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1 KYOTO IN QUESTION: A NORTH-SOUTH-OPEC MODEL OF FOSSIL-FUEL USE AND GREENHOUSE-GAS EMISSIONS JAMES GAISFORD* AND JULIA SAGIDOVA** Draft: Do not cite or quote without permission. Comments and suggestions are welcome. ABSTRACT: This paper assesses the environmental efficacy of the Kyoto Protocol on climate change. On the theory side, we present an elegant four-sector North-South-OPEC model of the world economy where fossil fuel use leads to greenhouse gas emissions. Kyoto-style commitments, which reduce the North s emission cap but do not constrain the South, tend to cause increases in global emissions as dirty good production is displaced from the relatively clean North to the dirtier South. When Southern firms can sell emission credits to Northern firms as allowed under the Clean Development Mechanism, further increases in world emissions will occur if the South initially uses a sufficiently small proportion of world fossil fuel. Our empirical analysis adds sector control variables to environmental Kuznets curve regressions for CO 2 emissions. The empirical results strongly support our theoretical premise that high-income countries adopt less emission intensive production techniques in each sector and, thus, are cleaner than low-income countries. We also find evidence of surprising emissions intensity reversals whereby manufacturing, which is initially more emission intensive than agriculture or services, becomes less emissions intensive at per-capita incomes in the range of 15,000 USD. In empirical simulations these emission intensity reversals lead to a provocative positive assessment of the outcome of Kyoto. As developed countries adopt a greater proportion of manufacturing activity than would otherwise be the case so as to meet their emission reduction targets, developing counties would be induced to put greater emphasis on agriculture and/or services, which for most of them are cleaner activities. JEL Codes: F10, F12, F18 * Corresponding Author: James Gaisford, Department of Economics, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4. gaisford@ucalgary.ca. Telephone: Fax: , ** Julia Sagidova, Department of Economics, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4.

2 KYOTO IN QUESTION: A NORTH-SOUTH-OPEC MODEL OF FOSSIL-FUEL USE AND GREENHOUSE-GAS EMISSIONS ABSTRACT: This paper assesses the environmental efficacy of the Kyoto Protocol on climate change. On the theory side, we present an elegant four-sector North-South-OPEC model of the world economy where fossil fuel use leads to greenhouse gas emissions. Kyoto-style commitments, which reduce the North s emission cap but do not constrain the South, tend to cause increases in global emissions as dirty good production is displaced from the relatively clean North to the dirtier South. When Southern firms can sell emission credits to Northern firms as allowed under the Clean Development Mechanism, further increases in world emissions will occur if the South initially uses a sufficiently small proportion of world fossil fuel. Our empirical analysis adds sector control variables to environmental Kuznets curve regressions for CO 2 emissions. The empirical results strongly support our theoretical premise that high-income countries adopt less emission intensive production techniques in each sector and, thus, are cleaner than low-income countries. We also find evidence of surprising emissions intensity reversals whereby manufacturing, which is initially more emission intensive than agriculture or services, becomes less emissions intensive at per-capita incomes in the range of 15,000 USD. In empirical simulations these emission intensity reversals lead to a provocative positive assessment of the outcome of Kyoto. As developed countries adopt a greater proportion of manufacturing activity than would otherwise be the case so as to meet their emission reduction targets, developing counties would be induced to put greater emphasis on agriculture and/or services, which for most of them are cleaner activities. JEL CODES: F10, F12, F18 1

3 1. INTRODUCTION This paper presents both a theoretical and empirical assessment of the environmental efficacy of the Kyoto Protocol on climate change. There is now overwhelming scientific evidence of climate change, strong evidence that human economic activity may be a significant contributing factor and mounting evidence that the changes in climate will cause economic effects that are generally negative and often substantive. 1 Against this backdrop, policy action addressing climate change appears to be reasonable, if only on precautionary grounds. Although greenhouse gas (GHG) emissions are a negative public good warranting coordinated global policy action, the theoretical model developed in this paper suggests that the Kyoto agreement is seriously flawed. Not only are there problems with the basic structure of the accord, which lacks constraints on developing countries, but also with the so-called Clean Development Mechanism or CDM, which allows firms in unconstrained developing countries to sell emission credits. Kyoto-style commitments, which reduce the North s emission cap but do not constrain the South or OPEC, strongly tend to lead to increases in global emissions because the reduction in fossil fuel use in the cleaner North is more than offset in the dirtier South. Paradoxically, the theoretical model suggest that if Northern countries such as the US do not make commitments or countries such as Canada fail to fulfill their commitments, the increase in world emissions becomes smaller. When firms in the South can sell emission credits to Northern firms as allowed under the CDM, there will be further increases in world emissions if the South-OPEC region initially uses a sufficiently small proportion of world fossil fuel. Emission credits indirectly subsidize fossil fuel use in South, which may lead to an increase in world emissions. 2 While our theoretical model indicates that the Kyoto Protocol may fail the most fundamental litmus test of reducing global GHG emissions, our empirical analysis paradoxically suggests that fortuitous emissions intensity reversals could come to the rescue. There appears to be very strong empirical support for our premise that rich capital abundant countries adopt cleaner production techniques, mainly by engaging in fossil fuel-saving investment. The 2

4 empirical evidence also suggests that, while the manufacturing sector is dirtier than agriculture or services at the per-capita income levels of most developing countries, surprisingly the reverse appears to be true at the per capita income levels of most developed countries. Because of these emission intensity reversals, the empirical outcome of Kyoto could be mutually favourable. As developed countries adopt or, more aptly, retain a greater proportion of manufacturing activity than would otherwise be the case so as to meet their emission reduction targets, developing counties would be induced to put greater emphasis on agriculture and/or services. Consequently, each group of countries expands its relatively clean sector. This paper introduces an elegant four-sector North-South-OPEC model of the world economy where fossil fuel use leads to GHG gas emissions. While the model follows in the general-equilibrium tradition of assessments of international trade and the environment, 3 the structure of this model is of particular interest. The world economy is comprised of two principal regions, North and South, with the latter further divided into OPEC and non-opec sub-regions. While OPEC shares most key features with the rest of the South, its abundant natural resource endowment allows it to set the world price of fossil fuel above the competitive level. There are two intermediate goods, fossil fuel and electricity, and two final goods, one dirty and the other clean. Fossil fuel and both final goods are freely traded, but electricity is non-tradable. All four sectors use labour and capital, and there is a natural resource that is specific to the fuel sector. Fossil fuel and electricity are used by households and by all sectors except the clean sector. While all fossil fuel using activity causes GHG emissions, fuel-saving investment is possible. Figure 1 outlines the sectoral structure of production in the world economy. [Insert Figure 1 about here] While we assume that there is an underlying technology that is common to all regions, our model takes a long-run perspective where capital is supplied (perfectly) elastically. North is assumed to have a lower user-cost of capital than the South, say due to a lower risk premium. North s lower user cost is equivalent to a general technological advantage, which is more pronounced in capital-intensive activities, including fuel saving. Lower capital costs in the 3

5 North, thus, lead to greater fuel saving than the South. Since the two regions will then have different emissions intensity, shifting the production of dirty goods from North to South in response to Kyoto agreement tends to cause greater world emissions. In the initial pre-kyoto situation we assume that North has at least an indirect cap on overall GHG emissions. If there were also an exogenous emissions cap in South, then the success of Kyoto-style reductions in North s emissions cap would be automatic. World emissions would fall on a one-for-one basis with reductions in the North s cap. If the South s cap were endogenous and determined through a policy game, then the possibility of carbon leakage through increased free riding looms as a possible issue (Hoel, 1991). As in Copeland and Taylor (2005), favourable income effects, at least in theory, may also lead to a tighter cap and endogenous reductions in South s emissions. The possibility of free riding appears to understate the potential for carbon leakage under the Kyoto Protocol. Suppose that at initial income and consumption levels, South s marginal benefit from the abatement of GHG emissions is less than the marginal cost of abatement with given Northern emissions and its own emissions completely unrestrained. Then, rather than an internal solution to the policy game, which is assumed in much of the literature, there would be a boundary solution with zero fuel-saving investment in South. On theoretical as well as empirical grounds, therefore, the notion that the counties of the South have effective endogenous or exogenous cap appears highly problematic. Consequently, our theoretical model assumes that there are no effective direct or indirect environmental controls on GHG emissions in the South such that its pre-kyoto emissions price is equal to zero. Since the North s emissions price will typically be positive, there is a further incentive for more fuel-saving investment in the North than the South. While there have been many detractors, 4 some of the theoretical literature has been relatively sanguine about the Kyoto Protocol. In an important paper, Copeland and Taylor demonstrate that unilateral emission reductions by the rich North can create self-interested emission reductions by the unconstrained poor South (2005, 205) if the positive income effects in the South are sufficiently strong. Nevertheless, this endorsement of Kyoto is highly 4

6 conditional. Implementation of policies such as international permit trade, which in other contexts might be broadly beneficial, may be mutually immiserizing and lead to increased emissions. In Copeland and Taylor s (2005) Kyoto model factor price equalization arises because the technology is uniform worldwide and all regions including the South have endogenous emissions caps, which can be likened to factor endowments. Consequently, even in the absence of international permit trade, there is a fully efficient world equilibrium with equal emissions prices. Consequently, all countries adopt the same production techniques and sector emission intensities are uniform across countries. This is important for Copeland and Taylor (2005) and contrasts sharply with the theoretical model we develop. If there are only dirty and clean goods, and not dirty and clean countries, then shifting the production of dirty goods from North to South in response to Kyoto would not tend to lead to greater world emissions. To investigate the degree of support for our model versus that of Copeland and Taylor (2005), we introduce sector variables controlling the value-added mix of the economy to otherwise conventional environmental Kuznets curve regressions. The empirical evidence strongly suggests that there are clean and dirty countries as well as clean and dirty goods. With the exception of agriculture, marginal sector CO 2 emissions intensities eventually decline as per capita income increases. Overall, strong environmental Kuznets relations persist despite the introduction of sector control variables. Nevertheless, the introduction of sector controls does help to resolve why support for inverted U Kuznets relations for CO 2 emissions has been much weaker for predominantly agricultural developing countries than for developed countries (for example, see Schmalensee et al., 1997; Holtz-Eakin and Selden, 1995; and Dinda, 2004). Given that countries with low capital costs accumulate more capital and become high-income countries, our empirical finding that emissions intensities decline as per capita income increases dovetails nicely with our theoretical model. The empirical finding that agriculture and services become more emission intensive than manufacturing at per-capita incomes in the order of 15,000 USD per annum, however, opens up the possibility of unanticipated favourable outcomes from Kyoto. 5

7 2. A THEORETICAL MODEL OF TRADE, FOSSIL FUEL USE AND EMISSIONS 2.1 Foundations We construct four-sector model of the world economy where the use of fossil fuel leads to GHG emissions. Reductions in emissions are possible through investment in a fuel-saving technology, but costly. We assume that there are two regions indexed by g consisting of North, N, and South, S. South is further divided into, OPEC and non-opec sub-regions denoted by S1 and S2 respectively. There are four outputs indexed by j: a clean good, C; a dirty good, D; electricity, E; and fossil fuel, F. Since electricity will be assumed to be non-tradable, electricity prices will differ across countries such that p N E " p S E. For clean goods, dirty goods and fossil fuel, which we assume are freely traded, the domestic price in each country will be equal to a common world price where p N j = p S j = p W j. Further, p W C =1 given that the clean good is chosen as the numeraire. Inputs, which are indexed by i, consist of intermediate goods and the services of standard factors of production. In addition to being consumed by households, fossil fuel and electricity are used as intermediate inputs in the production of dirty goods, electricity and fossil fuel. The standard factors are: labour, L; capital, K; and a natural resource, R. While capital and labour are used in the production of all goods, the natural resource is a specific factor used only in the production of fossil fuel. As is standard in much of the literature, emissions, M, can be likened to an additional factor of production (Copeland and Taylor, 1995, 2005). GHG emissions arise wherever fossil fuel is used. The use of fossil fuel by households, and in the production of electricity and final goods is intended to capture major sources of GHG emissions from transportation, electrical generation and industry respectively. In addition, the use of fossil fuel in producing fossil fuel helps to account for increasingly emission-intensive activities such as oil sands production in the energy sector itself. While for clarity and tractability we follow the norm in much of the literature by assuming that the clean good leaves no environmental footprint, our empirical analysis will later show that this assumption is more restrictive than is often thought. In the current setting, the clean good does not produce emissions either directly through using 6

8 fossil fuel or indirectly through using electricity. Figure 1, summarizes the input-output structure of the world economy. Each sub-region is endowed with a natural resource, Y g R, which is a specific factor used in the production of fossil fuel. For simplicity, we abstract from natural resource depletion issues by assuming fixed reserves of the resource. The North and the non-opec South behave competitively on the world fossil fuel market and, thus, fully utilize their natural resource endowments. In contrast, OPEC sets a binding minimum price for fossil fuel, p W F = p S1 F, which is above the competitive equilibrium level, by limiting the use of its natural resource endowment. While setting the world price of fossil fuel is OPEC s signature role in the model, it is assumed to be similar to the non-opec South in all other respects. While labour and the natural resource are assumed to be conventional factors of production with fixed endowments, we take a long-run approach where the supply of capital is perfectly elastic. 5 We assume that the user cost of capital in South lower in than North, say due to a lower risk premium: p S K > p N K. (1) While the technologies per se are the same across countries, the lower user cost of capital in North is equivalent to a technological advantage that becomes more pronounced in capitalintensive activities. At equal emissions prices, therefore, North has an advantage in the dirty good, which we assume to be more capital intensive than the clean good. Emissions prices, however, are not likely to be equal. In contrast to Copeland and Taylor (2005), we assume an initial corner solution in emissions policies where there are no overall caps on GHG emissions in South, but the North has at least an indirect cap on its GHG emissions, which is denoted by Y MN. 6 While in general p M N " 0, the imputed price of emissions is likely to be positive in North as a result its cap. Since firms in South do not have to pay to emit, the pre- Kyoto emissions price in South is equal to zero. Although the Clean Development Mechanism (CDM) of the Kyoto agreement introduces the possibility of credit market integration, there are 7

9 likely to be political as well as economic constraints on credit market transactions. The European Union and many environmental groups argued against the CDM and remain suspicious of it. Consequently, much of our focus will be on small increases in the degree of credit market integration in the vicinity of an initial pre-kyoto situation. 2.2 Emissions and Fuel-Saving Investment On the one hand, each unit of fossil fuel used, whether in production or in household consumption, is assumed to always generate one unit of emissions regardless of the particular use or scale of that use. This appears to be a reasonable simplification of reality because the direct abatement of GHG emissions appears to have been of limited importance to date, as our empirical analysis will confirm later. On the other hand, we will allow emissions to be reduced indirectly through investment in an auxiliary fuel-saving technology, which is assumed to be uniform across regions and common to all fuel uses including household consumption. In particular, if 1" µ g actual units of fossil fuel are combined with "( µ g ) units of capital in region g, then one efficiency unit of fossil fuel will be obtained, where: "( 0) = 0, "( 1) # $, "#( $ ) > 0, "## ( $ ) > 0. (2) Consequently, µ g represents the fuel saving associated with obtaining one efficiency unit of fossil fuel. Further, in the absence of any capital invested in the fuel-saving technology, one actual unit of fossil fuel can be used to obtain one efficiency unit. So-called standard production and consumption processes will subsequently be defined with respect to the number of efficiency units of fossil fuel that they use. While our formulation of the fuel-saving technology as exclusively reliant on capital is somewhat extreme, fuel saving is typically a very capitalintensive activity. The opportunity cost of using an efficiency unit of fossil fuel in the North, " N, includes spending on 1" µ N actual units of fossil fuel and the associated emissions permits plus expenditures on the fuel-saving technology: 8

10 " N F = ( 1# µ N ) p S1 N ( F + p M ) + $ ( µ N ) p N K. (3) The opportunity cost of an efficiency unit of fossil fuel in the South, " S, is different because firms in South do not pay to emit but they may receive credit revenue from reducing their GHG emissions and, thus, their fossil fuel usage below a business as usual baseline. If we let µ S represent the business-as-usual fuel saving in South, then the fuel saved beyond this level, µ S " µ S, is potentially available to be sold as credits to Northern firms at a price of p M N. The level of fuel savings that is eligible to be sold as credits, however, is constrained to be less than or equal to ". Given that we must also impose a non-negativity restriction, the credit revenue associated with a standardized unit of fossil fuel can be written as max{ min { µ S " µ S,#},0}p N M. Consequently, the resultant opportunity cost of an efficiency unit of fossil fuel in South is: " S F = ( 1# µ S )p S1 F + $ ( µ S ) p S K # max{ min { µ S #µ S,%},0}p N M. (4) From the standpoint of individual firms, the business as usual fuel saving, µ S, is parametric. Firms minimize the opportunity cost of fossil fuel by choosing the level of fuel saving to equate the marginal cost and marginal benefit. The first-order condition, which always applies in North and also applies in South when credits are unconstrained, is: p F S1 + p M N = p g K "#( µ g ), g = N,S. (5) A region s fully optimal fuel-saving level is an increasing function of p O g ( F + p M ) p g K, the price fossil fuel plus emissions relative to capital: µ g = µ " p S1 N g ( ( F + p M ) p K ), g = N,S ; where: µ " 0 ( ) = 0, µ " #( $ ) =1 %# ( $ ) > 0. (6) For the most part, we heroically assume that the business-as-usual baseline level of fuel-savings by South and OPEC has a solid economic foundation and, thus, is equal to the constrained optimum fuel-saving level for the case where there is no integration of emissions markets. With " = 0, the first-order condition for minimizing the opportunity cost of fossil fuel in South would be p S1 F = p S K "#( µ S ) yielding the business as usual baseline: µ S = µ " S1 S ( p F p K ). (7) 9

11 For discussion purposes, we will assume that p S1 F > p S K "#( 0) so that µ S is strictly positive and firms in South, as well as North, employ the fuel-saving technology to some extent. When the emissions credit constraint is binding, the level of fuel saving selected by firms in the South is equal to the business as usual level plus allowable credits: µ S = µ S + " = µ # p F S1 S ( p K ) + ", whenever: 0 " # " µ $S %µ S. (8) In an initial pre-kyoto situation where " = 0 and emission credits are completely absent, the business-as-usual level of fuel savings prevails. If the emissions credit constraint is gradually eased allowing greater degree of integration of emissions markets, fuel savings in South rises gradually. Eventually " if is increased beyond µ "S # µ S, the constraint becomes non-binding and actual fuel savings remain at µ S = µ "S. Figure 2 consolidates some intuitive but important results, which follow immediately from the fact that capital and thus fuel-saving is less expensive in North. Proposition 1. The fuel-saving level in North exceeds the fully optimal level in South, which in turn is greater than or equal to the actual level in South, which finally is greater than the business-as-usual level in South. Since the user cost of capital is higher in South than North, it has a higher marginal cost of fuel saving and a lower fully optimal level of fuel saving, µ "S < µ "N, as shown in Figure 2. The lower marginal benefit in the business-as-usual versus fully optimal case in South implies that µ S < µ "S or that its business as usual fuel savings are less than its fully optimal emissions. [Insert Figure 2 about here] Substituting equation (5) into (3) and yields the optimum opportunity cost function for an efficiency unit of fossil fuel for North: " N F = " #N F p S1 F, p N N ( K, p M ), (9) where: "# F $N " p F S1 = "# F $N " p M N =1% µ N, Drawing on equations (4) and (8), we write the South s constrained opportunity cost function as: " S F = 1# µ $ S1 S ( ( p F p K ) # %)p S1 F + & µ $ S1 S ( ( p F p K ) + %) + %p N M ' " S F ( p S1 F, p S K, p N M,%). (10) 10

12 where: "# F S "p S1 F =1$ µ S + &% µ S S1 S ( ( ) $ ( p F p K ))& % ( µ S ) $1, "# S F " p N M = $, "# S F "$ = p S K %&( µ S ) ' p S1 F ' p N M < 0. In the vicinity of an initial pre-kyoto situation where there are no emission credits, an increase in the North s emission price, increases the opportunity cost of fuel saving in North but leaves that of South unchanged. An increase in OPEC s fossil fuel price results in a larger increase in the opportunity cost of fossil fuel use in South than North because South engages in less fuel saving. Finally, South s opportunity cost falls by p M N when the constraint on emissions credits is eased and credit revenue begins to be forthcoming. 2.3 Diversified Production In a long-run competitive equilibrium, price must be equal to unit cost in each sector. Consequently, the zero-profit conditions for the three traded goods are: p W C =1= " C p g g ( K, p L ), g = N,S ; (11) p W D = " D p g g ( K, p L ) + p g E a ED + # g F a FD, g = N,S ; (12) p S1 F = " F p g K, p g g ( L, p R ) + p g E a FE + # g F a FF, g = N,S. (13) And, for non-traded electricity, we can write: p g E = " E p g g ( ( K, p L ) + # g F a FE )$ EE, g = N,S ; where: " EE # ( 1$ a EE ) $1 %1. (14) Notice that the underlying production technologies use intermediate inputs in fixed proportions denoted by a ij for i = E,F, but they allow substitution between primary factors. Since a Fj denotes the required input of efficiency units of fossil fuel, we emphasize that the auxiliary fuelsaving technology is implicitly incorporated into overall unit costs through the opportunity cost functions for fossil fuel use. Given that the clean good is the numeraire, we can solve the zeroprofit condition for the clean sector in each region to determine its equilibrium wage, p g L. The Southern wage must be lower than the Northern wage such that p SO L < p N L so as to offset the higher user cost of capital in South and OPEC. Substituting equations (9), (10) and (14) into (12) yields the following diversified production conditions: 11

13 p W D = " #N F p S1 F, p N N ( K, p M )A FD + $ D p N N ( K, p L ), (15) p W D = " S F ( p S1 F, p S K, p N M,#)A FD + $ D p S S ( K, p L ). (16) where: " j (#) $ % j (#) + % E (#)& EE a Ej, A ij " a ij + a ie # EE a Ej. Here, A ij denotes the overall use of input i in the production of one unit of good j inclusive of any use of the input in the underlying electricity required for one unit of traded good j. The NN and SS curves in Figure 3 are graphical representations of the diversifiedproduction conditions given by equations (15) and (16) for the North on the one hand and South and OPEC on the other. The NN curve is upward sloping because a higher Northern emissions price raises costs and necessitates a higher world price for dirty goods if firms in North are to continue to break even. In the initial pre-kyoto equilibrium where firms in South and OPEC do not participate in North s credit market because " = 0, the world price of dirty goods that is required for firms in South and OPEC to break even is independent of the emissions price in North making the SS curve horizontal. A necessary condition for an internal equilibrium is that the intercept of the SS curves exceeds that of the NN curve or that the unit cost of dirty-good production in South or OPEC evaluated at the equilibrium wage and a zero price of emissions in North is larger than corresponding minimum average cost in North. Lemma 1. Diversified production of clean and dirty goods both in North and in the South is possible if and only if the production of the dirty good inclusive its underlying electricity is more capital intensive than the clean good when North s price of emissions is equal to zero. A proof is provided in the Appendix. In an equilibrium where both the North and the South are diversified, North s more favourable access to capital gives it a latent comparative advantage in the dirty versus clean good, which is then counterbalanced by the costs of emission permits. [Insert Figure 3 about here] The diversification conditions given in equations (15) and (16) can be solved simultaneously for the world price of dirty goods and the North s price of emissions. Consequently, there is an initial equilibrium with diversified production both in North and in 12

14 South and OPEC when the world price of the dirty good is p DW " and the Northern price of emissions is p MN ". 7 Afterward, it is possible to recover: the fuel-saving levels of North and South using equations (7) and (9), the price of electricity in each region using equation (15), and natural resource rents in each region using equation (14). Proposition 2: Suppose that the North and both the OPEC and non-opec sub-regions of South are diversified and that the South initially engages in some fuel-saving activity. Both the world price of the dirty goods and the North s price of emissions are: (2a) increasing in OPEC s price of fossil fuel (2b) independent of the North s emission cap, and (2c) decreasing the degree of integration of emissions credits. Table 1 summarizes the comparative static properties that hinge on proposition 2. While formal elements of the proof of Proposition 2 are provided in the Appendix, the intuition underlying it can be readily established using Figure 3. A higher price of fossil fuel shifts the NN curve upward to a lesser extent than the SS curve because the South uses more fuel per unit output of the dirty good than North. To allow South to break even, there must be an increase in the North s emissions price as well as the world price of dirty goods. Natural resource rents rise because of the higher price of fossil fuel and electricity prices rise because of the higher opportunity costs associated with fossil fuel use. Turning to Kyoto-style environmental policy, both diversification curves in Figure 3 are independent of the North s emissions cap, Y N M, which has not yet entered the analysis. Consequently, the world price of the dirty good and the Northern price of emissions, along with electricity and resource prices, opportunity costs of fossil fuel and investments in fuel saving, remain unchanged in response to a reduction in the North s emissions cap. 13

15 TABLE 1: Features of a Diversified Equilibrium Increase in OPEC s S1 fossil fuel price, p F Decrease in North s N emission cap, Y M Increase in allowable emission credits, " North s emissions price, (+) zero ( ) p N M p S1 F," ( ) World dirty-goods price, p D W p F S1," ( ) Fuel-saving in North, µ N p F S1," ( ) Fuel-saving in South, µ S p F S1," ( ) Opp. costs of fossil fuel, g " F ( p S1 F,#), g = N,S Electricity prices, g p E ( p S1 F,"), g = N,S Natural resource rents, g p R ( p S1 F,"), g = N,S (+) zero ( ) (+) zero ( ) (+) zero (+) (+) zero ( ) (+) zero ( ) (+) zero (+) An increase in the emissions market integration parameter, ", leaves the NN curve unaltered in Figure 3. The SS curve, however, pivots downward from S S " to S S ". This implies that the world price of dirty goods falls to p DW "" and the North s price of emissions falls to p MN "". Relaxing the emissions credit constraint leads directly to an increase in fuel saving in South such that dµ S d" =1, but there is an induced decrease in North such that dµ N d" (( ) p N $ K # ( µ N )) "1 p N M % "& N ' < 0 because of the decline in North s emissions price. The = " 1" µ N opportunity cost of an efficiency unit of fossil fuel declines in South due to increased credit revenue and in North due to the lower emissions price. Lower opportunity costs of fossil fuel lead in turn to lower electricity prices in each region, higher natural resource rents. 2.4 National and International Markets With world and domestic prices determined by diversification requirements, we can now turn to an examination of quantity determination through market equilibria. Since electricity is a nontradable good, supply is equal to demand on each region s market: 14

16 Y g E = a ED Y g D + a EF Y g g ( F + X EH )" EE, g = N,S. (16) g Here, X EH represents the demand for electricity by the household sector in country g. On regional and sub-regional natural resource markets, utilization of use of the resource in the fossil-fuel sector must be less than or equal to the endowment: g a RF p R p g g g ( K, p R p L )Y h F " Y h R, g = N,S1,S2, where: a RF " ( ) = #$ F (") #p g R. (17) Shephard s lemma is used to obtain the demand for natural resource per unit of fossil fuel. In order to set the world price for fossil fuel above the competitive level, OPEC must underutilize its natural resource such that a RF (")Y S1 F < Y S1 R. Since condition (21) will hold with equality for North and the non-opec South, which behave competitively, we obtain the following fossil-fuel supply functions: ( ) = Y h g R a RF p R ( p S1 F,") p g g K, p R p S1 g ( ( F,") p L ) #1, g = N,S2. (18) Y F g p F S1," These supply functions are increasing in the both the fossil fuel price and allowable credits because an increase in either of these variables raises natural resource rents and thereby reduces the intensity of natural resource usage, which in turn allows greater output of fossil fuel. OPEC must produce sufficient fossil fuels such that the South s total fuel production balances with world demand minus Northern supply at the going price: Y F S = X F N + X F S "Y F N, where: Y F S " Y F S1 + Y F S 2. (19) Here X F g denotes the aggregate fuel demand in region g, which includes demand from final consumption and all fossil-fuel using lines of production: ( ) a FD Y g D + a FE Y g E + a FF Y g g F + X FH X F g = 1" µ g ( ), g = N,S. (20) Since we assume that consumers as well as firms make full use of the fuel-saving technology, it g is convenient to define X FH to be the demand for efficiency units of fossil fuel by the household sector in region g. After making use of equation (16), we can rearrange equation (20) to obtain: A FD Y g D = ( 1" µ g ) "1 X g F " A FF Y g g F " a FE # EE X EH where: " S p F S1,# g " X FH, g = N,S. (21) ( ) $ ( 1% µ S (&) % #) %1 > 0; " N ( p S1 F,#) $ ( 1% µ &N (')) %1 > 0; 15

17 Here, " N and " S are efficiency coefficients which convert the number of actual units of fossil fuel used into the larger number of efficiency units that would have been used if there had been no investment in the fuel-saving technology. demand: Equilibrium in the world market for the dirty good requires balance between supply and Y N D + Y S D = X N DH S + X DH. (22) The regional fuel requirements consistent with goods market equilibrium can be obtained using equations (18), (19) and (21) in conjunction with (22): " N # N X N F + " S # S X S W F = Z FH ( ) $ " S # S X F S or X N F = Z FH (" N # N ) (( ) (" N # N )). (23) where: Z W FH " Z N FH + Z S g g g FH ; Z FH " A FD X DH # a FE $ EE X EH # X g FH. Here, " g #1$ ( 1$ µ g )A FF, which is greater than zero but less than one, is the net quantity of fossil fuel available for use outside the sector for each unit of fossil fuel produced. It should be observed that " g is greater than zero but less than one and that " g # g = " g $ A FF. g In the goods market equation (23), Z FH represents the imputed demand for efficiency units of fossil fuel by final consumers in country g and Z W FH represents the corresponding imputed consumer demand for efficiency units of fossil fuel for the world as a whole. These variables include the indirect consumer demand for fossil fuel associated with the consumption of electricity and dirty goods as well as the direct consumer demand for fossil fuel per se. For aggregation purposes, all fossil fuel quantities are measured in efficiency units. Due to trade in fossil fuel and the dirty good, there is no direct connection between a region s aggregate demand for fossil fuel given by X g F and the imputed demand of its own final consumers given by Z g FH. g X jh The underlying demand for good j by final consumers in country g can be written as g = X jh ( p W D, p g E," g F,I g +# g ). Since consumers make use of the fuel-saving technology, the domestic opportunity cost of fossil fuel, " F g, appears in these consumer demand functions rather than OPEC s price of fossil fuel, p F S1. A region s income is equal to the sum of its GDP, I g, and its transfer income from emission credits, " g. 8 Domestic product is endogenous and typically 16

18 depends on product prices and factor endowments. For brevity, we can write South s GDP function as I S = I S p W D, p S S1 ( E, p F ), but for North we must write I N = I N p W D, p N E, p S1 N ( F,Y M ). 9 North s emissions its emissions cap, which is analogous to a factor endowment, is included because of the centrality of emission permit revenue to our analysis. The envelope theorem implies that the elasticity of North s income with respect to the emissions cap is equal to the income share of permit revenue, " M N # p M N Y M N I N, which seems likely to be of negligible magnitude. Using the consumer demand functions and GDP functions, the world s imputed consumer demand for efficiency units of fossil fuel is Z W FH be summarized as: where: Y M N W ( Z FH ) "Z W FH Z W FH = Z W FH p W D, p N E, p S E," N F," S F,# N,# S N (,Y M ), which can = Z W FH ( p S1 F,Y N M,"); (24) N Z W FH, " N # $ N N % j " j ; N ( "Y M ) =# N M $ N Z FH j= D,E,F and it is assumed that: " Z W FH "# > 0; " Z W FH "p S1 F < 0. Here, " is the overall income elasticity of imputed consumer demand for efficiency units of fossil fuel in country g, " g j is the income elasticity of consumer demand for good j and " g j is the share of good j in the imputed consumer demand for efficiency units of fossil fuel in country g. Assuming that the dirty good, electricity, and fossil fuel are all normal goods in North, the world s overall imputed consumer demand for efficiency units of fossil will decline if North tightens its emissions cap, but the proportionate decline will be of negligible magnitude if the share of credit revenue in North s income, " N M, is negligible. In accordance with proposition 2, either an increase in allowable emission credits or a decrease in OPEC s fossil fuel price must reduce the electricity prices and opportunity costs of fossil fuel in both regions as well as the world price of the dirty good. Consequently, it is reasonable to assume that the standardized overall consumer demand for fossil fuel is increasing in " and decreasing in p S1 F even though some innocuous restrictions are implicitly placed on the substitutability of goods in both consumption and production. 17

19 The linear, negatively sloped FF locus in Figure 4 and subsequent figures shows the regional fuel requirements that are consistent with goods market equilibrium given by equation (23). Since the North engages in greater fuel saving and uses less fuel per unit output than the South, it follows that " N # A FF > " S # A FF. Thus, the magnitude of the slope of the FF curve, (" S # S ) (" N # N ), is less strictly than one. By adjusting clean good production within each country, dirty good production can be switched across countries on a one-for-one basis in accordance with equation (22) within the limits set by the non-negativity requirements for all outputs. Consequently, more dirty good production and, thus, fossil fuel demand in South is associated with less dirty-good production and fossil fuel demand in North, which gives the FF curve its negative slope. Since the South engages in less fuel saving than the North, a one-unit decrease in fuel demand in North is always associated with a greater than one unit increase in fuel demand in South. Given that OPEC holds the price of fossil fuel constant, it must accommodate the increase in world usage by increasing its own production. 10 [Insert Figure 4 about here] We can now close the model by turning to the emissions market. In equilibrium North s emissions must be equated with the North s cap plus the emissions credits, which its firms buy from firms in South: X M N = Y M N + "# S X M S ; (25) Since " represents the allowable transfers per efficiency unit of fossil fuel and the efficiency coefficient " S gives the number of standardized of fossil fuel units per unit actually used in South, "# S represents the available emission credits per unit of fossil fuel used. Recalling that one unit of fossil fuel always generates one-unit of GHG emissions such that X F g = X M g for g = N,S, the emissions market equilibrium condition given by equation (25) can be graphed as the linear MM curve shown in Figure 4 and subsequent Figures. In an initial pre-kyoto equilibrium where " = 0 and credits are absent, the MM curve is horizontal because Northern emissions are fixed and independent of emissions by the South. 18

20 By solving the linear good-markets and emissions-market equilibrium conditions specified by equations (23) and (25), we can determine the equilibrium fossil fuel demands for each region, and thus for the world as a whole: ( ) = # S $ S Y N M + "# S W Z FH X F N p F S1,Y M N," X F S # S $ S + "# S # N $ N ; (26) ( p S1 F,Y N M,") = Z FH #$ N % N N Y M $ S % S + "$ N $ N %. N (27) S ( 1+ "# )Z FH $ (# N $# S N )Y M. # S % S + "# S # N % N (28) X W F ( p S1 F,Y N M,") = In Figure 4, there is an initial pre-kyoto equilibrium at the intersection of the F F " and MM curves where the levels of emissions and fossil fuel demand are X F N" = X M N" and X F S" = X M S" in North and South respectively. 11 Before assessing the impact of provisions of the Kyoto agreement on this equilibrium, it is helpful to establish a key result concerning fossil fuel prices. Proposition 3: Consider an initial pre-kyoto equilibrium where emissions credits are not traded and where the North and both the OPEC and non-opec sub-regions of South are diversified. If OPEC raises the price of fossil fuel, the levels of aggregate fossil fuel demand and GHG emissions drop in the South and the world as a whole, but remain unchanged in North. Thus, in an initial pre-kyoto equilibrium where credits are absent (i.e., " = 0), North s fossil fuel demand is fully constrained by its cap such that X N FH = Y M N, but the aggregate fossil fuel demand curves of the South and the world as a whole are negatively sloped. While mathematical details of the proof are provided in the Appendix, Figure 4 illustrates the salient features. An increase in the price of fossil fuel shifts the goods market curve inward from F F " to F F " due to greater fossil fuel saving in both regions and declines in the world s standardized overall consumer demand for fossil fuel which arises in response to increases in all fossil-fuel related prices. Since the MM curve is horizontal and does not shift, North s fossil fuel demand and emissions remain unaltered at X FN " = X MN " but South s fossil fuel demand and emissions fall to X FS "" = X MS ""

21 2.5 Kyoto-Style Reductions in the North s Cap and World GHG Emissions In the spirit of the Kyoto protocol, consider the impact of a reduction in North s emission cap with South s GHG emissions remaining uncapped. Proposition 4: Consider an initial zero-credit equilibrium where the North and both the OPEC and non-opec sub-regions of South are diversified. If the North tightens its emissions cap and OPEC holds the price of fossil fuel constant, then: (a) North s fossil fuel demand and emissions must decline, (b) South s fossil fuel demand and emissions will rise if and only if emission permit revenue comprises a sufficiently small share of North s income such that " N M # N < $ N % N X N F Z N FH, and (c) world fossil fuel demand and emissions will rise if and only if emission permit revenue comprises a sufficiently small share of North s income such that " N M # N < ( $ N %$ S )X N F Z N FH. While formal details of the proof are provided in the Appendix, the results are readily explained using Figure 5, which shows a case where emissions permit revenue constitutes a negligible share of North s income. 13 In such a case, tightening the emissions cap shifts the emissions market equilibrium locus downward from M M " to M M ", but leaves the FF curve representing goods market equilibrium unaltered. Consequently, there is a new equilibrium at X F N"" = X M N"" and X F S"" = X M S"". Since the magnitude of the slope of the FF curve is less than one, this immediately implies that the magnitude of the increase in fossil fuel use and emissions in South exceeds that of the reduction in North. This makes intuitive sense since consumer demand for fossil fuel itself and each fossil-fuel-using good remains constant. There is, however, a one-for-one displacement in footloose dirty-good production from the North to the South. Since the North engages in more fuel-saving activity than the South, this causes an increase in world emissions. There is not only so-called carbon leakage through the South, but this also outstrips the improvement in North leading to overall leakage at the world level. [Insert Figure 5 about here] If emissions permit revenue constitutes a non-negligible share of North s income and the North s imputed consumer demand for efficiency units of fossil fuel is normal, then declining 20

22 income in North will reduce world as well as Northern consumer demand and shift the FF curve inward displacing the final equilibrium inward from X FN "" = X MN "" and X FS "" = X MS "" along the M M ". World emissions will continue to rise if and only if the final equilibrium lies to the left of the pre-kyoto world fossil fuel isoquant, X FW ", which depicts combinations of use in North and South that hold world usage constant. The environmental impact of reducing the North s cap could only be neutral if the induced decline in national income in North was sufficiently large. Further, if the Kyoto Agreement were to be successful on the environmental front, it would be the result of even more pronounced adverse effects on national income. Proposition 4 assumes that OPEC will fully accommodate the increase (or decrease) in world demand for fossil fuel by changing its output. Suppose instead that OPEC allows its price to change and take the extreme case where it does not change its output at all. Corollary 4.1: If OPEC holds its fossil fuel output constant and allows its price to vary when North tightens its emissions cap, then the magnitude of the change in world fossil fuel use and emissions, whether positive or negative, will be attenuated but not reversed. Proof: If the world fossil fuel demand would rise (fall) when OPEC holds the price of fossil fuel constant, then the price will rise (fall) when output is held constant instead. This not only moderates the increase (decrease) in fossil fuel demand, but also causes increased (reduced) production in North and the non-opec South. The increase (decrease) in world fossil fuel output implies that worldwide fossil fuel use and emissions must rise (fall). QED In terms of Figure 5, the increase in OPEC s fossil fuel price would cause an additional inward shift of the FF curve, which is not shown. Consequently, the world equilibrium would be displaced inward along the M M " curve from X FN "" = X MN "" and X FS "" = X MS "" but not as far as the pre- Kyoto world fossil fuel isoquant, X FW ". 14 Now suppose that the North is comprised of two or more technologically equivalent countries and one or more of these countries opts out of an emissions reduction program. 21

23 Corollary 4.2: If the magnitude of the reduction in North s emissions declines cap from dy N M to "dy N M where 0 < " <1, then the magnitude of the change in world fossil fuel use and emissions, whether positive or negative, will be attenuated but not reversed. Clearly this corollary follows immediately from Proposition 4 and it can also be applied in conjunction with Corollary 4.1. Suppose that emission permit revenue constitutes a negligible fraction of North s income and that world emissions would rise due to a tighter cap in North as in Figure 5. If a sub-region in North refrains from cutting its emissions, then the magnitude of the downward shift in the MM curve will be reduced and there will be less displacement of fossil fuel use and emissions to the South. Consequently, the model suggests that if a developed country such as the US refuses to ratify the Kyoto accord, or a country such as Canada ratifies the accord but fails to meet its reduction commitments, there could be net environmental benefits for the world! The results of Proposition 4 and its associated corollaries would be weakened if either the North or South were not diversified. The prices of dirty goods and electricity and the opportunity costs of fossil fuel use would no longer be determined independently of the North s emissions cap. Consequently, tightening the cap would raise at least one of these prices and the likely reduction in the world s overall standardized consumer demand for fossil fuel would shift the FF curve inward. Once again, there would be a less than one-for-one increase in fossil fuel utilization in South, lessening or even reversing the increase in world emissions. While it appears that price-increase effects have frequently been assumed, they are highly dependent on the dimensionality of general equilibrium trade models (Dixit and Norman, 1980; Feenstra, 2005). In a long-run setting such as the present model where there are more traded goods than non-tradable primary factors, key product prices may be independent of factor endowments and, thus, may not change when the endowment of emission permits declines