e. quadratic on both output and abatement per unit of output. This implies that the average abatement cost is a function of both output and abatement per unit of output and its elasticities of output and abatement per unit of output are equal, q = z >0. It is reasonable to restrict our attention to abatement cost specifications for which the firms average abatement cost is at least as sensitive to changes in abatement per unit of output as to changes in output, z <0, q 0and z q. thus, the average abatement cost employed in the above example presents one of the extremes in the reasonable range. At this extreme, firms respond to the required reduction in emission by a higher reduction in output and lower abatement per unit of output relative to when z > q. 16 This implies that when q = z the output reshuffling effect due to permits trading is bigger relative to the case when z > q. Recall that the reason why the TEP regulation does not achieve welfare maximization is the excessive output reshuffling due to oligopolistic output market. Thus, the chosen abatement cost function does not restrict the generality of the welfare results derived. Appendix B In order to compare the two regulatory systems, we examine the effect of permits trading on social welfare, defined as the sum of consumer and producer surplus. Since we assume that m is the expenditure in the competitive numeraire sector, the marginal utility of income is one. We also assume that the aggregate emissions ceiling is the same under both systems of regulation and thus the effect of pollution on utility is exactly the same under both systems. Therefore, social welfare reduces to, W v = u(q v) cq v 2X i=1 K iv; v = C; T: (19) Since we have assumed a specific form for the utility derived from the consumption of Q, namely, u(q) = aq 1 = 2bQ 2, social welfare under each form of regulation, W v is W v =[ 1 = 2(p v +a) c]q v 2 i=1k iv. The difference of social welfare between TEP and CC regulation is: W T W C = h 1 (pt + pc) 2 c i (Q T Q C) 2X i=1 (K it K ic ): (20) The term in brackets in the right-hand side of equation (20) is positive. Furthermore, the industry s output under the TEP regulation, Q T, is at least not smaller than the output under the CC regulation, Q C. Thus, if aggregate abatement costs decrease as a result of permits trading, welfare is unambiguously higher under the TEP than under the CC regulation. Proof of Remark When d 2 > d 1 and e 1 = e 2, equation (18) yields, 2P " = 1C + 2C. Thus, when the only difference in the firms average abatement cost is in their intercept, industry s output is the same under the CC

14 78 EFTICHIOS SOPHOCLES SARTZETAKIS and TEP regulations. Simple inspection of equation (20) implies that the social welfare difference is equal to the difference of aggregate abatement costs between the CC and the TEP regulation. The difference in the aggregate cost of abatement under CC and a competitive TEP market is obtained by substituting the equilibrium values of the choice variables into both firms cost of abatement. 2X (K it K ic ) = i=1 = 2X 2X i=1 i=1 (z it q it z icq ic )[d i + e(z it q it + z icq ic )] (P " ) 2 2 ic 4e = icjc (P " ) 2 2e 0: (21) The aggregate cost of controlling emissions by a given amount is lower under a competitive TEP market than under the CC regulation. 17 The aggregate cost minimization property of the TEP regulation holds when aggregate output does not increase after permits trading is allowed. Clearly, when d 1 = d 2, which implies 1C = 2C, the difference in the aggregate cost of abatement is zero. The CC regulation yields the same welfare as the TEP regulation when both firms have the same abatement costs and the policy requires an equal reduction in emissions. When d 1 6= d 2, which yields 2C 6= 1C, total welfare is higher under a competitive TEP market than under CC. The difference in aggregate abatement costs, and thus in welfare, increases with the difference between the two firms marginal abatement costs. Proof of Proposition If the two firms average abatement cost functions have different slopes, e 2 > e 1, the permit price is smaller than the average of the Lagrange multipliers, 2P " < 1C + 2C. Both industry s output and aggregate cost of abatement are higher under TEP than under CC regulation. Although firm 1 does more abatement than firm 2, the cost savings resulting form this reallocation of abatement effort are dominated by the increase in the required aggregate abatement. 2X i=1 (K it K ic ) = (P " ) 2 2 (P " 2 ) ic + 4e i 4e j 2 jc = (ei + ej)(p " ) 2 e i 2 jc e j 2 ic 4e ie j > 0: (22) When industry s output increases after trading of emission permits is allowed, the cost minimization property of the TEP regulation does not hold. In this case we have to examine whether the aggregate abatement cost difference outweighs the increase in aggregate welfare due to the increase in output. Substituting Q C and Q T from equations (11) and (16) respectively, and the difference of aggregate abatement costs between CC and TEP from equation (22) into the welfare difference in equation (20) yields, W T W C = 4(a c) 2P " ( ic + jc) (a c) 6 (ic + jc 2P " ) (e i + e j)(p " ) 2 e j 2 ic e i 2 2j : (23) 3b 4e ie j

15 TRADEABLE EMISSION PERMITS REGULATIONS 79 We make the following simplifying assumptions: d = 0 and Ē=(1 )[2(a c)/3b], where 0 < < 1 is the percentage reduction in emissions required by the regulation. Using these assumptions, the values of the Lagrange multipliers in equation (12) and of the permit price in equation (17) become, ic = 2ei(b + 2ej2 )(a c) ; and " 4e ie j(a c) P = ; (24) X where X =3b(e i +e j)+4e ie j 2, =3b 2 +4b(e i +e j) 2 +4e i e j 4. Using the above values of the Lagrange multipliers and the permit price we derive ic + jc 2P " = 6b2 (e i e j) 2 (a c) ; X ic + jc + 2P " = 2(a c) [(b(e i + e j )+4e ie j 2 )X+4e ie j ]; X (e i + e j)(p " ) 2 e i 2 jc e j 2 ic = 2 2 (a c) 4e ie j X 2 [4e 2 ie j(e i + e j) 2 [e i(b + 2e j 2 ) 2 + e j(b + 2e i 2 ) 2 ]X 2 ]: (25) Substituting the above expressions into the welfare difference, equation (23) yields, W T W C = 2b(ei ej)2 2 (a c) 2 3X 2 [X + 2 [(b(e 2 i + e j )+4e ie j 2 )X+ 4e ie j ]] 2 2 (a c) 2 [4e ie j(e i + e j) X [e i(b + 2e j 2 ) 2 + e j(b + 2e i 2 ) 2 ]X 2 ]: (26) Finally, substituting into equation (26) the values of X and yields W T W C = b(ei ej)2 2 (a c) 2 3X 2 [b 3 (e 2 i + e j)( ) +6b 2 (e i+ e j) 2 2 (4 +)+24b 2 e ie j 2 (1 + ) +32e 2 ie 2 j 6 (1 ) +b(e i+ e j)e ie j 4 (56 20)]: (27) Given that 1 > 0, it is clear that W T > W C. Thus, even when aggregate output increases as a result of permits trading, social welfare is higher under the TEP relative to the CC regulation. QED. Notes 1 Minimization of aggregate cost of achieving a given reduction in emissions. 2 Buchanan (1969) has shown that a Pigouvian tax levied on a monopolist, while reducing the environmental externality, increases the product market distortion. In the presence of market imperfections, an additional policy instrument is required for the full resolution of the problem. Here, we assume that policy makers cannot intervene in the product market by using a combination of instruments. 3 We use tradeable emission permits regulations to represent systems of economic incentives. Pure competition in the market for permits ensures that the equilibrium permits price is equal to the environmental tax required to achieve the same reduction in emissions. 4 This type of command and control regulation is usually referred to as performance standards. Alternatively the policy maker can specify the technology of meeting the performance standards, a

16 80 EFTICHIOS SOPHOCLES SARTZETAKIS type of command and control referred to as design standards. We use performance standards because under this form of command and control the policy maker can control, ex-ante, the emissions level. For a comparison of the two types of command and control see Besanko (1987). 5 The emissions ceiling is decided through consultations with interest groups, and is influenced by international agreements. 6 When policy makers have complete information about demand and cost structure, they can derive the welfare maximizing allocation of emission quotas. In such a case, command and control systems are superior to tradeable emission permits systems (see Hung and Sartzetakis 1994). 7 Under the assumption of competitive permits market, the initial allocation of emission permits does not affect the equilibrium. Since we have already assumed that policy makers do not have enough information to derive the welfare maximizing allocation of emission quotas, the allocation scheme does not influence our results. 8 In his example, Malueg imposes this additional constraint on the permit price. In general, this would imply that the demand for emission permits is not equal to supply. Malueg avoids this difficulty by using marginal abatement cost functions that increase stepwise. However, with such functions, the marginal abatement costs are not necessarily equalized among firms. Indeed, in Malueg s example, the marginal cost of abatement differs between the two firms after trading. Thus, the cost minimizing property of permits market is not present. 9 Malueg also recognizes the importance of considering alternative designs to the tradeable emission permits regulation (see Malueg 1990, p. 73). 10 If the allocation of extra permits is anticipated by the low-abatement-cost firms, they will sell more of their stock of existing permits, eliminating the effect of the policy. 11 For a discussion of the design of the 1990 Clean Air Act Amendments and particularly the allocation of temporary emission permits see Torrens et al. (1992). 12 Unit for unit, all the emissions must be matched by an equivalent amount of permits. Firms are awarded a budget of permits that, when summed across all firms, does not exceed the cap set by the environmental authority. 13 A quadratic abatement cost yields downward sloping demand for emission permits. We have chosen the simplest specification in order to illustrate the effects of permits trading while maintaining the properties of competitive permits markets. In Appendix A we discuss the implications of this particular abatement cost function. 14 The more profitable firm looses market share to the less profitable firm reducing aggregate profits. This is one of the preliminary results of our current research in this topic. 15 This is a common assumption, see for example Dasgupta (1982) and Malueg (1990). 16 Consider the extreme case in >0and@k/@q = 0, which imply z >0, q =0.In this case, firms have a smaller incentive to decrease output, as an alternative to increasing abatement per unit of output, relative to the case when q = z > 0, since a decrease in output results in lower emissions but does not affect the average abatement cost. Both firm s output and abatement per unit of output will be higher when q = 0 than when q = z. 17 Since ( ic jc) 2 0, then 2 ic + 2 jc 2 ic jc, and further ( ic+ jc) 2 4 ic jc. When e i = e j we have that 2P " = ic + jc, thus the last equation yields that (P " ) 2 ic jc. References Baumol, W. J. and W. E. Oates (1988), The Theory of Environmental Policy. Cambridge: Cambridge University Press. Besanko, D. (1987), Performance Versus Design Standards in the Regulation of Pollution, Journal of Public Economics 34, Borenstein, S. (1988), On the Efficiency of Competitive Markets for Operating Licenses, Quarterly Journal of Economics 103, Buchanan, J. M. (1969), External Diseconomies, Corrective Taxes, and Market Structure, American Economic Review 59, Dasgupta, P. (1982), The control of Resources. Cambridge: Harvard University Press.

17 TRADEABLE EMISSION PERMITS REGULATIONS 81 Hung, M. N. and E. S. Sartzetakis (1994), On Welfare Consequences of Permits Trading Under Imperfect Competition, Working paper, GREEN, Départment d économique, Université Laval, Québec. Malueg, D. A. (1990), Welfare Consequences of Emission Credit Trading Programs, Journal of Environmental Economics and Management 19, Misiolek, W. S. and H. W. Elder (1987), Exclusionary Manipulation of Markets for Pollution Rights, Journal of Environmental Economics and Management 16, Sartzetakis, E. S. (1993), Cost-Efficiency and Welfare Comparison of Tradeable Emission Permits to Command and Control, Working paper, Cahier 93-21, GREEN, Département d économique, Université Laval, Québec. Torrens, I. M., J. E. Cichanowicz, and J. B. Platt (1992), The 1990 Clean Air Act Amendments: Overview, Utility Industry Responses, and Strategic Implications, Annu. Rev. Energy Environ. 17, von de Fehr, N.-H. M. (1993), Tradeable Emission Rights and Strategic Interaction, Environmental and Resource Economics 3,