Who should abate carbon emission? Graciela Chichilnisky and Geoffrey Heal June 1993, revised October 1993 Discussion Paper No. 683 to appear in Economic Who should abate carbon emissions? An international viewpoint GRACIELA CHICHILNISKY* GEOFFREY HEAL1" June 1993, revised October 1993 ABSTRACT. We review the optimal pattern of carbon emission abatements across countries in a simple multi-country world. We model explicitly (with the model in Chichilnisky [4]) the fact that the atmosphere is a public good. Within this framework we establish conditions for it to be necessary for optimality that the marginal cost of abatement be the same in all countries. These condition are quite restrictive, and amount to either ignoring distributional issues between countries or operating within a framework within which lump-sum transfers can be made between countries. These results have implications for the use of tradeable emission permits, which as normally advocated will lead to the equalization of marginal abatement costs across countries. The observation that the atmosphere is a public good implies that we may need to look at a Lindahl equilibrium rather than a Walrasian equilibrium in tradeable permits. Key words: Carbon dioxide, environment, global warming, abatements, emission, public good, marginal abatement costs, emission permits, tradeable permits. JEL Classification: Q2, H4. 1. WHO SHOULD ABATE? The 1992 Rio Convention acknowledged the need for international co-operation in responding to the threat of climate change posed by the rapidly increasing concentration of CO2 in the atmosphere. There are however substantial differences of opinion both about the main issues and about the framework for resolving them. Industrial countries typically focus on the potential problems posed by the growth of population in developing countries, and on the environmental pressure from carbon emissions that this could create over the next half century. Abatement efforts, they feel, should be initiated in the developing countries. On the other hand, developing countries view the carbon emission problem as one which originates historically and currently in the industrial countries, and one which requires their immediate action. Indeed, the large majority of all carbon emissions, about 73%, originate currently and historically in *Professor of Economics, Columbia University, New York, NY 10027. t Professor and Senior Vice Dean, Columbia Business School, New York NY 10027. 1 Letters Who should abate carbon emissions? An international viewpoint 2 the OECD countries and in the ex-Soviet Union; the developing countries have almost 4/5 of the world's population yet contribute at most 30% of all carbon emissions1. CO2 emissions are a by-product of animal life, and of economic activity which involves burning fossil fuels. The rapid increase in the concentration of CO2 in the atmosphere which has occurred since the second world war has become a matter of great concern, as it could lead to major and irreversible climate changes. This concentration affects us all equally, because COi mixes uniformly throughout the planet's atmosphere. From the economic viewpoint, therefore, the abatement of carbon emissions increases our consumption of a public good, a "better" atmosphere. However, this differs from the classic public good in that it is not produced in a centralized fashion. Its production is decentralized: each consumer of the atmosphere is also a producer. Each country uses the atmosphere as a "sink" for the carbon emissions which are a by-product of its economic activities. We have therefore a public good which is independently produced as well as consumed by all, a case which is closer to that of an economy with externalities, e.g. Baumol and Oates [1] and Heal [7]. The classic questions of optimality in the provision of the public good now become questions about the optimal abatement levels of the different countries. Who shall abate, and by how much? And how are the optimality conditions for abatement related to the countries' levels of income, their marginal costs of abatement, and the efficiency of their abatement technologies? We find some answers to these questions in a simple model of the world economy (introduced in Chichilnisky [4]) consisting of a finite number of countries2. Each country has a utility function which depends on the consumption of a public good and of a private good, such as income. The production of private good emits carbon dioxide as a by-product, and in each country the private good can be transformed into the public good through an abatement technology. We show that Pareto efficiency dictates that the marginal cost of abatement in each country must be inversely related to that country's marginal valuation for the private good (Proposition 1). In particular, it is not generally true that Pareto optimality requires that marginal abatement costs be equated across countries: this is true only if marginal utilities of income are equated across countries, either by assumption or by lump sum transfers across countries. If richer countries have a lower marginal valuation of the private good, then at a Pareto efficient allocation, they should have a larger marginal cost of abatement than the lower income countries. With diminishing returns to abatement, this implies that they should push abatement further. There is a presumption in the literature that efficiency requires equalization of 1 2 There is more detail in Chichilnisky [2] [3] [4], and Chichilnisky and Heal [5] It is, in fact, consistent with that of Baumol and Oates [1], Chapter 4. Who should abate carbon emissions? An international viewpoint 3 marginal abatement costs: this presumption underlies proposals for the use of uniform carbon taxes and tradeable carbon emission permits (Weyant [9], Coppel [6]). However, in view of the public good nature of the atmosphere and the fact that carbon emissions are produced in a decentralized fashion, efficiency will not in general require the equalization of marginal costs of abatement across countries without lump sum transfers. In a two-country example we show that, at an efficient allocation, the quantity of income allocated by a country to abatement is inversely proportional to the level of income—or consumption—of that country, with the constant of proportionality increasing with the efficiency of the country's abatement technology (Proposition 2). The equalization of marginal costs would be necessary for Pareto efficiency if the goods under consideration were private goods. But in our case we are dealing with a public good, i.e. one which, by definition, is consumed by all in the same quantity: the atmospheric CO2 concentration. This public good is "produced" by the CO2 emissions (or by the abatement of these emissions) of a finite number of large agents, namely the countries. In this sense, it differs from the classical treatments of Lindahl and Bowen, which were extended subsequently by Samuelson, see Atkinson and Stiglitz, p. 489, footnote 3, [8]. In those cases the public good is produced by a single agent, as is the case for a law and order or defense. 2. PARETO EFFICIENT ABATEMENT STRATEGIES Consider a world economy with N countries, N > 2, indexed by n = 1,...,N. Each country has a utility function un which depends on its consumption of private goods c n , and on the quality of the world's atmosphere, a, which is a public good. Formally, un(cn,a) measures welfare, where un : R2 —>• R is a continuous, concave function and dunldcn > 0, dun/da > 0. The quality of the atmosphere, a, is measured by for example the reciprocal or the negative of its concentration of CO2. The concentration of CO2 is "produced" by emissions of carbon, which are positively associated with the levels of consumption of private goods, c n ,: i.e. N a = ^2<in where an = $ n (c n ), for each country n = 1,..., N, $'n < OVn. (1) n=l a is a measure of atmospheric quality overall, and an is an index of the abatement carried out by country n. The "production functions" $ n are continuous, and show the level of abatement or quality of the atmosphere decreasing with the output of consumption. An allocation of consumption and abatement across all countries is a vector (c1,ai,...,cN,aN) € R2N'. An allocation is called feasible if it satisfies the constraint (1). A feasible allocation (ci,a\,..., c*N, ax*) is Pareto efficient if there is no other feasible solution at which Who should abate carbon emissions? An international viewpoint 4 every country's utility is at least as high, and one's utility is strictly higher, than at (c?,a*,...,c^,a;v*). A Pareto efficient allocation must maximize a weighted sum of utility functions N W(ci,...,Cn,a) = n=l with Yin ^n = 1 subject to feasibility constraints. Varying the Ans, one traces out all possible Pareto efficient allocations. The Xns are of course exogenously given welfare weights, and a standard set of weights is An = 1/N for all n. We are assuming in this formulation that utilities are comparable across countries. This means that we cannot change the units of measurement of utility in any country without making similar changes in other countries. Each country n faces a constraint in terms of allocating total endowments into either consumption cn or atmospheric quality, an, represented by the function $ n . Then a Pareto efficient allocation is described by a solution to the problem: N Max W(cu ..., cn, a) = ]T Anun(cn, a), (2) 71=1 N subject to an = <I>n(cn), n — 1...N and a = ^ an. (3) n=l Note that, by definition, the marginal cost of abatement is the inverse of the marginal productivity of the function $ n : MCn(an) = -I/KM (4) A Pareto efficient solution solves problem (2). Proposition 1. At a Pareto efficient allocation (c^, a^,..., cj^-, a^v*), the marginal cost of abatement in each country, MCn(a^), is inversely proportional to the marginal valuation of the private good cn, \ndun/dcn. In particular, the marginal costs will be equal across countries if and only if the marginal valuations of the private good are equal, i.e., Xndun/dcn is independent of n. Proof. . The solution to the maximization problem (2) must satisfy the first order conditions: N n=l Who should abate carbon emissions? An international viewpoint 5 for each country j = 1...N. Since at a Pareto efficient allocation the expression (Yln=i Xndun/da) is the same constant for all countries, denoted K, and since, as noted in (4) we have that a Pareto efficient allocation is characterized by: and the proposition follows. <0> Proposition 1 shows that the product of the marginal valuation of private consumption and the marginal cost of abatement in terms of consumption, is equal across countries. Writing this product Xjduj/dcj.dcj/da, we see that it can be interpreted as the marginal cost of abatement in country j measured in utility terms, i.e. in terms of its contribution to the social maximand ]Tn \wn( c ru a)- An immediate implication is that in countries which place a high marginal valuation on consumption of the private good, typically low income countries, the marginal cost of abatement at an efficient allocation will be lower than in other countries. If we assume an increasing marginal cost of abatement (diminishing returns to abatement), then this of course implies lower levels of abatements in poor countries than in rich countries. Under what conditions can we recover the "conventional wisdom" that marginal abatement costs should be equalized across countries? We need to equate the terms Xndun/dcn across countries. This could be dome by assumption: we can just decide as a value judgment that is an input to the planning problem that consumption will be valued equally on the margin in all countries. Given the enormous discrepancies between the income levels in OECD countries and countries such as India and China, and the need for all of them to be involved in an abatement program, such a value judgment seems most unattractive. It is however implicitly done in simulation models which seek to maximize world GNP or similar measures. There is an alternative possibility. Modify the original problem to allow unrestricted transfers of private goods between countries: Max W(cu c2, .c n ,.., a) = £ n A n u n (c n , a) subject to an = $n(yn) and a = J2an and Y^Vn^T.Cn . . This is the same as before except that we now distinguish between the consumption of the private good by country n, denoted c n , and the production of the private good by country n, denoted yn. These need not be equal. In addition we now require the sum of the consumptions across countries to equal the sum of the productions " J2Vn = Z)c n , instead of having these equal on a country by country basis. By this modification we are allowing the transfer of goods between countries, i.e., we are Who should abate carbon emissions? An international viewpoint 6 allowing lump sum transfers. Note that this is not a model of international trade, which would require the imposition of balance of trade constraints. Clearly the first order conditions now are just An &f =uVn tf (6) (7) Set K = £ 9-?fc. Hence from (6) and (7) we get K9-^ = -KK as before. However, we now have an extra condition (6)- namely ^n^* Substituting this into (8) gives v = -$'nK (8) = v Vrz. which of course implies that physical marginal cost is the same across all countries, as v and K are common to all countries. So if we solve an optimization problem that allows unrestricted transfers between countries, and we make the transfers that are needed to solve this problem, it will then be efficient to equate marginal abatement costs. Consider now the case of two countries, each with a Cobb- Douglas utility function, un(cn,a) = can{af-a = c«( a i + a 2 ) 1 " a , where the abatement production function $ n is an = $n(cn) = K{Yn - c n ) 1 / 2 , kn > 0, for n = 1,2, for example, k\ = k and A?2 = 1. This allows us to accommodate potentially different efficiencies of abatement across countries. For simplicity, the two countries are assumed to have the same utility function. In this case: Proposition 2. At a Pareto efficient allocation, the fraction of income which each country allocates to carbon emission abatement must be proportional to that country's income level, and the constant of proportionality increases with the efficiency of the country's abatement technology. Who should abate carbon emissions? Proof. . An international viewpoint Our problem (2) can now be written as: MaxCuC2 W(ci,c2) = 1 2 Max [cf [hp! - d) / + (Y2 - c,) 1 / 2 ] 1 " + c? [k^ - d ) 1 ^ + (Y2 Let The first order conditions for a maximum are then: aca-i Ai-a and _ ii2(Yx - ci)-1/2Ar {c«A~a(l - a) + cj(l - c*)A"a} = 0 j " 1 A1"" - 1/2(Y2 - c 2 )" 1/2 {c?A-a{l - a) + c£(l - a)A" a } = 0, which simplify to: Since a < 1 this implies that for Pareto efficiency, the income allocated to abatement by each country (an = Yn — cn, n = 1,2) must be proportional to the income level, or the level of consumption, of the country (cn). Furthermore the larger is the abatement productivity of a country (k = &i), the larger is its abatement allocation as a proportion of income. 0 3. ABATEMENT COSTS, TAXES AND EMISSION PERMITS While the atmosphere is a classic public good in terms of consumption, it is produced in a decentralized way, and the first order conditions for efficient allocation and provision of this "good" are different from the classical ones and closer to those characteristic of a general externality, as modeled in Heal [7]. Once the optimal consumption/abatement levels in each country are found, then quotas on emissions could be assigned to each country on the basis of these levels, and permits could be issued and freely traded as financial instruments across countries on the basis of these quotas. A system of permits for carbon emissions has of course been contemplated for some time, but as far as we know, the country-by-country quotas for these permits have not been connected to the optimality conditions for the allocation of public goods produced in a decentralized way. It would be desirable to ascertain what form of market organization for the permit market would be required in order to reach efficiency. For example, would it involve uniform pricing as in a competitive market, or rather personalized prices as in a Lindahl equilibrium? This should be a subject for further research. Who should abate carbon emissions? An international viewpoint 8 REFERENCES [1] Baumol, W.J. and W. Oates, (1977 and 1988) The Theory of Environmental Policy, Cambridge University Press. [2] Chichilnisky, G. (1993) "North-South Trade and the Dynamics of Renewable Resources", Structural Change and Economic Dynamics, Oxford University Press, to appear. [3] Chichilnisky, G. (1992) "Global Environment and North-South Trade" Technical Report No. 31,Stanford Institute of Theoretical Economics, Stanford University, Stanford California 93405. [4] Chichilnisky, G. (1993)"The Abatement of Carbon Emissions in Industrial and Developing Countries", The International Conference on the Economics of Climate Change, OECD/IEA Paris, 14-16 June 1993. [5] Chichilnisky, G. and G. M. Heal (1993) "Global Environmental Risks" Journal of Economic Perspectives, Symposium on Global Climate Change, in press. [6] Coppel, J.(1993) "Implementing a Global Abatement Policy: Some Selected Issues", The International Conference on the Economics of Climate Change, OECD/IEA Paris 14-16 June 1993. [7] Heal, G. (1990) "Economy and Climate: A preliminary Framework for Microeconomic Analysis" Agricultural Management and Economics: Commodity and Resource Policies in Agricultural Systems, (eds. R. Just and N. Bockstael), Springer Verlag, 1990. [8] Atkinson, A. and J. Stiglitz, J. (1980) Lectures on Public Economics, McGraw Hill. [9] Weyant, J. (1993) "Costs of Reducing Global Carbon Emissions: An Overview" Journal of Economic Perspectives, Symposium on Global Climate Change, in press. 1993-94 Discussion Paper Series Department of Economics Columbia University 420 W. 118 St., Room 1022 New York, N.Y., 10027 Librarian: Angie Ng The following papers are published in the 1993-94 Columbia University Discussion Paper series which runs from November 1 to October 31. Domestic orders for discussion papers are available for purchase at $5.00 (U.S.) each and $140.00 (U.S.) for the series. Foreign orders cost $8.00 (U.S.) for individual paper and $185.00 for the series. To order discussion papers, please send your check or money order payable to Department of Economics, Columbia University to the above address. Please be sure to include the series number for the paper when you place an order. 671. Investment in U.S. Education and Training Jacob Mincer ( Nov. 1993) 672. 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Herd Behavior, the " Penguin Effect ", and the Suppression of Informational Diffusion: An Analysis of Informational Externalities and Payoff Interdependency Jay Pil Choi ^ 'yt£ ,--- '„ -^ c % - 1992-93 DISCUSSION PAPER SERIES Department of Economics Columbia University 420 W 118th St., 1022 IAB New York, NY 10027 Librarian: Ms. Angie Ng The following papers are published in the 1992-93 Columbia University Discussion Paper Series which runs from July 1 to June 30. Individual discussion papers are available for purchase at $5.00 (U.S.) each for domestic orders and $8.00 (U.S.) for foreign orders. Subscriptions to the Series are available at a cost of $185.00 (U.S.) per foreign subscription and $140.00 (U.S.) per domestic subscription. To order discussion papers, please send your check or money order payable to Department of Economics, Columbia University to the above address. Please make sure 10 include the series number of the paper when you place an order. 612. 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