Economics Letters 69 (2000) 235–238
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On the long-run efficiency of auctioned vs. free permits
*
Catherine L. Kling, Jinhua Zhao
Department of Economics, Heady Hall, Iowa State University, Ames, IA 50011, USA
Received 23 August 1999; accepted 25 April 2000
Abstract
When marketable permits affect the entry / exit decisions of competitive firms, the efficient proportion of auctioned vs. free permits depends on the pollutant’s nature. All permits should be auctioned for global pollutants, and some should be free for local pollutants. 2000 Elsevier Science S.A. All rights reserved.
Keywords: Tradable emission permits, Long-run efficiency, Auctioned permits, Free permits
JEL classification: Q20
1. Introduction
With the passage of the Kyoto Protocol and the success of sulfur trading in the U.S., tradable emission permits are becoming an increasingly popular tool in pollution control. One of its major advantages is that under rather general conditions, efficiency can be achieved regardless of the initial distribution of permits among firms. However, the literature has ignored a related and important issue: whether the initial permits should be auctioned to firms or given away free. The most prevalent thinking on this issue is that the decision can be made purely on political grounds, presumably with no efficiency losses. This has been specifically mentioned as another beneficial aspect of marketable permits relative to emission taxes (Xepapadeas, 1997; Baumol and Oates, 1988).
In this paper, we seek to make an important and apparently overlooked point: auctioned and free permits have different long-run efficiency implications. Depending on the nature of the pollutant, part or all of the permits should be auctioned. As Carlton and Loury (1980) have shown, to achieve long-run efficiency in a competitive industry, the regulatory authority needs to control both the pollution level of each firm and the number of firms. Obviously with a single policy tool such as the total number of permits, it will be difficult to achieve both objectives. However, we show that the proportion of free permits can effectively be used as the second policy tool.
*Corresponding author. Tel.: 11-515-294-5857; fax:11-515-294-0221.
E-mail address: jzhao@iastate.edu (J. Zhao).
236 C.L. Kling, J. Zhao / Economics Letters 69 (2000) 235 –238
Our results are relevant for two typical situations: one in which a new set of permits are allocated in each period and one in which a set of permits are allocated one time only, but the permit policy is anticipated by firms. In the first case, since new permits are issued in each period, free permits represent a periodic ‘‘subsidy’’ to existing firms, clearly affecting their entry and exit decisions. One example is the five-year lead phase-out program of the 1980s where permits were accrued quarterly. In the second case, if a firm expects that the permits will be given free for the firms existing at the future moment of policy change, it may enter the industry before the provision takes place or delay its exit until after the policy change. Given that the policy debate concerning emissions trading is typically protracted, firms likely have ample opportunity to anticipate the government’s policy choice. Finally, entry and exit can also be considered as a surrogate for firms’ other responses such as increasing or decreasing emissions before the policy.
2. A model of optimal permit allocation
Consider a perfectly competitive industry with n identical firms. The aggregate inverse demand function for its output is given by P(?) and the cost function of each firm is given by c( q, a), where q
is its output and a its abatement effort. The cost function follows standard assumptions: c .0,
q c .0, c .0, c .0, and c .0. The emission of an individual firm is given by e( q, a), with
qq a aa qa
e .0, e .0, e ,0, and e .0. Following Carlton and Loury (1980), let D(n, e) be the
q qq a aa
environmental damage caused by the industry’s emission, with D $0, D $0, and the Hession
n e
matrix of D being positive semi-definite.
Let E be the total number of permits issued to the industry and e the permits given free to each0 firm with the remaining permits auctioned off at the market price. Since there is a one to one correspondence between E and the equilibrium price of the permits, denoted as p, we can model p and
e as the two policy tools.0
Given p and e , each firm’s profit isp5P(nq)q2c( q, a)2p(e( q, a)2e ), where e( q, a)2e is
0 0 0
the number of permits the firm must purchase at the market price. The industry equilibrium is characterized by
P(nq)2c ( q, a)2pe ( q, a)50, (1)
q q
c ( q, a)1pe ( q, a)50, (2)
a a
and the zero profit condition p50. If the government is to choose q, a, and n, its optimization
nq
problem is max u( q, a, n); e P(x) dx2nc( q, a)2D(n, e( q, a)). The first order conditions are
q,a,n 0
given by
P(nq) 2c ( q, a)2D (n, e)e ( q, a) /n50 (3)
q e q
c ( q, a)1D (n, e)e ( q, a) /n50 (4)
a e a
P(na)q2c( q, a)2D (n, e)50. (5)
n
C.L. Kling, J. Zhao / Economics Letters 69 (2000) 235 –238 237
where q, a, and n are evaluated at their respective optimal levels. Corresponding to p*, the total
*
*
*
number of permits issued to the industry is given by E*5n( p*, e )e( q( p*, e ), a( p*, e )). We
0 0 0
D
define´ (n, e)5D (n, e)e /D(n, e) to be the elasticity of pollution damage with respect to each firm’s
e e
D
emission, and ´ (n, e)5D (n, e)n /D(n, e) to be the elasticity with respect to the number of firms.
n n
Proposition 1. The efficient proportion of free permits is given by
D
Therefore: (a) all permits should be free if and only if´ 50; (b) all permits should be auctioned if
n
D D D D
and only if´ 5´ ; and (c) part of the permits should be auctioned when ´ .´ , that is when the
e n e n
pollution damage is more sensitive to the emission level of each firm than to the number of firms.
To understand the intuition of Proposition 1, note that pe0 is an income transfer from the government to the firm. Such a subsidy will reduce a competitive firm’s scale q and emission e and raise the number of firms. This is because a competitive firm produces at the point where the average cost equals the marginal cost. A subsidy reduces the average cost, and since marginal cost is increasing in q, the firm will reduce q in response to the subsidy. Since a subsidy always raises the total supply of the industry, it will raise the number of firms as each firm’s output is reduced. Since the total emission level is fixed at E, each firm’s emission e5E /n will decrease. Therefore, if the
environmental damage is more sensitive to each firm’s emission level than to the number of firms, a subsidy is needed to reduce the emission level, even though it raises the number of firms. However, all permits being free may also be inefficient because the number of firms may be too high and the scale of each firm may be too low.
3. Implications of the pollutant’s damage function
Proposition 1 indicates that the optimal proportion of free permits depends on the characteristics of the pollution damage function. For uniformly mixed pollutants, only the aggregate emission matters,
D D
¯
thus D(n, e)5D(ne), and ´ 5´ . In this case, all permits should be auctioned. Pollution problems
e n
falling into this category include global warming, ozone depletion, and regional air pollutants such as acid rain.
For purely local pollutants, a firm’s emission causes damage only in a restricted area, and the damage function may be represented by D(n, e)5nd(e), where d(?) is the damage caused by a single
D
The special damage function requires that each firm’s pollution damage be completely independent of
1 D
To see this, note that´ 2e 15(d9(e)e2d(e)) /d(e). The numerator is increasing in e and equals zero at e50, thus is
D
positive for e.0. Thene .1 for e.0.
238 C.L. Kling, J. Zhao / Economics Letters 69 (2000) 235 –238
other firms’ emissions. For example, if the firms are geographically separate such that their emissions do not mix, this damage function would be appropriate.
Some pollutants cause both local and global damages. For example, nitrogen oxides contribute to
¯
both global warming and local smog. Then the damage function may be a weighted sum of D(ne) and
nd(e), and again some, but not all, of the permits should be freely distributed. Another example of a
weighted sum damage function is when there are multiple regions, each with several firms. If emissions between regions do not mix, but emissions among firms within a region do mix, a weighted sum damage function would be appropriate. Pollution problems falling into this category might include water pollution, local air pollution, noise, etc.
Some highly toxic substances, such as airborne carcinogens and radioactive nuclear waste, cause extremely high damage in a local area even at low concentration levels. Enough damage is done at these levels that additional emission causes little more damage. The appropriate damage function for these pollutants in the relevant emission range is D(n, e)5nd(e) with d9(e)$0 and d0(e),0. Then
D D 2
*
we can show that e ,15e . In this case, e ,0, meaning that in addition to auctioning off all
e n 0
*
permits, the government should require each firm to hold e0 permits more than its actual emission
3
level. Such a policy helps to reduce the number of firms, while increasing the scale of each firm. This result is desirable: for highly toxic pollutants of which a single drop can kill all the fish in a river, it is better to have big plants in few areas than small plants in a large number of areas (so that only few rivers face the devastating risk).
The above possibilities describe most of the common pollutants and are most relevant for policy design. It is in fact difficult to imagine a realistic situation where the number of firms do not matter [i.e. D (n, e)50] so that all permits should be free.
n
Acknowledgements
The authors are a professor and an assistant professor in the Department of Economics at Iowa State University. We thank an anonymous referee for helpful comments. The usual disclaimer applies.
References
Baumol, W.J., Oates, W.E., 1988. The Theory of Environmental Policy, 2nd Edition. Cambridge University Press. Carlton, D.W., Loury, G.C., 1980. The limitation of pigouvian taxes as a long-run remedy for externalities. Quarterly Journal
of Economics 45, 559–566.
Xepapadeas, A., 1997. Advanced Principles in Environmental Policy. Edward Elgar.
2
ˆ
The procedure is similar to Footnote 1. We only need to show that d9(e)e2d(e),0 for the relevant range of e. Suppose e
ˆ ˆ
is the critical level after which d9(e) becomes small. Since e is low and d(e ) is high (due to the toxic nature of the
ˆ ˆ ˆ ˆ ˆ
substance), low d9(e ) means that d9(e )e2d(e ),0. Further, d0(e),0 for e.e means that d9(e)e2d(e) is decreasing in e, ˆ
implying d9(e)e2d(e),0 for e.e. We assume that the second order condition in the government’s decision problem
(3)–(5) are still satisfied. This is true if the cost function c( q, a) is sufficiently convex in a. 3
