Bilateral Negotiations on Emissions Abatement among Heterogeneous Countries

Transcription

1 Noah Kaufman Working Paper Fall 2008 Bilateral Negotiations on Emissions Abatement among Heterogeneous Countries I. Introduction The successful implementation of international environmental agreements ( IEA ) regarding the abatement of greenhouse gas emissions will require participating countries to overcome a number of obstacles. First, and extensively covered in the literature, is the issue of enforcement. Since there is no world government, IEAs are not binding in any meaningful sense, so an agreement must be selfenforcing. A self-enforcing agreement has two components: a participant cannot be made better off by leaving the agreement, and a non-participant cannot be made better off by joining the agreement. Selfenforcing agreements are very tough to achieve in practice because of the strong incentives to free-ride that result from the non-excludable nature of abatement benefits. Second, and far less frequently covered in the literature, is the reality that the efficacy of an IEA will depend in large part on the participation of a small number of specific and heterogeneous countries. In particular, as of 2004, the U.S., the EU, China and India accounted for over 60% of annual manmade carbon dioxide emissions 1, with this percentage expected to grow only larger in the coming years. Any agreement that is unable to support these specific countries will in all likelihood result in an insignificant improvement over unilateral actions. Eyckmans and Finus (2007) divide the world into six regions and use a revised version of the popular RICE model 2 to simulate the global welfare impacts of coalitions of particular regions to abate greenhouse gas emissions. They conclude that the identity of members may matter more than the number of participants for the success of cooperation. Put differently, the commonly held view that high participation indicates success of an IEA proves to be wrong. In particular, in their simulations of the welfare impacts of potential coalitions, China and the Rest of World region (including primarily India and other developing countries) are included in each of the top 12 welfare increasing coalitions. For these reasons, the inclusion in an IEA of specific, pivotal 1 Data per Carbon Dioxide Information Analysis Center, 2 Model created by Nordhaus and Yang (1996) 1

2 countries is an additional layer of complexity added to the difficulties of achieving self-enforcing agreements. The Kyoto Protocol is the result of an IEA among many non-pivotal countries. The developing countries are not responsible for any meaningful abatement, and the U.S. has refused to participate as long as developing countries such as China and India are not given abatement responsibilities 3. Kyoto may be a step in the right direction, but it will likely have only a small impact on the global growth of greenhouse gas emissions. Despite the difficulties mentioned above, the economics literature has recently produced a number of papers that predict meaningful international cooperation regarding the abatement of greenhouse gas emissions, in effect overturning Barrett s (1994) result that a high degree of cooperation can be achieved only when the differences between global net benefits under the non-cooperative outcome and the full cooperative outcome are small. Specifically, Barrett (2001), McGinty (2006), and Caplan and Silva (2007) are among the papers with optimistic predictions of international cooperation compared to Barrett s original model. In this paper, I attempt to explain why the predictions of these recent papers have not been mirrored by any real world examples of cooperative success. Barrett (2001) lays the conceptual foundation for the predictions of increased cooperation by demonstrating that certain asymmetries between countries promote greater global cooperation. He finds that if there are countries with differing benefits to an IEA, the countries that benefit the most can pay those that benefit the least in return for their cooperation. This diminishes the problem of freeriding since the differences between countries essentially commit them to particular roles in the process. Barrett assumes rich countries pollute more and benefit more from abatement activities, and should therefore transfer resources to poor countries, whereby efficiency in the model is increased and both countries can potentially realize gains above a non-cooperative outcome. Similarly, McGinty (2006) argues that symmetric models may vastly understate the degree of abatement achievable by a self-enforcing IEA, and, the conventional wisdom that self-enforcing IEAs cannot achieve substantial gains when the gains to cooperation are large does not hold when nations are asymmetric. In the McGinty model, countries differ in benefits and costs of abatement. As in Barrett (2001), McGinty s solution requires international transfers among signatories to increase efficiency and to induce significant cooperation among asymmetric countries. 3 Text of a Letter from the President to Senators Hagel, Helms, Craig, and Roberts, March 13,

3 Caplan and Silva (2007) employ a representative agent model with two regions that are identical with respect to preferences and technologies, but differ in endowments. They describe a three stage process in which regions first choose to participate in an IEA, then select their optimal policies, and finally consent to transfers from an international organization. The paper concludes that as long as the international organization is the Stackleberg follower, it can align the incentives of the regions and induce a scheme that is equitable, efficient and implementable in equilibrium. These results are discussed in more detail in Section V. In the model presented below, I will change the assumptions from the literature in a few key respects. First, as in Caplin and Silva, but unlike much of the literature, I will consider bilateral negotiations between developed and developing regions. This focuses on the specific, pivotal countries mentioned above, and avoids cooperative but ineffective solutions like Kyoto. Next, I will consider a different type of asymmetry among regions. The heterogeneity in the papers mentioned above relates to the costs and benefits of abatement, and in certain cases to the endowments of resources. None of these papers consider any underlying differences in preferences regarding abatement of greenhouse gas emissions. Considering the wide range of actual responses we have seen around the world to the threat of environmental damages, the assumption that the benefits from emissions abatement enter the utility functions of each region identically could be a serious oversimplification of reality. For this reason, I will consider the impact of differing preferences across regions. Finally, the model will use an explicitly specified utility function for each region that emphasizes corner solutions. This has two potential advantages compared with the utility functions seen in Caplan and Silva (2007), among others. The previous literature has assumed that regions have smooth utility functions, which will not lead to corner solutions in general due to Inada conditions. However, in the real world, we have witnessed no meaningful cooperation on greenhouse gas abatement between countries such as the U.S. and China, and many developing countries have stated they cannot afford to slow down the growth of their economies to combat a problem that was largely created by the developed world. It is therefore important to allow for the possibility that these countries can rationally choose not to contribute at all to global abatement. In other words, it is important to consider corner solutions in the model. Another advantage of using specified utility functions is that they permit a more intuitive interpretation of the model s findings compared to the unspecified utility functions seen in the literature. 3

4 I conclude that cooperation between developed regions such as the U.S. and the E.U. and developing regions such as China and India could potentially be impossible to achieve in the near future. In fact, the cooperation of these developing countries may not necessarily lead to increased efficiency as the literature has suggested. The model presented in this paper is primarily intended to point out the uncertainty with which we should view the predictions of recent papers on this topic. The contribution of this uncertainty is the signal it sends to developed countries that have been hesitant to unilaterally tackle the issue of greenhouse gas emissions. Bush administration officials, among others in the developed world, have long held the view that unilateral abatement would in effect surrender their countries bargaining chips, and allow developing countries to continue to free ride. This paper indicates that waiting for the cooperation of developing countries may be a waste of time. Unilateral emissions abatement may be the only option available. The structure of the remainder of this paper is as follows. Sections II presents a model economy. Section III characterizes Pareto efficient solutions to the model. Section IV looks at a decentralized endowment economy with heterogeneous regions, and the potential resulting competitive equilibria. Section V looks at the potential for cooperation from the use of international resource transfers. Section VI expands on the implications of the transfers needed to induce international cooperation. Section VII concludes. II. The Model Following Caplan and Silva, I consider an economy consisting of two regions indexed by j, j=1,2. Region 1 will represent a developed region such as the U.S. or the E.U., and region 2 will represent a developing region such as China or India. Each region is assumed to have a central regulator that chooses its region s policies by maximizing the total utility of the region, which is positively dependent on both consumption and abatement of global greenhouse gas emissions 4. Indifference curves are assumed to be L-shaped in the consumption-global abatement plane: U(a j, c j, x j + x -j ) = min{a j * c j, x j + x -j }, for j= 1,2, 4 The convention in the literature is for utility to be negatively dependant on emissions. I assume positive dependence on emissions abatement because it simplifies the analyses in the following sections. 4

5 y-axis: Total Abatement Contributions (x j + x -j ) where c j 0 is the total consumption of region j, x j 0 are contributions to global abatement (thus x j + x -j = total global abatement), and a j is a parameter for the environmental awareness of region j. Environmental awareness refers in this model to a region s level of concern for the damages that will be inflicted on the environment by greenhouse gas emissions. I assume an endowment economy in which the regulator for region j must adhere to the following budget constraint: c j + x j = w j, for j=1,2, where w j is region j s endowment, representing the region s annual income or a measure of economic growth, which for simplicity is exogenous in this model. The units are adjusted so that each good has a price equal to one. On account of the Leontief utility functions, each region will attempt to equalize global abatement (x j + x -j ) and consumption multiplied by the environmental awareness parameter (a j * c j ). In other words, each region has increasing preferences in both today s consumption and the consumption of future generations (which will be positively impacted by abatement contributions). The parameter a j determines the relative weights placed on the present versus the future by way of the complementarity between the level of environmental awareness and global abatement spending. A high level of environmental awareness will lead to a relatively large portion of the resource endowment used to fund global abatement, while a low level of awareness will lead to larger expenditures on consumption goods. Taking the abatement contribution of the other region as given, each region s maximization of its utility will lead to one of the two following results. The first, displayed as point A in Chart 1 below, Chart 1 Chart 2 Budget Constraint 45 degree line Budget Constraint 45 degree line x -j B Indifference Curves x j A x -j x-axis: Environmental Awareness Parameter (a j ) * Consumption (c j ) 5

6 occurs when region j has the resources required to equalize the two terms of the utility function. The second result, displayed as point B in Chart 2, occurs when region j does not have the resources required to equalize the two terms of the utility function (since x -j > a j * w j ), and therefore contributes only to consumption (c j = w j, x j = 0). The regions preferences differ only in regard to the parameter for environmental awareness. I assume that a 1 > a 2. In other words, holding all else equal, contributions to global abatement are more beneficial to a developed region than to a developing region. This assumption requires that there are fundamental differences between developed and developing regions preferences toward the abatement of emissions. The following are brief justifications of this assumption. Anecdotally, there is plenty of evidence from the real world to suggest that as a region develops economically, it also develops a heightened concern for the long-term future of the environment. To begin with, the countries with binding emissions targets under the Kyoto Agreement are generally the most developed countries in the world, less the U.S. The developing countries have thus far been unwilling to take this step. This is hardly surprising since many developing countries, China and India included, have been somewhat preoccupied with more imminent concerns of widespread poverty. It seems only natural that until the necessities for survival can be provided to citizens, countries will focus more on their current issues and less on those of the future. In this way, abatement of emissions acts as a luxury good. The assumption of a 1 > a 2 requires further that this difference in environmental awareness would remain even if the regions endowments were equal. Caplan and Silva (2007), among other previous papers, implicitly assumes that rich and poor regions become identical when transfers of resources serve to equalize endowments. However, regional preferences have been cultivated over many generations, influenced undoubtedly not only by wealth but also by other cultural factors. Developed and developing regions have differing preferences toward the environment that in all likelihood would not disappear immediately due to a transfer of resources. Consider an example involving two individuals in a comparable situation. One earns $1 million per year and plays tennis twice per week, and the other earns $20 thousand per year and plays no tennis. Would equalizing their incomes immediately cause them to play an equal amount of tennis? Or would the previously poor individual spend his additional resources on more familiar goods? Applying this metaphor to the current situation, developed countries have been able to spend resources in recent decades not only on directly combating environmental damages, but also on educating their citizens on the importance of becoming better stewards of the environment. This education gap has created an 6

7 abundance of environmental advocates in developed regions who will derive a greater benefit from abatement contributions than will less educated citizens. This greater benefit from abatement contributions is represented by the difference between a 1 and a 2 in the model. More formally, the difference between a 1 and a 2 can be justified through the treatment of a j as an endogenous variable in region j s optimization problem. In this case, region j would need to invest resources in a j to raise its level of environmental awareness. This idea of endogenous preference formation follows from Becker and Murphy (1988) and Mulligan (1997), among others. Rapaport and Vidal (2007) use endogenous preference formation to model the intergeneration altruism of parents toward their children. In their model, all parents are affected to some extent by the welfare of their children, but they can also invest their time and other resources in shaping their own preferences toward more concern for their children when they realize that this change will raise their own utility: It is because they rationally anticipate the effects of their actions on their future preferences and life-cycle utility that parents purposefully accumulate intergenerational altruism through the purchase of childoriented goods (e.g. time spent interacting with children). Their model assumes that this intergenerational altruism increases by some function of the investment of resources. Rapaport and Vidal s measure of parent-to-child altruism has a natural analogous interpretation in the setting of preferences toward environmental issues. Investing time and resources in improving the environment provides a benefit to environmentally educated individuals that cannot simply be measured by the direct impact on the environment of global emissions abatement. To include endogenous preference formation in this model, each region would choose levels of consumption, contribution to global abatement and investment in environmental awareness to solve the following utility maximization problem: Max [Min(f(q j ) * c j, x j + x -j )], such that c j + x j + q j = w j, where q j refers to the resources invested in environmental awareness and f(q j ) refers to the level of environmental awareness. I assume f is a strictly positive, strictly increasing and strictly concave function. Rapaport and Vidal establish in their model that parents invest resources to accumulate parentchild altruism if and only if their wealth exceeds a specific endogenously determined threshold, which is interpreted as the minimal level of income beyond which individuals have satisfied their own physiological constraint and can start to shape their preferences by honing their altruistic trait beyond its natural degree. I show a similar result below. If a region s endowment of resources is below a 7

8 certain threshold of economic growth, this region will not invest in the accumulation of environmental awareness. Proposition 1: If w j > w b, there exists a unique q j є (0, w j ) solution to region j s maximization problem. If w j < w b, the solution to region j s maximization problem is q j = 0. The proof is given in Appendix A. It follows that assuming the relative endowment of the developing region is below this threshold, only the developed region will invest in environmental awareness. On account of the assumptions on the function f, f(q 1 ) > f(0). In other words, the environmental awareness of the developed region is strictly greater than that of the developing region, or, a 1 > a 2. III. Pareto Efficiency A Pareto efficient allocation in this model is obtained by selecting {c j, x j } j=1,2 to maximize: U 1 (a 1, c 1, x 1 + x 2 ) subject to: U 2 (a 2, c 2, x 1 + x 2 ) V, and (1) c 1 + c 2 + x 1 + x 2 = w 1 + w 2, where V is a strictly positive constant. First, consider the case of unspecified, smooth utility functions as in Caplan and Silva. It is straightforward to show that equation (1) and the following conditions characterize a Pareto efficient solution: (2) U 1 x 1 / U 1 c 1 = 1 U 2 x 1 / U2c 2 (3) U 2 x 2 / U 2 c 2 = 1 U 1 x 2 / U 1 c 1, where the notation U 1 c 1 refers to the partial derivative of region 1 s utility function with respect to its own consumption. I will return to the interpretation of these conditions when discussing the decentralized scenario in the next section. With the Leontief preferences of this model, a Pareto efficient allocation must satisfy equation (1) and one of the three following sets of conditions: Case 1 High Global Welfare Solutions: (4) a 1 * c 1 = x 1 + x 2 (5) a 2 * c 2 = x 1 + x 2 Case 2 Low Global Welfare Solution A: 8

9 a 1 * c 1 = x 1 + x 2 a 2 * c 2 < x 1 + x 2 Case 3 Low Global Welfare Solution B: a 1 * c 1 < x 1 + x 2 a 2 * c 2 = x 1 + x 2 To see why efficiency requires one of these cases to be satisfied, first note that if neither equation (4) nor (5) holds with equality, taking resources from the larger sides of the equations and distributing them to the smaller sides will be a Pareto improvement. Next, note that neither a 1 * c 1 > x 1 + x 2, nor a 2 * c 2 > x 1 + x 2 can occur in an efficient allocation, because in that case, a region could be made better off and the other region no worse off by shifting resources from consumption to abatement contributions. Thus, only the three cases described above remain. The level the global welfare (U 1 + U 2 ) is necessarily higher in Case 1 than in either Cases 2 or 3. This follows due to the concavity of the minimum function. Since U 1 + U 2 = min{a 1 * c 1, x 1 + x 2 } + min{ a 2 * c 2, x 1 + x 2 } is the sum of two identical and strictly concave functions, its value will be greatest when resources are distributed such that the arguments inside the two functions are equal. This is precisely the situation in which equations (4) and (5) hold. IV. The Decentralized Scenario When there is no cooperation among regions, each region j will solve its own Cournot-style maximization problem subject to its budget constraint, taking the abatement action of the other region as given. I assume the endowment of region 1 is strictly greater than that of region 2, since region 1 represents the developed region. Region j solves: Max [Min(a j * c j, x j + x -j )], such that c j + x j = w j. The positive impacts of each region s abatement spending on the other region s utility are externalities unaccounted for in the utility functions. 9

10 First, let us return to the general case with smooth utility functions. Along with the budget constraint, the following conditions, stating that each region s marginal rate of substitution between abatement contributions and consumption are equal, characterize a competitive equilibrium: (6) U 1 x 1 / U 1 c 1 = 1 (7) U 2 x 2 / U 2 c 2 = 1 It is evident that the externalities lead to an inefficient solution. Comparing equations (6) and (7) to the efficient conditions of equations (2) and (3), the inefficiency results from the terms in (2) and (3) expressing the ratio of the marginal utility to region j of an additional unit of abatement by region -j to the marginal utility of consumption of region j. Caplan and Silva refer to this type of inefficiency as externality distortion 5. The Leontief preferences of this model, however, produce different results. As I will show below, the efficient Cases 1 and 2 will be decentralized equilibrium solutions. To see this, note that with the assumptions of w 1 > w 2 and a 1 > a 2, region 1 will always have the necessary resources to ensure that the following condition holds with equality: (8) a 1 * c 1 = x 1 + x 2 The condition a 2 * c 2 > x 1 + x 2 can clearly never hold in equilibrium. If it did hold, region 2 would shift resources from consumption to abatement spending. A resulting equilibrium must therefore fall into either Case 1 or Case 2 of the efficient allocations described in the previous section. The relative endowments will determine when the best responses of the regions will result in an efficient, High Global Welfare Solution, and when they will result in an efficient, Low Global Welfare Solution. Charts 3 and 4 below display why the utility function specifications are important. Chart 3 displays the resulting equilibria for two choices of x 2. Note that the best response curve for region 1 is the 45 degree line from the origin. At any point along this line, condition (8) will hold with equality. When region 2 selects an abatement contribution of x 2, the efficient allocation A will result. When region 2 selects an abatement contribution of zero (x 2 =0), the allocation that results (point B) will still be efficient (because it is still on the 45 degree line). Therefore, region 1 s utility level will change based on the abatement contribution of region 2, but this change will not impact efficiency. 5 In Caplan and Silva s model, there is a second type of inefficiency, referred to as market distortion, that results from changes in the international terms of trade between a polluting and a non-polluting good. Market distortion will not occur in this paper s model because of the assumption of only one consumption good. 10

11 ` Chart 3 Chart 4 Budget Constraint 45 line / Best Response Curve 45 line C x 1 x 2 x 1 A Indifference Curves x 2 D x 2 x 1 B x 1 x 2 x-axis: Environmental Awareness Parameter (a 1 ) * Consumption (c 1 ) Indifference Curves Chart 4 displays the general case in which region 1 has a smooth utility functions. The same two choices of x 2 are shown. A shift in region 2 s abatement contribution from x 2 to zero (x 2 = 0) will shift the equilibrium from point C to point D. As long as the term for the externality distortion is nonzero ( U 2 x 1 / U 2 c 2 = 0 ), neither of these points will be efficient solutions. Potential equilibrium allocations in the model with Leontief preferences can therefore be grouped into two categories that I will label E1 and E2: E1: a 1 * c 1 = x 1 + x 2 = a 2 * c 2, c 1 < c 2 x 1 > x 2 ; E2: a 1 * c 1 = x 1 + x 2 > a 2 * c 2, x 1 > x 2 = 0. Type E1 equilibria are High Global Welfare Solutions, as described in the previous section. For these allocations, the regions have the same total utility. Since region 1 has a higher level of environmental awareness than does region 2 (a 1 > a 2 ), it prefers to devote a lower portion of its endowment of resources to consumption. Since c 1 < c 2 and w 1 > w 2, it follows from the budget constraints that region 1 s contribution to global abatement is strictly higher than the contribution of region 2 (x 1 > x 2 ). 11

12 Type E2 equilibria are Low Global Welfare Solutions. For these allocations, the utility of region 1 is strictly greater than that of region 2. Region 2 does not contribute at all to global abatement in these equilibria. To see this, note that if x 2 were strictly positive, and (9) a 2 * c 2 < x 1 + x 2, then region 2 would shift resources from abatement contributions to consumption until a 2 * c 2 = x 1 + x 2. It follows that as long as condition (9) is an inequality, x 2 = 0. Type E1 equilibria will result when the difference in initial resource endowments is relatively small. In this situation, the relative benefit that region 1 receives from its greater endowment is counteracted by the relative benefit region 2 receives by contributing less to the public good. But while the difference in endowments can continue to grow unboundedly, region 2 cannot continue to contribute less to the public good (since negative abatement contributions are not feasible in this model). Once region 2 s contribution to global abatement is zero, any additional divergence in endowment will strictly benefit region 1. Type E2 equilibria will result from initial resource endowments for which the difference between w 1 and w 2 is beyond this threshold. Even though efficiency is achieved in equilibrium, total global welfare could be greater if the endowments of resources were closer to each other. This result that global welfare can be increased by transferring resources to the developing region mirrors many of the results in the literature. I will discuss this connection between this paper and the literature further in the next section. Type E2 equilibria are far more justifiable as depictions of reality than type E1 equilibria. In a type E1 equilibrium, the total consumption of the developing region is greater than that of the developed region. In the real world, this is clearly not the case. Data show that developed countries consume more and have far greater endowments of resources as defined in this model. Table 1 below displays GDP values for the relevant regions: Table 1: GDP and Population Statistics GDP Population Country/Region ($Billions) (Millions) European Union 14, United States 13, People's Republic of China 6,991 1,327 India 2,989 1,140 12

13 Moreover, there has been little to no cooperation in regard to greenhouse gas abatement between the heterogeneous regions that are discussed in this paper. Consistent with the characterization of the type E2 equilibria, developing countries such as China and India have been hesitant to risk slowing down the growth of their economies by devoting resources to emissions abatement efforts. On the other hand, the E.U. has already acted virtually unilaterally with a program to decrease global greenhouse gas emissions. And despite the inaction of the U.S. government, there is widespread support in the U.S. for Congress to follow the E.U. s lead in the upcoming years. V. A Three-stage Cooperative Game The recent literature has been optimistic in predicting cooperation among heterogeneous regions regarding the abatement of greenhouse gas emissions. Typically, this cooperation is achieved via the actions of an international organization ( IO ) with the ability to transfer resources among participating countries. Caplan and Silva (2007) describe an economy similar to the model in this paper, with bilateral negotiations between the central regulators of a rich and poor region. In this section, I will briefly explain how the game theoretic process of their model induces cooperation in an efficient and implementable equilibrium, and how this process could be applied to the model I have described above. Caplan and Silva utilize a three-stage game among a rich region, a poor region, and an IO. In the first stage, each region decides whether or not to participate in a coalition with the other. If either region decides not to participate, in the second stage, both regions simply maximize their own utility, as in the decentralized scenario of the previous section. If both regions choose to participate in the coalition, however, then each will choose its policy taking as given not only the action of the other region, but also the anticipated action of the IO in the third stage. In this third stage, with the regions policies already determined, the IO acts as a Stackelberg follower and transfers resources from one region to the other in accordance with a previously agreed upon equity principle. Specifically, the IO retains the relative rankings of international welfare levels of the decentralized case by ensuring that the ratios of each region s utility in the cooperative case to its utility in the decentralized case are equal. With this setup, Caplan and Silva find that efficiency in their model is restored since the anticipation of the transfers serve to align the incentives of the regions by forcing them to account for the impact of their own abatement spending on the other region s utility. The excess burden is therefore removed, and the IO has a larger pool of resources to distribute among the regions. The transfer scheme is implementable (it is a subgame perfect equilibrium) because the equity principle 13

14 ensures that each region is at least as well off as in the decentralized case, so each region will choose to participate. Cooperation among the rich and poor regions in abating global greenhouse gas emissions has thus been achieved. If a similar multi-stage game with international transfers is set up in this paper s model with Leontief preferences, transfers can no longer improve efficiency. As shown above, the equilibria are already efficient. Moreover, it is straightforward to show that any transfer of resources from region 1 to region 2 will make region 1 strictly worse off than had the transfer not occurred 6. Therefore, international transfers cannot be sustained in any subgame perfect equilibrium in this model. VI. Transfer Implications While transfers cannot increase efficiency in this model, it may be useful to determine the necessary transfers to induce the developing region to contribute to abatement, and therefore reach a higher level of total global welfare. Most other papers in the recent literature utilize cooperation on emissions abatement as a vehicle for increasing efficiency and total global welfare. However, these papers do not offer any interpretation of the magnitudes of the required transfers. Given the fairly innocuous assumption that smaller transfers are more politically feasible than larger transfers, the size of transfers could be a factor in explaining why we have not seen the type of cooperation predicted in the literature. The explicit utility functions of this paper yield a straightforward interpretation of the magnitudes of the necessary transfers to induce the developing region to contribute. Since this model is very nearly a special case of the models from the literature, the magnitudes of the necessary transfers will likely be similar. Consider the more realistic case described in Section IV in which the endowments are such that a type E2 equilibrium (a Low Global Welfare Solution) results. In this equilibrium, region 2 will not contribute to global abatement. Assuming for a moment that region 1 would agree to resource transfers to promote cooperation and higher global welfare, what level of transfers to region 2 would be necessary to shift to a High Global Welfare Solution? The transfers would need to be sufficient to reduce to the difference in endowments between the regions within the threshold of endowment divergence described above. Only then would a type E1 equilibrium (a High Global Welfare Solution) result. 6 This is due in part to the implicit assumption that the marginal costs of abatement to the regions are equal. 14

15 Recall that in a type E1 equilibrium, the consumption of region 2 is higher than that of region 1. Simple back-of-the-envelope calculations can roughly display the potential implications of this result. Total 2007 consumption was approximately $9.7 trillion in the U.S., $4.9 trillion in China and $2.1 trillion in India 7. In order to just equalize the consumption of the developed and the developing regions, a $2.4 trillion transfer from the U.S. to China or a $3.8 trillion transfer from the U.S. to India would be required. And since the consumption of region 2 actually needs to be strictly greater than that of region 1, even greater transfers would be necessary for a High Global Welfare Solution to be an equilibrium result. Transfers of this magnitude, even if individually rational, would arguably be politically infeasible regardless of how they were structured. VII. Conclusion This paper asks why previous papers have predicted meaningful international cooperation on the abatement of greenhouse gas emissions, and yet the real world has not produced examples of this success. I have offered a few potential explanations. First, the literature generally has not focused on the importance and unique challenges that come with the inclusion of a developing country such as China or India in the agreement. Additionally, depending of the form of the assumed preferences, an efficient solution may be one in which the developed region unilaterally contributes to abatement spending. With the Leontief preferences in the model I have presented, as long as the difference in resource endowments among the regions is above a certain threshold, efficiency does not involve any cooperation on abatement contributions. Finally, I have given an indication of the magnitude of international resource transfers needed to raise global welfare to its highest possible level. The necessary transfers may be too large to be politically feasible. Even if these transfers were optimal, a second best solution may be needed. Previous papers have not reached these conclusions. They generally have not focused on the importance of the participation of particular developing countries such as China and India, and the unique challenges that inducing their cooperation may present. Additionally, the assumption in previous papers that regions have identical preferences toward global abatement contributions may 7 Using GDP data for the U.S., China and India, and consumption data for the U.S., I assumed the ratio of consumption to GDP is equal across countries. 15

16 disregard underlying cultural differences among regions, and generally does not allow for the corner solutions that have been observed in real world negotiations. Finally, previous papers have not considered the magnitudes of necessary transfers. These results indicate that the recent policies of the U.S. and other developed countries to refrain from abatement spending until developing countries such as China and India agree to cooperate may be misguided. It is often assumed that although the developed countries were responsible for the vast majority of the emissions in the atmosphere, all countries will need to act in concert to respond to the problem. However, if cooperation with developing countries such as China and India cannot be achieved, unilateral action of the developed countries may be the only remaining option. This model in this paper could be improved in a number of ways going forward. First, I have considered only bilateral negotiations. While a small number of autonomous regions do contribute a huge percentage of greenhouse gas emissions, it would be useful to consider negotiations between at least three or four regions as well. Additionally, the assumption that the marginal benefit of abatement contributions is equal across regions for all levels of contributions may need to be revised. Finally, the concept of environmental awareness that I have considered in this paper may be better suited for a dynamic rather than a static model. Along these lines, it may be interesting to examine a model in which the preferences of the developing region can evolve as the region develops. Appendix A: Following Rapaport and Vidal, I will show that there exists an endogenously determined wealth threshold below which region 2 will not contribute to accumulating environmental awareness. First, I assume that the regions are in the efficient equilibrium in which: (10) f(q 1 ) * c 1 = x 1 + x 2 (11) f(q 2 ) * c 2 = x 1 + x 2. I substitute both conditions (10) and (11) into (x j + x -j ) in (1), and solve these two resulting equations simultaneously, yielding: (12) c j = f(q -j ) (w j + w -j - q j - q -j ) / [(1 + f(q j )) (1+f(q -j )) 1], for j=1,2. Then, I solve for the level of global abatement by plugging equations (12) back into (1): x 1 + x 2 = f(q 1 ) f(q 2 ) (w 1 + w 2 q 1 q 2 ) / [f(q 1 ) + f(q 2 ) + f(q 1 ) * f(q 2 )] The maximization problem for the representative agent of region 2 can then be written with an equivalent reduced form utility function in terms of q j : 16

17 Max [H(q 2 )], where H(q 2 ) = f(q 1 ) f(q 2 ) (w 1 + w 2 q 1 q 1 ) / [f(q 1 ) + f(q 2 ) + f(q 1 ) f(q 2 )] Taking a derivative with respect to q 2, H (q 2 ) is the same sign as: (13) G(q 2 ) = f(q 1 )^2 * f (q 2 ) * (w 1 + w 2 - q 1 - q 2 ) - f(q 1 ) * f(q 2 ) * [f(q 2 ) * (1 + f(q 1 )) + f(q 1 )] I then take the derivative of (13) with respect to q 2 : (14) G (q 2 ) = -f(q 1 )^2 * f (q 2 ) + f(q 1 )^2 * f (q 2 ) * (w 1 + w 2 - q 1 - q 2 ) -f(q 1 ) * f(q 2 ) * *f (q 2 ) * (1 + f (q 1 ))] f(q 1 ) * f (q 2 ) * [f(q 2 ) * (1 + f(q 1 )) + f(q 1 )] Condition (14) is strictly negative since the function f( ) is strictly positive, strictly increasing and strictly concave. This has two implications. First, H(q 2 ) is strictly concave, so a solution to H (q 2 ) = 0 will result in a maximum value. Second, G(q 2 ) is strictly decreasing in q 2. Case 1: Assume q 1 = w 1, c 1 = x 1 = 0. Then, G(w 2 ) = - f(q 1 ) * f(q 2 ) * [f(q 2 ) * (1 + f(q 1 )) + f(q 1 )] < 0 An interior solution for q 2 (q 2 > 0) therefore requires G(0) > 0, which implies w 2 > f(q 1 ) * f(0) * [f(q 2 ) * (1 + f(q 1 )) + f(q 1 )] / [f(q 1 ) * f (0)+ = w a > 0, where w a is a minimum wealth threshold below which q 2 = 0. Case 2: Assume q 1 < w 1 G(w 2 ) will be unambiguously larger than it was in Case 1 in which q 1 = w 1, which leads to 2 subcases: Case 2a: G(w 2 ) >= 0 Since G(q 2 ) is strictly decreasing, q 2 = w 2, and therefore c 2 = x 2 = 0 Case 2b: G(w 2 ) < 0 Then, as in Case 1, G(0) > 0 for an interior solution, implying w 2 > w b > 0, where w b is a minimum wealth threshold below which q 2 = 0. In both Cases 1 and 2a, note that one region s consumption is zero, and therefore its utility is zero, which cannot be optimal with strictly positive endowments. Therefore, I exclude these cases from consideration, leaving Case 2b, in which w b is the endogenously determined threshold above which a region will accumulate environmental resources, and below which it will not. I have thus far assumed that equations (10) and (11) bind. This result can also be applied to the equilibria for which: f(q 1 ) * c 1 = x 1 + x 2 f(q 2 ) * c 2 < x 1 + x 2, 17

18 and x 2 = 0. To see this, note that there is an equilibrium of type E1 (see Section IV above) for which x 2 = 0 (this is the exact point at which an additional unit of divergence between the endowments will lead to an equilibrium of type E2). At this equilibrium, there is an efficient solution in which, due to the proof above, q 2 = 0. Region 2 must have been maximizing the product c 2 * f(q 2 ) at this point. If q 2 = 0 maximizes this product in the High Global Welfare equilibrium in which x 2 = 0, it will also maximize this product in the Low Global Welfare equilibrium in which x 2 = 0. Therefore, the endogenously determined minimum wealth threshold described above applies to type E2 equilibria as well. I have therefore shown that as long as region 2 s endowment is below a certain threshold, the decentralized solution will lead to an equilibrium in which the poor region does not invest in accumulating environmental awareness and potentially does not contribute at all to global abatement. References Barrett, S. (1994), Self-enforcing international environmental agreements, Oxford Economic Papers, 46, Barrett, S. (2001), International cooperation for sale, European Economic Review, Volume 45, Issue 10. Becker, Gary S., Murphy, Kevin M. (1988), A theory of rational addiction. Journal of Political Economy 96, Botteon, Michele and Carraro, Carlo (1997), Environmental Coalitions With Heterogeneous Countries: Burden- Sharing and Carbon Leakage, Fondazione Eni Enrico Mattei Working Paper No Buchner, B. and Carraro, C. (2006), US, China and the Economics of Climate Negotiations, Environmental Agreements: Politics, Law and Economics Caplan, Arthur J., Cornes, R. C., & Silva, E. C. D. (2003). An ideal kyoto protocol: Emissions trading, redistributive transfers and global participation, Oxford Economic Papers, 55, Caplan, Arthur J. and Silva, Emilson C. D. (2007), An equitable, efficient and implementable scheme to control global carbon dioxide emissions, International Tax and Public Finance. Chichilnisky, G., Heal, G., and Starrett, D. (2000), Equity and efficiency in environmental markets: global trade in carbon dioxide emissions, In G. Chichilnisky and G. Heal (Eds.), Environmental. Markets: equity and efficiency, New York: Columbia University press. Eyckmans, J., Finus, M. (2007), Measures to enhance the success of global climate change treaties, International Environmental Agreements: Politics, Law and Economics. Hoel, M., & Schneider, K. (1997). Incentives to participate in an international environmental agreement, Environmental and Resource Economics, 9(2), McGinty, M. (2006), International environmental agreements among asymmetric nations, Oxford Economic Papers. Mulligan, Casey B. (1997). Parental Priorities and Economic Inequality. The University of Chicago Press. Rapaport, H. and Vidal, J.P. (2007), Economic growth and endogenous intergenerational altruism, Journal of Public Economics 91, Silva, E. and Zhu, X. (2008), Global trading of carbon dioxide permits with noncompliant polluters, International Tax and Public Finance. 18