Equity constraints and efficiency in the tradeable permit market. By Cathrine Hagem Department of Economics, University of Oslo and CICERO, Center for International Climate and Environmental Research. and Hege Westskog CICERO, Center for International Climate and Environemental Research,P.O. Box 119, Blindern, N-0318 Oslo, Norway. Abstract We analyze how a permit allocation rule could be designed to both meet necessary equity consideration and effectiveness requirements. Taking equity considerations into account when allocating tradeable permits to different agents, could lead to dominant agents exploiting their market power in the permit market. Hence, the emission target is no longer met at least cost. We show that it is possible to design an allocation rule that both satisfy the equity considerations and lead to a cost-effective system.
Equity constraints and efficiency in the tradable permit market. 1 Introduction Under many tradeable permit systems, permits are allocated to the participants of the system for free; i.e. they are not auctioned but handed out to the agents at no costs for them. This is for instance so with the EU emission trading system (European Parliament 003). When allocating permits in this way, equity considerations are often very important both as an explanation why permits are allocated for free, but also for deciding how these free permits should be divided between agents that participate in the tradeable permit system (Ringius et al 00). However, the way permits are allocated, or how large shares that are given to the different participants, could be decisive for the costeffectiveness of the system. If the allocations lead to a competitive permit market, the emissions target will be achieved at least costs. In fact as long as the allocations do not influence the strategic position of the competitive agents, that they remain competitive, the way permits are allocated do not affect efficiency (ontgomery 197). On the other hand, if the permits are allocated such that some agents become large traders of permits, the target will no longer be achieved at least costs. Exploitations of market power leads to a sub-optimal distribution of abatement across agents and thus increases the total cost of achieving the target for emissions reduction (Hahn 1984). It is a well known result that changing the distribution of permits between agents or subsidizing a monopolist per unit sold leads to a cost efficient permit sale 1 1 See Hahn (1984) or Westskog (1996) for a discussion of how the distribution of permits matters for efficiency. or analysis of an efficient subsidy of output from a monopolist, see inter alia Tirole (1988). Another approach to reducing the inefficiency caused by a dominant agent exercising market power in the permit market is taken by Hagem and Westskog (1998). They consider how different designs of intertemporal permit trading systems could reduce this inefficiency.
However, both of these policies imply a redistribution of cost across agents. Equity considerations are often an important element when the distribution of permits between agents is decided both nationally and internationally. And this sets restrictions on permits allocations and may make it infeasible to subsidize/tax a dominant permit seller per unit sold/bought. Equity consideration could of course be taken care of through lump sum transfers. However, within international permit trading systems, money transfers may not be acceptable means of cost distribution. or instance, in the Kyoto protocol, the only policy instrument for distribution cost across participants is the initial allocation of permits across countries. At the national level there exist other distributive mechanisms (other taxes/transfers) that could be used to correct unwanted equity effects. However, international trade rules sets restrictions on the possibilities for financial transfers/tax reductions. Also, for a regulator it is often not clear when the initial distribution of permits is made, whether agents will exercise market power or not.,3 In this case, subsidizing agents per unit sold to correct for market imperfection will lead to a non efficient outcome if it turned out that the agent acted as a price taker Equity considerations for permit allocations between agents could include different elements. It could for instance relate to the different agent s cost of meeting their commitments, or it could be based on historical emissions. (See Ringius et al 00). In this paper we use the term regulator in two senses. At the national level, this is the regulatory authority, while at the international level this would be the terms of the agreement which the parties have agreed to. 3 This will among other things depend on how the permit systems are designed, which agents are included in the system, are some left out and is a national permit system linked to an international system. As an example, consider the Kyoto Protocol. The distribution of permits for the Kyoto period is likely to make Russia a large seller of permits ( see Böhringer and Löschel 003 and Weyant and Hill 1999). Whether Russia will exploit its potential market power in the permit market will depend on its domestic climate policy. Allocating permits across several domestic agents and let them trade in the international permit market will lead to a competitive market, whereas letting one agent take care of the international permit sale would probably lead to a situation where that agent exploit its ability to keep a high permit price through a restriction on permit sale. Hence, when deciding how permits should be allocated, it would not be known how the agents will behave in the market. 3
The approach in this paper is that the regulator wants to achieve a specific distribution of costs across agent. 4 With this perspective, we analyze how the regulator can fulfill any given target for the distribution of cost and at the same time ensure a cost effective agreement when the only policy instrument is the allocation of endowment of permits to the agents. In the following we set up a simple one period model with a dominant seller and a competitive fringe, and discuss how a permit allocation rule could be designed that both take equity and efficiency into consideration. The model To illustrate our point, we start out with a simple model for a tradable permit system with only types of agents. We consider the case where the regulator has a target for the distribution of cost across agents. urthermore, we assume that the regulator and both type of agents have perfect information about all agents cost of reducing their own emission. There is one potential dominant agent in the permit market. We will in the following assume that this agent is a large seller of permits, and is hereafter referred to as the monopolist, and denoted 5. All other agents are so small buyers or sellers that they are considered to be price takers. These are referred to as the fringe and denoted. The fringe is in total net buyers of permits. 4 The Kyoto Protocol differentiates the targets between developed countries (the Annex B countries). The countries with former centrally planned economies and countries with income highly dependent on production/consumption of fossil fuels and associated energy-intensive products got relatively lower targets than other developed countries. The costs implications of the participation in an agreement and a country s capability to deal with these costs were an important consideration behind these differentiated targets (see for instance Ringius et al (00). Also, within the EU, the way their total Kyoto target (8% reduction on total for the EU) were distributed between the EU countries, signifies that cost considerations was an important element in the considerations taken for how to allocate emission reduction targets between the EU-countries. The low income countries of the EU-region like Portugal and Greece were given much lower targets for reductions (in fact they could increase their emissions) than the other regions of the EU (See for instance European Environment Agency (004). 5 The general conclusions of the paper are not affected whether we have a monopolist or a monopsonist. 4
The agents are allocated a total endowment of permits equal to, where denotes the agent (=,). The sum of the endowments allocated to the agents fulfills the total emission constraint agreed upon; denoted Q and equals the sum of emissions from the agents: Q = Q + Q = e + e (1) where e signify the emission of agent : Q When permits are tradable the agents cost of their emission targets are given by the loss in income due to a reduction in their own emissions and their net cost of permits purchased. Let R ( e ) define the income of agent of being able to emit e. We assume that R ( e ) are twice continuously differentiable. The marginal income from emitting e ( R ( e )) are positive and strictly decreasing, that is R ( e ) >0 and R ( e ) <0. This signifies that as emission reductions are conducted, income is reduced. The larger the reductions in emissions, the higher is the cost (loss in income) of additional emission reductions. In a competitive permit market the agents will maximize their income from emission minus the costs of buying permits (or plus the income of selling permits) subect to the emission constraint, which is given by: Q + q = e () where q is the amount of permits bought (-q is the amount of permits sold). Hence, the agent s maximization problem is: Π = (3) max R ( e ) p q q, e Subect to () The solution to this problem is: p = R ( e ) (4) 5
Which implies that each agent sets its emission level where their marginal income from emissions is equalized to the permit price, which results in a cost-effective outcome where marginal income are equalized across agents. Let e be the solution to (4). urthermore, let BaU e denote agent s emission before the agreement took place (Business as Usual emission). The agent s total cost of participating in the agreement is given by TC = R e R e + p e Q (5) BaU ( ) ( ) ( ) Since we have assumed that the regulator has perfect information about all agents income functions it can derive the permit price in a competitive permit market. Hence, under a perfectly competitive permit market, we see from (5) that the regulator can achieve its preferred distribution of cost by an appropriate distribution of the initial endowments of permits Q. and this will ensure a cost effective distribution of emission across agents. Let P denote the competitive permit price and let TC denote the regulator s target for the distribution of cost of the agreement. urthermore, let denote the initial allocations of Q s that ensures that the target for the distribution of costs between agents is achieved in a competitive permit market, that is, Q Q is the number of permits allocated free of charge which makes the right hand side of (5) equal to TC, for p= P. This preferred distribution of cost may give an agent a dominant position in the permit market. If a dominant agent exercises market power, the permit price will be higher than P, and the cost distribution will not be as intended, nor will the system be cost effective..1 Design of the allocation rule The question we ask in this paper is how the regulator could construct an allocation rule for permits which prevents the exploitation of market power; i.e that is cost-effective; and at the same time ensure the preferred distribution of cost ( TC ). We suggest an 6
allocation rule where permits are allocated twice to the agents during the period; i.e. a share of the total amount of endowments are kept by the regulator, and allocated after the permit price is observed in the market for permits. At the beginning of the period the agents are allocated a fixed amount of permits denoted, 1 Q. The endowment of permits for the second round of allocations that is conducted, is dependent on the outcome of the permit price. If the price observed before the second round of permit allocations, turns out to be the competitive permit price, the agent is given an amount of permits for the second round equal to. However if the price of permits are higher than the competitive price, the endowment is increased/reduced for the fringe/monopolist by a constant factor of β times the difference between the observed permit price and the competitive price P. Hence, the allocation for the second round of Q allocations equals Q + β ( p P ) where β = β. This signifies that we can write the allocation rule for each agent as: Q = Q + Q + β ( p P) (=,), (6) 1 Hence, when the permit price exceeds the competitive price, P, the permit allocation benefits the fringe and punishes the monopolist through a reduction in the endowments of permits for the monopolist when p> P, when the second round of permit allocations are conducted. Let β respectively 1 β. The total emission constraints for the fringe and monopolist are given by, e = Q + Q + β ( p P) +q (7) e = Q + Q β ( p P) q (8) 1 7
The allocation rule is known to all agents at the beginning of the period. Since all agents know each others costs of emission reductions and can hence derive the competitive permit price, all agents can also deduct the second round allocation of permits when they observe the permit price. Consequently, there can only be one equilibrium price in the market due to the possibilities for arbitrage if the price changes over time. Hence, the price observed before the second round of allocation will be the equilibrium price for the whole period. The regulators problem is now to seek for a distribution of permits between agents that secure the intended cost distribution between agents and at the same time achieve costeffectiveness. This implies that the regulator seeks to find a value for β which maximizes the total income from emissions given the emission constraint and at the same time is acceptable on the grounds of equity. In order to do this the regulator must know the agents response to the allocation rules given by (6). 3 Permit trading with a dominant agent In this section we examine the case where there is a dominant agent with the possibility to exercise market power, and analyze how the allocation rule (6) influences the distribution of emission across agents and hence the cost-effectiveness of the system. In order to derive the monopolist s choice of permit sale, and hence the determination of emissions across agents, we first derive the fringe s demand functions for permits, found from the solution to the fringe s optimization problem. 3.1 The ringe s optimizing problem The fringe will maximize the income from emissions minus the costs of buying permits which is equivalent to the maximization problem given by (3) subect to (7). The solution to this problem is given by: p = R ( e ) (9) and the constraint (7). This defines the inverse demand function for permits given by: 8
p = pe ( ). (10) It follows from our assumptions about the income functions that the price the fringe is willing to pay for the permits is decreasing in its own emissions, i.e.: p e = R ( e ) < 0. (11) 3. The onopolist s optimizing problem If the dominant agent exploits its market power, it seeks to maximize its income from emissions plus the income from selling permits given its emission constraints. max Π ( e ) = R ( e ) + p( e ) q (1) e, q s.t. (8) and (1). Inserting for q from the monopolist s emission constraint (8), and inserting for e from the total emission constraint (1), we can rewrite the monopolist s maximizing problem to: = (13) 1 max Π ( e ) R( e) + p( Q e) Q + Q β p( Q e) P e e The first order condition of this optimization problem is: p p R ( e) q p 1 β = 0 e e (14) The second order condition of this maximization problem is given by: p p p R ( e) + (1 β ) + ( q β p) e e ( e ) (15) If the monopolist s profit function is concave in e, (15) is satisfied, and we have a unique solution to the monopolists profit maximizing problem. If the monopolist s profit function is not concave, the regulator s achievement of a cost effective distribution of emission, through β, becomes difficult because the monopolist s choice of emission 9
(depending on β ), is discontinues 6. We will in the following ignore that problem by assuming that the monopolist profit function is concave in e. (We know that is the case p with linear marginal income functions as that implies R( e) = 0). ( e ) Let e ( β ) be the solution to (14). rom the first order condition of the maximization problem (13), we observe that for β equal to zero, that is, when the allocation of permits is not dependent on the permit price, we see that R` ( Q e ( β )) = p> R( e ( β )). This means that the fringe emits too little and the monopolist emits too much compared to first best. The question is if we can find a correction of the endowment of permits for the second round of allocations, that leads to a cost-effective solution. This is a solution where p = R ( e ). 4 The optimal design of the allocation rules for permits. As mentioned above, the regulator would seek to find a value for β which maximizes the total income from emissions given the emission constraint and at the same time is acceptable on the grounds of equity. In the following we derive how the total income is influenced by an increase in β. If this is positive, this would signify that by allocating more permits to the fringe when the price of permits exceeds the competitive price, the total income would increase. Hence, we would approach a competitive outcome. The total income of the agents (TR) is a function of the total emission constraint, Q, and the distribution of emission across agents e ( β )). Hence, TR is given by: TR = R Q e + R e β (16) ( β ) ( ( β )) ( ( )) 6 This problem is discussed in Guesnerie and Laffont (1978). 10
We find that: TR e ( β ) Re ( ) Re ( ) = + β β e e (17) We see that the second part of the expression of the left hand side of equation (17) will be negative when R ( e ) > R ( e ) which would as discussed above be the case when the monopolist exercises market power in the permit market. urther, we find from total differentiation of (14) that Π p ( β ) β ( p P) e e e = = < 0 β Π A ( e ) Where A is the expression for the second order condition for profit maximization which we have assumed is negative. Hence, TR > > β 0 when R ( e ) R ( e ),which implies that a first best solution could be achieved with a sufficiently large increase in β. β should be increased until cost effectiveness is achieved, i.e. where R ( Q e ( β )) = R ( e ( β )) (18) Let β be the solution (18). β leads to a cost effective distribution of emissions and the equilibrium price would equal the competitive price ( p( e ) = R ( e ( β ) = P). We see from equation (5), from the definition of Q, and from the allocation rule (6), that the regulator realizes its preferred distribution of cost if 1 Q Q Q + = and β = β 11
urthermore, if the dominant agent acts as a price taker (see footnote 3.), the equilibrium price in the market would be the competitive price (which is not influenced by β ). And 1 the regulator would realize its preferred distribution of cost as long as Q + Q = Q. Hence we can conclude the following; A permit allocation system which allows for adustments overtime can be designed to lead to a cost effective solution, for any preferred distribution of cost across agents, both when the dominant agent exercises market power and when it acts as a price taker. 5 Concluding remarks In this paper we have constructed an allocation rule for permits which fulfill a regulators target both for efficiency and for the distribution of cost. We have assumed that all agents and the regulator have perfect information about the agents cost of emission reduction before the first round of permit allocation. This is obviously a simplification of a reality. The regulator may over- or underestimate the agent s abatement cost and hence estimate a competitive permit price which deviates from the true competitive price. If all agents act as price takers, this miscalculation will not influence the cost effectiveness of the allocation rule, (the competitive outcome would occur when true costs are observed by the agents), but it will no longer fulfill the regulators target for cost distribution. However, as long as the regulator has over- or underestimated the agents abatement costs, an allocation rule which did not adust the allocation according to the observed price (β=0), would not achieve the preferred distribution of cost either. If we are in a situation where the dominant agent exploits its market power, the miscalculation of the agents cost of emission reduction will also result in a situation where the monopolist sale of permits will deviate from first best. Hence, with significant uncertainty about the in the agents cost of emission reductions we cannot in general say whether the regulator prefer the allocation rule we have suggested compared to an allocation rule with no adustment term. 1
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