Download Tradeable Emission Permits Regulations in the Presence of

Environmental and Resource Economics 9: 65–81, 1997.
c 1997 Kluwer Academic Publishers. Printed in the Netherlands.
65
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-efficiency1 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 regulations3 in the presence of imperfectly competitive product markets
and compares these systems to command and control systems in terms of their
VICTORY: PIPS No.: 113212 MATHKAP
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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 quotas4 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
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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
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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, ei = qi , where is the rate of emission, and is assumed to
be the same for both firms. The firms can reduce emissions by either reducing
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TRADEABLE EMISSION PERMITS REGULATIONS
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output or controlling emissions. Firm i’s total cost of controlling emissions is Ki
= ki (zi ,qi )zi qi , where qi , is firm i’s output, zi is firm i’s abatement per unit of
output and ki is the average cost of controlling emissions. ki is assumed to be a
non-decreasing function of both the output and the abatement per unit of output: ki
= ki (qi ,zi ), with kq 0, kz 0, and kqz 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 Ēi , i = 1, 2, be firm i’s emission quota, with 2i=1Ēi = Ē.
Note that, qi zi qi = Ēi . Given firm i’s emissions ceiling Ēi , its constrained profit
maximization problem is,
maxqi ;zi Li
= (a bQ)qi cqi ki(qi ; zi)zi qi + i[Ei ( zi )qi]:
(2)
Assuming that the regulatory constraint is effective and excluding corner solutions,
the first order conditions are
a
2bqi
ki qi
i
bqj c ki (zi ; qi)zi @k
@qi zi qi i ( zi ) = 0;
@ki z q + q = 0;
@zi i i i i
(3)
(4)
and
Ei ( zi )qi = 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 = ki + [@ ki /@ zi ]zi . Under a CC regulation that
prohibits resale of emission quota, the value of an emission quota is limited to the
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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
z
iC
qiC = 21b [a c iC ziC kiC (iC
)]
1
qjC ;
2
(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 NDi =
( zi )qi Ēi . In equilibrium, 2i=1 NDi = 0.
Firm i’s profit maximization problem is
maxqi ;zi i
= (a bQ)qi cqi ki (zi ; qi)zi qi P "[( zi)qi Ei];
(7)
where, P" is the equilibrium permit price. The first order conditions are
a
and
2bqi
i
"
bqj c ki zi @k
@qi zi qi P ( zi) = 0;
i
"
ki qi @K
@zi ziqi + P qi = 0:
(8)
(9)
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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:
qiT = 21b [a c P " ziT kiT (iTq iTz )]
1
qjT ;
2
(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.
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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, Ki = [d + ei zi qi ]zi qi , where d, ei > 0 represent technological
parameters.13 Abatement technologies differ between firms, with e2 > e1 so that
firm 1 has a more efficient abatement technology. Using this specification, the
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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,
qiC = a c (32biC jC ) ;
QC = 2(a c) 3b(iC + jC ) : (11)
The equilibrium level of firm i’s Lagrange multiplier is also derived,
2
2
iC = 2ei (b + 2ej )[3b2(a+ 4bc()e +3beE)i] 2++b[43eb e+24(2ej + ei )r ]d
i
j
i j
(12)
The difference between the two firms’ Lagrange multipliers is
2
iC jC = b(ei e3j )[b22+(a4b(ec)+ e3)bE2]+ 42ebe (e4i ej )d :
i
j
i j
(13)
Rearranging terms, equation (13) can be written as follows,
2
iC jC = 3b (3ebi2 +e4jb)[(e2(+a e )c2 +d4)e=e3b4 E ] :
i
i
i j
(14)
Under the above specification of abatement cost, equation (4) yields, ziC qiC =
(iC d)/2ei . Excluding corner solutions, ziC > 0, qiC > 0, this implies that iC
> d, i = 1, 2. This inequality along with aggregate output QC = [2(a c) (iC +
jC )]/3b, implies that
2
E ) :
C
iC jC > 3b23+b 4(eb(i e +ej e)(Q
2
4
i
j ) + 4ei ej (15)
Inspection of equation (15) reveals that e2 > e1 implies 2C > 1C , since QC Ē
= AiC + AjC > 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,
"
QT = 2(a c3)b 2P :
"
qiT = a c3b P ;
(16)
Substituting the two firms’ output and abatement into the permits market clearing
condition, 2i=1 NDi = 0, the equilibrium permits price is also obtained,
P " = 2ei ej [2(3ab(e c+) e 3)b+E 4] e+e3b(2ej + ei )d :
i
j
i j
(17)
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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,
2
2
P " = ei (3b + 23ebj (e )+jCe +) +ej4(e3be+22ei )iC :
i
j
i j
(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(ei ej )(j i ) < 0. We
have shown above that ei > ej implies jC > iC . Therefore, the competitive permit
price is no greater than the average of the Lagrange multipliers, i.e. ei 6= ej ) P"
< (i + j )/2, while ei = ej ) 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 ei 6= ej ,
while it remains the same when ei = ej .
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. d2 > d1 and e1 = e2 ,
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, ei 6= ej . 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:
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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.
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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, Benoı̂t 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), Département d’économique, Université Laval and the Centre
for International Business Studies (CIBS), University of British Columbia.
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TRADEABLE EMISSION PERMITS REGULATIONS
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
0 and z
q . thus, the average abatement cost employed in the above
in output, z < 0, q
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,
Wv
= u(Qv )
cQv
2
X
=
Kiv ;
v
= C; T:
(19)
i 1
Since we have assumed a specific form for the utility derived from the consumption of Q, namely,
u(Q) = aQ 1=2 bQ2 , social welfare under each form of regulation, Wv is Wv = [1=2 (pv + a) c]Qv
2i=1 Kiv .
The difference of social welfare between TEP and CC regulation is:
WT
WC
=
h1
(pT + pC )
2
i
c
(QT
QC )
2
X
=
(KiT
KiC ):
(20)
i 1
The term in brackets in the right-hand side of equation (20) is positive. Furthermore, the industry’s
output under the TEP regulation, QT , is at least not smaller than the output under the CC regulation,
QC . 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 d2 > d1 and e1 = e2 , 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
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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.
2
X
=
(KiT
KiC )
=
i 1
2
X
=
(ziT qiT
ziC qiC )[di + e(ziT qiT
+ ziC qiC )]
i 1
=
2
X
(P " )2
4e
=
i 1
2iC
" 2
= iC jC2e (P ) 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 d1 = d2 , 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 d1 = d2 , which yields
2C = 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.
6
6
Proof of Proposition
If the two firms’ average abatement cost functions have different slopes, e2 > e1 , 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.
2
X
=
(KiT
KiC )
i 1
" 2
= (P )4e
2iC
i
+
=
(P " )2
4ej
(ei + ej )(P " )2
ei 2jC
4ei ej
2jC
ej 2iC
> 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 QC and QT 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,
WT
WC
= (a
c)
(iC
4(a
+ jC
3b
c)
2P " )
2P " (iC
6
+ jC )
(ei + ej )(P " )2
ej 2iC
4ei ej
ei 22j
:
(23)
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79
TRADEABLE EMISSION PERMITS REGULATIONS
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 + 2ej )(a
c)
2
; and P "
(a
= 4ei ej X
c)
;
(24)
where X = 3b(ei + ej ) + 4ei ej 2 , = 3b2 + 4b(ei + ej )2 + 4ei ej 4 .
Using the above values of the Lagrange multipliers and the permit price we derive
= 6b (ei
2
ej )2 (a
X
c)
iC
+ jC
iC
+ jC + 2P " = 2X(a c) [(b(ei + ej ) + 4ei ej 2 )X + 4ei ej ];
2P "
(ei + ej )(P " )2
ei 2jC
4ei ej
ej 2iC
=
;
2 2 (a c)2
[4ei ej (ei + ej )2
X 2 2
[ei (b + 2ej 2 )2 + ej (b + 2ei 2 )2 ]X 2 ]:
(25)
Substituting the above expressions into the welfare difference, equation (23) yields,
WT
WC
=
2b(ei
ej )2 2 (a c)2
[X + 2[(b(ei + ej ) + 4ei ej 2 )X +
3X 2 2
2 2 (a c)2
4ei ej ]]
[4ei ej (ei + ej )2 [ei (b + 2ej 2 )2 +
X 2 2
ej (b + 2ei 2 )2 ]X 2 ]:
(26)
Finally, substituting into equation (26) the values of X and yields
WT
WC
=
ej )2 2 (a c)2 3
[b (ei + ej )(18 + 27) + 6b2 (ei +
3X 2 2
ej )2 2 (4 + ) + 24b2 ei ej 2 (1 + ) + 32e2i e2j 6 (1 ) + b(ei +
b(ei
ej )ei ej 4 (56
20)]:
(27)
Given that 1 > 0, it is clear that WT > WC . 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.
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
2
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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 which, @ k/@ z > 0 and @ 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 2iC + 2jC
2iC jC , and further (iC +jC )2
4iC jC .
"
When ei = ej we have that 2P = iC + jC , thus the last equation yields that (P" )2 iC jC .
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