Self-enforcing environmental agreements and trade in fossil energy deposits

Transcription

1 Fakultät III Wirtschaftswissenschaften, Wirtschaftsinforatik und Wirtschaftsrecht Volkswirtschaftliche Diskussionsbeiträge Discussion Papers in Econoics No Deceber 2015 Thoas Eichner Rüdiger Pethig Self-enforcing environental agreeents and trade in fossil energy deposits

2 Universität Siegen Fakultät III Wirtschaftswissenschaften, Wirtschaftsinforatik und Wirtschaftsrecht Fachgebiet Volkswirtschaftslehre Hölderlinstraße 3 D Siegen Gerany ISSN Available for free fro the University of Siegen website at Discussion Papers in Econoics of the University of Siegen are indexed in RePEc and can be downloaded free of charge fro the following website:

3 Self-enforcing environental agreeents and trade in fossil energy deposits Thoas Eichner Departent of Econoics, University of Hagen Rüdiger Pethig Departent of Econoics, University of Siegen Abstract This paper analyzes the foration of self-enforcing cliate agreeents, or stable cliate coalitions, when all countries have the option to fight cliate change by purchasing (the right to extract) fossil-energy deposits. First, we consider the stand-alone deposit purchase policy and then cobine that policy with the option to tax or subsidize the supply of deposits. In either case, coalitions of any size turn out to buy deposits while the non-cooperative countries do not. In case of the standalone deposit purchase policy either no coalition is stable or the grand coalition is the only stable coalition. If the two-instruent policy is ipleented, all countries inside and outside the coalition are better off than in case of the stand-alone deposit policy, but the conditions for stable grand coalitions are ore favorable under the stand-alone deposit policy than under the two-instruent policy due to weaker free-rider incentives. JEL classification: Key words: C72, Q38, Q58 cliate coalition, deposit, fuel, Nash, self-enforcing IEA Eichner: Departent of Econoics, University of Hagen, Universitätsstr. 41, Hagen, Gerany, eail: Pethig: Departent of Econoics, University of Siegen, Hölderlinstr. 3, Siegen, Gerany, 1

4 1 The proble Scientific evidence suggests that stabilizing the world cliate at safe levels requires a assive reduction of greenhouse gas eissions, notably carbon eissions fro burning fossil fuels. That calls for an effective and encopassing international environental agreeent (IEA). The first legally binding IEA on cliate change, the Kyoto Protocol, achieved little ore than business as usual, and it is unclear whether the ongoing negotiations towards a broad and deep follow-up agreeent will be successful. Therefore, iproving our understanding of the conditions for effective IEAs is iportant. One of the key issues not yet well understood is how the choice of cliate policy instruents influences the conditions for the foration of stable and effective cliate conditions. There is a large literature studying self-enforcing environental agreeents. The early workhorse odel of Barrett (1994), Hoel (1992), Carraro and Siniscalco (1993) and further analyzed by Diaantoudi and Sartzetakis (2006) and Rubio and Ulph (2006) has been extended into various directions. E.g. Hoel and Schneider (1997) introduce transfer schees in the coalition foration process, Finus and Pintassilgo (2013) study uncertainty and learning, and Eichner and Pethig (2013, 2015) extend that odel by copetitive arkets and international trade. This literature is quite pessiistic about large and deep stable cliate coalitions and finds that whenever the gains fro cooperation would be large stable coalitions achieve only little. An exception is Eichner and Pethig (2015) who show that international trade ay render the grand coalition stable when countries use eission taxes. The prevailing approach to cliate policy both in practice and in the environentaleconoics literature is the reduction of carbon eissions via eission caps, eission taxes or cap-and-trade systes. Supply-side policies are uch less studied and ipleented. The present paper focuses on a special supply-side cliate policy, the international trade in (the right to extract) fossil energy deposits. The idea is to itigate cliate change through buying and preserving soe of those deposits that would otherwise have been exploited. While Boh (1992) questions the usefulness of that policy, if it stands alone, 1 Harstad (2012) points out that a arket for fossil-energy deposits and other inerals already exists between countries and international copanies as well as between countries First, we assue that the fuel arket and deposit arket equilibrate siultaneously. In contrast, Harstad (2012) considers a sequential gae at which the deposit arket clears prior to the fuel arket.. Here we follow Harstad in investigating the utilization of such a arket as an 1 Boh (1992) considers the stand-alone deposit purchase policy as "rather farfetched", because it is very costly and increases the fuel price. The practicability and political viability of trading fossil energy deposits is a serious issue which the present paper disregards, however. Our analysis ais to iprove our understanding of the econoics of deposit trading. 2

5 instruent of international cliate policy. Specifically, we ai to explore the foration and effectiveness of self-enforcing IEAs, when there is a world arket for deposits and the governents cliate policy takes the for of purchasing deposits with the intention to prevent their exploitation. We envisage a world of syetric countries all of which extract, trade, and consue fossil energy, called fuel for short. All countries suffer fro cliate daage caused by global carbon eissions that are proportional to global fuel consuption. In that analytical fraework we investigate the conditions under which IEAs are self-enforcing when all countries inside and outside the cliate coalition have the option to sell and/or buy deposits. To our knowledge, the only analytical studies of the deposit purchase policy are Boh (1993) and Harstad (2012, 2010). Boh (1993) considers a given sub-global coalition that unilaterally ais to ipleent a predeterined global eission-reduction goal either by reducing its fuel deand or by a special ix of capping its fuel deand and purchasing deposits. The present paper neither sets an eission-reduction goal nor ais to copare the cost-effectiveness of deand-side policies and (ixed) supply-side policies. Harstad (2012, 2010) analyzes coalition foration in a world econoy of heterogeneous countries where global carbon eissions generate cliate daage. A sub-global coalition itigates cliate daage by eans of the purchase of deposits cobined with caps on the deand and supply of fuel. Harstad s rearkable result is that when deposits are traded between the coalition and producers any coalition size ay be stable (see Harstad 2010, Proof of Proposition 5). 2 Conceptually, we adopt Harstad s analytical fraework, but deviate fro it in various ways. First, we take a different approach to odeling the deposit arket. While Harstad conceives of that arket as a set of bilateral deposit trades that exhaust all utual advantages, we odel the deposit arket in a standard way with a unifor price. Second, we do not adopt Harstad s three-instruent policy design of deposit purchases and caps on the deand and supply of fuel. In addition, in Harstad (2012, 2010) non-coalition ebers are inactive, i.e. they do not have any cliate policy. Instead, we investigate two different supply-side policies. One is the stand-alone deposit purchase policy and the other is a cobination of that policy with a tax or subsidy on doestic deposit supply. All countries set these policy instruents regardless of whether they are in the coalition or not. Third, while Harstad (2012, 2010) assues that the daage function is linear, we follow Barrett (1994), Diaantoudi and Sartzetakis (2006) and Rubio and Ulph (2006) and study coalition foration for quadratic daage. Fourth, we assue that the fuel arket and deposit arket 2 Harstad (2010) is the discussion paper version of Harstad (2012). In soe parts, especially in the section that describes coalition foration, Harstad (2010) is ore detailed than Harstad (2012). 3

6 equilibrate siultaneously. In contrast, Harstad (2012, 2010) considers a sequential gae at which the deposit arket clears prior to the fuel arket. In sharp contrast to Harstad (2012, 2010) we find that either no coalition is stable or the grand coalition is the only stable coalition. After having set up the analytical fraework in Section 2, we study in Section 3.1 the gae between the coalition and the non-cooperative fringe countries. The coalition plays Nash against the fringe countries and each fringe country plays Nash against the coalition and all fellow fringe countries. We characterize the equilibriu allocations for alternative coalition sizes (Proposition 1) and show aong other things that coalition countries sell and buy, whereas fringe countries sell but do not buy deposits. The inforation how the countries equilibriu payoffs (welfares) depend on the coalition size is needed for exaining the coalition stability in Section 3.2. There we derive necessary and sufficient conditions for the stability of the grand coalition (Proposition 2) and also show that either no stable coalitions exists or the grand coalition is the only stable coalition (Proposition 3). The analysis of Section 3 is based on the assuption that profit-axiizing extraction firs deterine the supply of deposits. In practice, governents ay want to consider the option of taxing or subsidizing the supply of doestic deposits in addition to purchasing deposits. We deal with that policy-ix in Section 4. In the corresponding Nash equilibriu with a coalition of given size both fringe countries and coalition countries iprove their welfare. Turning to the stability issue we show that the fringe countries free-riding incentives increases which renders the grand coalition unstable ore unlikely copared to the regie without subsidy. 2 The analytical fraework 2.1 Copetitive equilibriu with given deand for deposits We consider 3 n identical countries each of which produces a standard consuption good (quantity x s i) and fossil energy (quantity e s i), called fuel for short, fro doestic deposits. Each country uses its endowent r of a coposite input to produce both goods according to the siple production functions x s i = r x and e s i = ( 2 r 2 e. is a positive constant and r x and r e are the respective inputs. Iposing full eployent, r e +r x = r, we conveniently 3 We keep the description and discussion of the analytical fraework short, because, essentially, our basic odel is that of Harstad (2012). )1 4

7 represent the supply side of each country s econoy by the transforation function 4 x s i = T (e s i) = r K(e s i) with K(e s i) := 2 (es i) 2. (1) K(e s i) is the cost of extracting the aount e s i of fuel expressed in units of the productive factor. Following Harstad (2012, p. 85), we interpret the extraction cost function K as a function that iplicitly orders country i s (sall) deposits according to their extraction costs such that K e s i (e s i ) "... is a apping fro country i s deposits, ordered according to costs, to the arginal extraction cost of these deposits." 5 The greenhouse gas carbon dioxide is generated proportional to fuel consuption. With a suitable choice of units, e d i represents both fuel consuption and carbon eissions. Global eissions cause the cliate daage ( ) ( D e d := δ 2 e d 2 ) (δ > 0 and constant) (2) in each country. The representative consuer of country i, consuer i for short, derives the utility B ( ) e d i := ae d i b ( ) e d 2 2 i (a,b > 0 and constant) (3) fro consuing fuel, the utilityx d i fro consuing goodx, and suffers fro cliate daage (2). Her overall utility is u i = B ( ( ) ei) d +x d i D. (4) The deand for the consuption good is x d i = y i p e e d i, p e is the fuel price, p x 1 is the price of the consuption good 6 and y i = T(e s i )+p ee s i is incoe in ters of the consuption good in the no-policy regie. Consuer i takes y i, p e, p x and the prevailing cliate daage as given and axiizes (4) with respect to e d i. The axiization yields B e d i (ed i ) = p e and the fuel deand function e d i = E di (p e ) := B 1 e d i e d (p e ) = a p e, (5) b where B 1 is the inverse of the arginal benefit function B e d e d i i. Each country i hosts a fir, fir i for short, that extracts the aount e s i of fuel and sells it on the fuel arket at price p e. In addition, it offers the aount zi s of fuel in situ on the deposit arket 7 at price p z. 4 Upper case letters denote functions and subscripts attached to the denote derivatives. 5 We characterize a deposit by the aount of fossil fuel in the ground that can be extracted and by the cost of extracting that fuel. 6 Due to the siple production function of the consuption good, x s i = r x, the factor price is also unity. 7 In the present section we assue that fir i is entitled to sell (the right to exploit) deposits. An alternative assuption is that governents own the deposits and are entitled to sell (the right to exploit) the country s deposits. We will take up the issue of governent control on supplying deposits in Section 4 below. Note also that the deposit supply of price-taking welfare axiizing governents is equivalent to the deposit supply of profit-axiizing price-taking firs. 5

8 More precisely, the ite the fir offers on the deposit arket is the right to exploit specific deposits that store the aount z s i of fuel. To avoid clusy wording we refer to z s i and z d i as deposits supplied and deanded, respectively. Next, we specify the deposits fir i either exploits, or sells unexploited, or leaves in the ground unsold. To that end, suppose for the tie being there is no deposit arket. Then the fir s axiization of profit T(e s i )+p ee s i yields the first-order condition K e s i (e s i ) = p e and the fuel supply function e s i = Φsi (p e ) := K 1 e (p s i e ) = p e, (6) wherek 1 e (p s i e ) is the inverse of the arginal extraction cost functionk e s i. In ters of deposit language, (6) eans that fir i exploits all deposits with extraction costs K e s i (p e ) p e. The fir obviously has an incentive to offer deposits with extraction costs K e s i (p e ) > p e, which it would not exploit in the absence of deposit trading. However, countries that consider buying deposits do so for one and only one reason: to reduce total fuel extraction and consuption. That is, they seek to prevent the extraction of fuel that is stored in those deposits which the extraction firs would have exploited in the absence of deposit trading. They therefore only buy deposits with extraction costs K e s i (p e ) p e, no atter in which country the deposit-selling fir is located. Since all firs observe that constraint, the fuel supply is when fir i offers the deposits z s i for sale. e s i = Φsi (p e ) z s i = p e zs i, (7) Each fir generates a profit fro producing and selling fuel and receives the revenues p z zi s fro selling the deposits zi s. Fir i s total incoe therefore is p e [ Φ si z s i] K [ Φ si (p e ) z s i] +pz z s i. (8) Taking p e and p z as given, it axiizes (8) with respect to z s i, and thus deterines its fuel supply as K e s i (p e ) = p e p z Cobining (7) and (9) leads to or e s i = E si (p e p z ) := K 1 e s i (p e p z ) = p e p z. (9) z s i = Φsi (p e ) E si (p e p z ) = p z. (10) The siultaneous deterination of the supply functions (9) for fuel and (10) for deposits deonstrates the strong interdependence of the arkets for deposits and fuel. In view of the fuel deand (5) and the fuel supply (9) the fuel-arket clearing condition is E d (p e ) = E s a p e (p e p z ) or = p e p z. (11) b 6

9 Equation (10) specifies each fir s deposit supply. The deand for deposits, zi d, is a policy paraeter of country i s governent. In gae theoretic language, zi d is country i s strategy. Under the preliinary assuption that soe (feasible) profile ( z d 1,...,zd n) of strategies is given, the condition for deposit arket equilibriu is, z d = [ Φ s (p e ) E s (p e p z ) ] or z d = np z. (12) Suing up, the equations (11) and (12) deterine the prices of fuel and deposits that clear the arkets for any given profile of strategies ( z d 1,...,zd n). Forally, (11) and (12) iply price functions P e and P z such that the equilibriu prices are ( ) ( p e = P e z d := a +b + a z d and p z = P z (+b)n z d ) := z d n. (13) 2.2 Two bencharks: Business as usual and social optiu Suppose now all countries seek to enhance their residents welfare by purchasing deposits in order to curb cliate daage. All countries act independently and siultaneously, and they take into account both the other countries strategies (= deposit deands) and their own deposit deand s ipact on arket equilibria. Specifically, each country realizes that its deposit purchase influences the equilibriu prices (13) of fuel and deposits. By assuption, fir i chooses the supply of deposits, but the (governent of) country i takes into account how its fir s deposit supply z s i = Φ si (p e ) E si (p e p z ) fro (10) changes when the equilibriu prices (13) change with variations of z d i. Country i = 1,...,n takes z d, i, as given and axiizes with respect to z d i w i = B [ E di (p e ) ] +T [ E si (p e p z ) ] [ p e E di (p e ) E si (p e p z ) ] [ D Φ s (p e ) ] [ z d p z z d i Φ si (p e )+E si (p e p z ) ] (14) subect to (13). In the Appendix A we deterine the corresponding first-order condition, which is the sae across countries, when we ipose syetry, i.e. when we set z d i = z d for all i, = 1,...,n. In the resultant Nash equilibriu, which we refer to as business-as-usual (BAU), each country s purchase of deposits turns out to be z BAU = aδn 2 (+b) 2 (n 1)+(+b)+δn2. (15) To assess the allocative distortion in business-as-usual, observe that efficiency is char- 7

10 acterized by the three rules 8 B e d i (e d i) } {{ } = B ed ) i, = 1,...,n, (consuption efficiency) (16) =p e K e s i (e s i } {{ } ) = K es (es ) i, = 1,...,n, (production efficiency) (17) =p e p z ) nd e ( e d = B e d i (e d i ) } {{ } =p e K es (es i i } {{ } ) i, = 1,...,n. (daage internalization) (18) =p e p z Equation (16) requires equal arginal willingness-to-pay for fuel across countries, which is satisfied according to (2). Equation (17) requires equal arginal extraction costs across countries, which is satisfied according to (9). Equation (18) requires that the arginal benefit of purchasing deposits, nd e := d(nd) d, equals the arginal cost of purchasing deposits, p z, ed in all countries. Interestingly, since (16) and (17) are fulfilled, the right-hand side of (18) is the sae for all i, but the question is whether the equality sign in (18) holds. We show in the Appendix A that each country s socially optial deposit purchase is aδn 2 z OPT = (+b)+δn2. (19) and hence z OPT > z BAU. Moreover, fro (5) and (13) follows ed = an +b +b zd. Cobined with (15) and (19) we get e d BAU > ed OPT and D e(nz BAU ) > D e (nz OPT ). Hence the efficiency rule (18) is violated in business-as-usual because both the arginal and the total cliate daage are excessive. 3 Coalition foration with deposit trading 3.1 Coalition-fringe equilibria with coalitions of given size Suppose now the first countries, 1 < n, are ebers of a cliate coalition C := {1,2,...,} (with C for coalition) and all countries in the reaining group F := { + 1,...,n} (with F for fringe) are non-cooperative. Each fringe country i F plays Nash against the coalition and against all fellow fringe countries. The coalition acts as a single player whose payoff is the aggregate welfare C w and who plays Nash against all fringe countries. Taking advantage of syetry, we treat all countries equally within their group and therefore set zi d = z c for all i C and zi d = z f for all i F fro the outset. 8 See also Harstad (2012), equation (1). 8

11 The (executive body of the) coalition takes z f as given and axiizes the aggregate welfare of the coalition countries, w c = { B [ E dc (p e ) ] [ +T [E sc (p e p z )] p e E dc (p e ) E sc (p e p z ) ] [ ] } D Φ s (p e ) (z c +(n )z f ) p z [z c Φ sc (p e )+E sc (p e p z )],(20) subect to (13). 9 As shown in the Appendix A, soe rearrangeent of the first-order condition produces a link between z c and z f, denoted z c = R c (z f,), such that each coalition country s best reply to predeterined z f is [ z c = R c (z f,) := ax 0, R ] c (z f,). (21) Likewise, we reconsider the first-order condition of axiizing (14) with respect to z d i subect to (13), adapt the notation of deposit purchases appropriately, and turn the odified equation into another link between z c and z f, denoted z f = R f (z c,). With this inforation, we write each fringe country s best reply to z c as [ z f = R f (z c,) := ax 0, R ] f (z c,). (22) The Nash equilibriu, referred to as coalition-fringe equilibriu, is a strategy tuple (z c,z f ) satisfying z c = Rc (z f,) and z f = Rf (z c,). Solving (21) and (22) for z c and z f yields z c = R c (0,) = aδn 3 2(+b) 2 (n )+[(+b)+δn 2 ] (23) and zf = 0. That is the fringe countries find it in their self-interest not to purchase any deposits. Thus they entirely leave the burden of itigation to the coalition. The equilibriu prices p e = a +b b (+b)n z c, p z = n z c and p e p z = a +b (+2b) (+b)n z c (24) follow fro cobining (13) and (23). Since the equilibriu deposit supply is unifor across countries, (23) cobined with the deposit arket equilibriu specifies the equilibriu supply as zc /n. The ain results are suarized in10 Proposition 1. equilibriu is characterized as follows: For any given coalition size {2,..., n 1}, the coalition-fringe (i) The coalition buys deposits but the fringe countries do not. 9 (13) is applied after replacing zd by z c +(n )z f. 10 The proof of Proposition 1(ii) can be found in the Appendix A. 9

12 (ii) The total aount of deposits bought is saller and total eissions are larger than in the social optiu. The total aount of deposits bought is increasing and aggregate eissions are declining in the coalition size. (iii) There is no trade in fuel. The coalition pays for the deposits by exporting the consuption good. (iv) Fuel consuption and production are efficient, but global cliate daage is excessive. 11 (v) The fringe countries are better off than the coalition countries because their consuption of the consuption good exceeds the coalition countries consuption of that good by the aount p z z c. That the fringe countries refrain fro buying deposits in the coalition-fringe equilibriu is a striking and unexpected result. 12 If the fringe countries could, they would even respond to the coalition s equilibriu purchase zc with negative deposit deand - which is econoically infeasible, however. The fringe countries reluctance to buy deposits is a strong for of free riding. The coalition presents the with an extent of cliate daage reduction so large that they prefer spending their incoe on ore consuption rather than on the purchase of deposits. It is interesting to note that in the business-as-usual scenario of Section 2 all countries do purchase deposits, although they do not cooperate. Therefore, it is not the lack of cooperation, which explains the zero deposit deand. The explanation rather is the difference in country size, recalling that the coalition is treated as a single country that is ties as large as each fringe country. According to Proposition 1(v) the fringe countries are better off than coalition countries for any given coalition size. All countries welfare position is the sae except that coalition countries buy deposits, p zz c, at the expense of the consuption good while fringe countries buy an extra aount of the consuption good for the oney not spent on deposits. As we will show below the fringe countries strong free-rider advantage does not prevent the fro oining the coalition under certain conditions. We have characterized above coalition-fringe equilibria in the paraetric odel as well as the allocative changes resulting fro exogenous variations of the coalition size. To obtain additional results and to prepare for the analysis of coalition stability in the next section we now present a nuerical illustration, called Exaple 1, that consists of the paraeters That is, (16) and (17) hold, but (18) fails to hold. 12 It is unexpected because we are not aware of analyses of cliate coalition foration with policy instruents other than deposit trading in which the fringe countries refrain fro cliate policy altogether. 13 The paraeter r, the endowent of the productive factor, needs not be specified here, because it enters the outcoes in an additive way and thus leaves the results undistorted. 10

13 = 110, a = 100, b = 100 2, δ = 1 and n = 100. The focus of Exaple 1 is on (exogenous) variations of the coalition size. Although coalition sizes are integers, it is convenient to consider equilibriu values as functions whose doain is the interval [0, n]. Forally, we introduce the notation e s c = e d c = e s f = ed f = E(), p e = Pe (), p z = Pz (), w c = Wc (), w f = Wf (), z c = Zc () and z s c = z s f = Z s () Z c () Z s () Z c () Z s () Figure 1: Deposit purchase and the coalition s deposit iports (Exaple 1) According to the left panel of Figure 1 each country s deposit sales Z s () and each coalition country s deposit purchases Z c () are progressively increasing in the coalition size, and for any given the coalition country s purchase Z c () exceeds its sale. That is necessary for equilibriu on the deposit arket because the fringe countries do not buy deposits. In fact, the vertical distance between Z c () and Z s (), that is Z c () Z s () = n Zs (), constitutes the coalition countries iports of deposits paid for by exports of the consuption good. As the right panel of Figure 1 shows, these iports decrease in. They decrease only slightly when is sall and ediu, but they rapidly approach zero when is large and approaches n P z () E() P e () P z () Figure 2: Fuel consuption and the prices for fuel and deposits (Exaple 1) 11

14 According to the left panel of Figure 2 the deposit price is progressively increasing in while the producer price of fuel, p e p z, decreases when gets larger. Since (9) holds for all countries, each country s fuel production and consuption ust be decreasing in, which is shown in the right panel of Figure 2. As an iplication, the cliate daage D[nE()] is also strictly declining in A 0.06 W f () 5 W f () 0.04 W c () W c () B Figure 3: Welfare of coalition and fringe countries (Exaple 1) In the left panel of Figure 3 the graph of each country s welfare W v (), v = c,f, is progressively increasing in the coalition size and for any given fringe countries are better off than coalition countries. The welfare difference is W f () W c () = P z ()Z c () = Z c () 2. The right panel of Figure 3 is an enlarged segent of the graphs of the welfare functions W f and W c for high values of. 14 We will coe back to that panel when we discuss the issue of coalition stability below. 3.2 Stability of cliate coalitions In the preceding Section 3.1 we have presupposed the existence of cliate coalitions of alternative sizes, and our focus has been on characterizing the coalition-fringe equilibriu and its change following exogenous variations of the coalition size. Now we turn to the issue of coalition stability. Since supranational authorities for the effective enforceent of IEAs are not available, such agreeents will not be concluded unless they are self-enforcing in the sense that no coalition country has an incentive to defect and no fringe country has an incentive to oin the cliate agreeent. In foral language, an IEA with {2,...,n} signatories is said to be self-enforcing - or equivalently, a coalition of size is said to be 14 The only reason why the shapes of the graphs in the left and the right panel of Figure 3 differ significantly, are the different scales on the vertical and horizontal axes of both panels. 12

15 stable - if it satisfies the conditions 15 W c () W f ( 1) 0 and W f () W c (+1) 0, (25) known as the condition of internal and external stability, respectively. Our subsequent stability analysis focuses on the (in)stability of the grand coalition. First, we show that the grand coalition is unstable in the Exaple 1 introduced above. Then we show that a sufficiently large increase of the paraeter b in the otherwise unchanged Exaple 1 renders the grand coalition stable. Next we characterize the paraeter subspace in which the grand coalition is stable (Proposition 2) and finally provide insight in the (non-)existence of subglobal stable coalitions (Proposition 3). Necessary and sufficient for the stability of the grand coalition is the condition for the internal stability, W c (n) W f (n 1) 0. Whether that condition holds in Exaple 1 can be conveniently exained in the right panel of Figure 3. In that figure, the point A represents W f (99) and the point B represents W c (100). Fro W c (100) < W f (99) follows that the grand coalition is not stable in Exaple 1. Next we change the paraeter b in Exaple 1 fro b = to b = 575,000 and denote the resultant paraeters as Exaple 2. Figure 4 contains the graphs of the welfare functions W c and W f of Exaple 2. When we check the stability of the grand coalition in Figure 4 (proceeding as in Figure 3) we readily get W c (100) W f (99) = The coparison of the Figures 3 and 4 shows that the shapes of the welfare curves are very siilar. In both cases the coalition countries welfare rises when oving fro = n 1 to = n. However, the increase W c (100) W f (99) is rather sall in Exaple 1, but larger in Exaple W f () W f () W c () A B W c () Figure 4: Welfare of coalition and fringe countries (Exaple 2) Since the only difference in the specification of the Exaples 1 and 2 is the size of the paraeter b, it clearly is that difference which causes the difference in their stability pattern. 15 This concept of self-enforceent or coalition stability was originally introduced by D Aspreont et al. (1983) in the context of cartel foration and was first applied to the foration of IEAs by Hoel (1992), Carraro and Siniscalco (1993) and Barrett (1994). 13

16 Econoically, an increase of the paraeter b aounts to an inward shift of all fuel deand curves. 16 That shift reduces fuel consuption and hence cliate daage. In other words, the Exaples 1 and 2 suggest that the grand coalition is the ore likely stable, the lower the deand - i.e. the preference and willingness-to-pay - for fuel. The striking finding that the grand coalition ay be stable calls for analyzing the deterinants of stability in ore detail. In fact, it is possible to specify copletely the paraeter subset in which the grand coalition is stable. Proposition 2. (i) In the space of feasible paraeters 17 the grand coalition is stable, if and only if F(,b,δ,n) := 2b 2 b(n 2 2n 3) 2 (n 2 2n 1) δ(n 1) 2 n 2 > 0. (26) (ii) Ceteris paribus, the grand coalition is the ore likely stable, - the lower the fuel extraction costs (F < 0); - the lower the deand for fuel (F b > 0, if b > (n 2 2n 3)/4); - the less severe the cliate daage (F δ < 0); - the saller the total nuber of countries (F n < 0). Proposition 2 is a strong result because the inequality (26) is a necessary and sufficient condition for the stability of the grand coalition. (26) allows exploring the role of paraeters for the (in)stability of the grand coalition. To develop an intuition for the ipact of paraeter variations on stability, observe that increasing fuel deand (b ) and increasing cliate daage per unit of eissions (δ or n ) tend to destabilize a stable (grand) coalition, ceteris paribus, because these paraetric shifts directly or indirectly increase total cliate daage. The ipact of the fuel-deand paraeter b has already been clarified above in the transition fro Exaple 1 to Exaple 2: Lower values of b increase the deand for fuel, increase eissions and cliate daage and thus tend to destabilize the grand coalition according to (26). Total cliate daage, i.e. the cliate daage sued over all countries, is increasing in the paraeters n and δ. Since F(,b,δ,n) decreases in n and δ, successively increasing values of n and δ eventually render the grand coalition unstable. Thus, with regard to the paraeters b, δ and n the thrust of Proposition 2 is that the grand coalition is stable if total cliate daage produced by these paraeters is not too severe. 16 More precisely, the shift takes the for of a rotation of all countries deand curves towards the origin around the invariant choke price p e = a. 17 The crucial feasibility constraint is the non-negativity of fuel deands. We have carefully observed that constraint in our nuerical siulations. 14

17 To iprove further our understanding of the role of the paraeter b for the stability of the grand coalition, suppose the coalition of size = n 1 prevails and consider the only fringe country s cost and benefit of oining the coalition. Its benefit of oining consists of the cliate daage reduction, forally captured by 18 D(n 1) D(n). Its cost of oining the grand coalition consists of consuption welfare foregone, forally reflected by K f (n 1) K c (n), where K f (n 1) is the only fringe country s consuption welfare defined as the welfare derived fro its consuption of fuel and the consuption good. These costs and benefits are plotted in Figure 5 for variations ofb. For sall values ofbthe fringe country suffers fro assive losses of consuption welfare, while the benefit fro cliate daage reduction is sall. Increasing b slightly reduces the cliate daage and thus diinishes the benefit of oining the coalition. However, increasing b also reduces the loss of consuption welfare but uch ore than the benefit. As a consequence, there exists a positive value of b, say b in the right panel of Figure 5, at which cost and benefit curves intersect such that the grand coalition is stable if and only if b b D(99) D(100) K f (99) K c (100) K f (99) K c (100) D(99) D(100) b b b Figure 5: The last fringe country s benefit and cost of oining the given coalition of size = n 1 = 99 depending on the size of the paraeter b P z (99;b) Z s (99;b) P z (99;b)Z s (99;b) b b Figure 6: Deposit price, deposit supply and the fringe country s deposit export for a given coalition of size = n 1 = 99 depending on the size of the paraeter b 18 Observe that D() = D(e d c +(n )e d f ), Kc () = B(e d c )+x d c and K f () = B(e d f )+xd f. 15

18 The reason for the assive losses of consuption welfare for sall values of b lies in the coalition s purchase of deposits shown in the right panel of Figure 6. Recall that aong the countries in the grand coalition there is no trade of deposits. In contrast, in case of a coalition of size n 1 the fringe country s (consuption) welfare is larger than the coalition country s (consuption) welfare due to the revenues fro selling deposits. If the fuel deand is high (low b), the coalition seeks to avoid high cliate daage by purchasing any deposits at a high price as shown in the left panel of Figure 6. Hence for sall values of b large daages are tantaount to a large deposit incoe of fringe countries that renders the grand coalition unstable. The effect of variations in the paraeter is puzzling. Saller values of iply lower fuel extraction costs. The dependence of the only fringe country s cost and benefit of oining the grand coalition on is illustrated in Figure 7. While the fringe country s benefit is slightly decreasing in, the cost is first strongly increasing and then decreasing in. Figure 7 reveals that the cost and benefit curves intersect at soe point iplying that the grand coalition is [un]stable for all < [>]. Observe that the less expensive fuel extraction the ore fuel is consued, the higher are eissions and the higher is the cliate daage. As a consequence for sall values of the coalition purchases any deposits (see the right panel of Figure 8). One ight expect that the coalition s expenditures on deposits are high, but due to very low deposit prices the expenditures are low as shown in the left panel of Figure 8. The fringe country s low incoe fro selling deposits reduces its consuption welfare only slightly for sall values of, as shown in the left panel of Figure 8, which in turn ensures the stability of the grand coalition K f (99) K c (100) K f (99) K c (100) D(99) D(100) D(99) D(100) Figure 7: The only fringe country s benefit and cost of oining the coalition of size = n 1 = 99 depending on the size of the paraeter 16

19 P z (99;) P z (99;)Z s (99;) Z s (99;) Figure 8: Deposit price and the fringe country s deposit export for a given coalition of size = n 1 = 99 depending on the size of the paraeter We have extensively focused on the conditions under which the grand coalition is stable, because an all encopassing international cliate agreeent is of utost interest. As indicated above, we now briefly turn to the question whether there are also stable coalitions that do not encopass all countries. The answer is given in 19 Proposition 3. Suppose that n 4. (i) Either no coalition is stable (ii) or the grand coalition (of size = n) is the only stable coalition. Finally, we turn to the potential gains of cooperation. There is a folk theore of the international environental agreeent literature stating that "... the equilibriu size of a stable IEA is sall except when the potential gains fro cooperation are also sall" (Karp and Sion, 2012). 20 An indicator for the potential gains fro cooperation is the relative welfare gap w OPT w BAU w OPT 100 that easures the relative welfare gain of oving fro BAU to the social optiu. The left panel of Figure 9 shows the relative welfare gap for variations of the paraeter b. The welfare gap is decreasing in b and the grand coalition is stable for b > b. Hence the saller the gains fro cooperation the ore likely it is that the grand coalition is stable. We conclude that the relation between the size of the paraeter b and the stability of the grand coalition is in line with the folk theore entioned above. Turning to extraction costs, we observe that the relative welfare gap is decreasing in as illustrated in the right panel of Figure 9, but that the coalition is stable for <. Hence the relation between the size of the paraeter and the stability of the grand coalition is at variance with the folk theore according to which large (and effective) coalitions are unstable, unless the potential gains fro cooperation are sall. 19 The proof of Proposition 3 is given in the Appendix A. 20 See also Barrett (2003). 17

20 w OPT w BAU w OPT w OPT w BAU w OPT b b Figure 9: The welfare gap in Exaple 1 depending on the size of the paraeters b ( b = 548,766) and ( = 1.02) 4 Coalition foration with deposit trading and deposit supply regulation In the previous Section 3, the only cliate policy instruent at the governents disposal was the purchase of deposits. Our assuption was that the extraction firs own all doestic deposits and are free to sell (the right to extract) the. In practice, any governents probably would not leave deposit sales at the doestic extraction firs discretion because reserves of natural resources and fossil energy are of einent national interest. We therefore extend the analysis of the last section by providing the governents with the option to tax or subsidize the supply of doestic deposits. Suppose, the price at which country i s extraction fir can sell deposits is p z + σ i, which eans that if σ i > 0 [σ i < 0], deposit sales are subsidized [taxed]. 21 We will refer to σ i as a (deposit supply) subsidy if its sign is unspecified keeping in ind that we deal with a (deposit supply) tax, if σ i < 0. The iportant feature of the extended odel is that all governents now act strategically with respect to two policy paraeters, the deposit purchase zi d, as before, and the subsidy rate σ i. The odifications of the foral odel required by the introduction of the subsidy are straightforward and therefore delegated to the Appendix B. Instead of discussing here the details of introducing the subsidy on equilibriu prices and values in Exaple 1 as in Section 3, we turn directly to the welfare changes and the stability conditions of the grand coalition Governent i ay induce its extraction fir to supply ore (σ i > 0) or less (σ i < 0) deposits than in the absence of subsidization. If it should not want to sell doestic deposits at all, it siply sets σ i = p z. 22 The interested reader is referred to the Appendix B for a detailed discussion of Exaple 1 with subsidies. 18

21 In Figure 10, solid [dashed] curves relate to the odel with [without] subsidies and the superscript σ indicates the welfare in the odel with subsidies for Exaple 2. According to the left panel of Figure 10, for any given coalition size [2,n 1] both fringe countries and coalition countries iprove their welfare in the coalition-fringe equilibriu when using the subsidy. Since the welfare of the grand coalition is independent of the regies with and without subsidies, the welfare loss W f (n 1) W c (n) increases in the scenario with subsidy. That is shown for Exaple 2 in the right panel of Figure 10. The consequence for the stability of the grand coalition is surprising. While in Exaple 2 the grand coalition is stable in the regie without subsidies, the subsidy increases the fringe country s welfare fro point A to point C and thus raises it above the welfare of a coalition country in the grand coalition that is given by the point B (W cσ (100) W fσ (99) = ) in Figure 10. We conclude that introducing the subsidy akes free-riding ore attractive and akes the instability of the grand coalition ore likely W fσ () W cσ () W f () W f () W c () C B A W fσ () W cσ () W c () Figure 10: Welfare of the fringe country and the coalition (Exaple 2) As in Section 3.2, it is desirable to gain ore general inforation on the deterinants of the stability of grand coalitions in the regie with subsidies. A systeatic analysis delegated to the Appendix C yields Proposition 4. (i) In the space of feasible paraeters the grand coalition with deposit trading and deposit subsidies is stable, if and only if F σ (,b,δ,n) := b 2 (3n 2) 2 b(5n 4 18n 3 +6n 2 +10n 5) 2 (5n 4 18n 3 +15n 2 2n 1) δ(n 1) 3 n 2 (5n 3) > 0. (27) (ii) Ceteris paribus, the grand coalition is the ore likely stable, - the lower the fuel extraction costs (F σ < 0); 19

22 - the lower the deand for fuel (Fb σ > 0, if b > (5n4 18n 3 +6n 2 +10n 5)/[2(3n 2) 2 ]); - the less severe the cliate daage (Fδ σ < 0); - the saller the total nuber of countries (Fn σ < 0). The coparison of the Propositions 2 and 4 suggests that the role of paraeters for securing stable grand coalitions is siilar with and without subsidies. The note-worthy differences between both regies that generalize our findings in Exaple 2 are presented in Proposition 5. For n 4 the set of paraeters with stable grand coalitions is saller in case of deposit policies with deposit-supply subsidies than without. If there is a stable grand coalition in case of subsidies, it is also stable in the absence of subsidies. The reverse stateent does not hold. 5 Concluding rearks We analyzed the foration of self-enforcing cliate agreeents, or stable cliate coalitions, when all countries have the option to fight cliate change by purchasing (the right to extract) fossil-energy deposits, and we also allowed for cobining that policy with taxes or subsidies on the supply of deposits. We found that all coalition countries buy deposits but the noncooperative countries do not. In the policy regie without taxes/subsidies, we provided necessary and sufficient conditions for the stability of the grand coalition. The additional availability of the tax/subsidy instruent iproves the countries welfare, but renders less favorable the conditions for stable grand and sub-global coalitions. The deposit purchase policy turns out to be appealing with regard to its favorable conditions for stable (grand) coalitions. Two caveats need to be reephasized, however. First, it is not clear how robust our results - and those of earlier pertaining literature - are because tractability requires iposing restrictive assuption. Second, it is unclear how severe the difficulties are to fight cliate change with such supply-side policies in practice, especially when one accounts for the iportant role of tie which we disregarded in the present paper. In our view, further thorough theoretical and applied analyses of such policies are warranted, since the search for effective eans to fight cliate change is urgent and since the present paper suggests that the incentives to for self-enforcing IEAs of supply-side cliate policies are proising. 20

23 References Barrett, S. (2003): Environent and Statecraft. Oxford University Press, Oxford UK. Barrett, S. (1994): Self-enforcing international environental agreeents. Oxford Econoic Papers 46, Boh, P. (1993): Incoplete international cooperation to reduce CO 2 eissions: alternative policies. Journal of Environental Econoics and Manageent 24, Carraro, C. and D. Siniscalco (1993): Strategies for the international protection of the environent. Journal of Public Econoics 52, D Aspreont, C., Jacquein, A, Gabszewicz, J.J. and J.A. Weyark (1983): On the stability of collusive price leadership. Canadian Journal of Econoics 16, Diaantoudi, E. and E. Sartzetakis (2006): Stable international environental agreeents: An analytical approach. Journal of Public Econoic Theory 8, Eichner, T. and R. Pethig (2013): Self-enforcing-environental agreeents and international trade. Journal of Public Econoics 102, Eichner, T. and R. Pethig (2015): Self-enforcing international environental agreeents and trade: taxes versus caps, Oxford Econoic Papers, forthcoing. Finus, M. and P. Pintassilgo (2013): The role of uncertainty and learning for the success of international cliate agreeents. Journal of Public Econoics 103, Harstad, B. (2012): Buy coal! A case for supply-side environental policy. Journal of Political Econoy 120, Harstad, B. (2010): Buy coal? Deposit arkets prevent carbon leakage, NBER working paper No Hoel, M. (1992): International environental conventions: the case of unifor reductions of eissions. Environental and Resource Econoics 2, Hoel, M. and K. Schneider (1997): Incentives to participate in an international environental agreeent. Environental and Resource Econoics 9, Karp, L. and L. Sion (2013): Participation gaes and international environental agreeents: A non-paraetric odel. Journal of Environental Econoics and Manageent 65, Rubio, S.J. and A. Ulph (2006): Self-enforcing agreeents and international trade in greenhouse eission rights. Oxford Econoic Papers 58,

24 Appendix Appendix A Derivation of (15): The first-order condition of axiizing (14) is given by [ dw i = D dzi d e p z (zi d zi)p s z z D i d e ( ) np e = δ z d P z zd i Pz }{{} =zi s δ ( np e z d ) n + a Pe b Φ s p e +e d i e s i p z Φ si p e ]P e z d i n Pe P z } {{ } e d i es i Pz b n(+b) = 0. (A1) In a syetric Nash equilibriu the equalities z s i = z d i and e s i = e d i hold and (A1) siplifies to dw i dz d i = δ ( np e z d ) P z [ δ ( np e z d ) ] n Pz b n(+b) = 0. (A2) Inserting the price functions P e and P z fro (13) and setting zd = nz BAU, we solve (A2) for z BAU and obtain (15). We insert (15) in P e and P z and plug the outcoe into the welfare function (14) to get w BAU = a2 [b(n 1)+n][b 2 (n 1)+n( (n 2)nδ)+b((2n 1) (n 1)n 2 δ)] 2[b 2 (n 1)+b(2n 1)+n(+nδ)] 2.(A3) Derivation of (19): Maxiizing aggregate welfare nw i = nb [ E di (p e ) ] +T [ E si (p e p z ) ] ( p e e d e) s [ D Φ s (p e ) z d ] p z } {{ } =0 ( z d z) s } {{ } =0 (A4) 22

25 subect to (13) yields d(nw i ) d zd = nb e d i E di p e P e zd = B e d }{{} i +b + K e s i }{{} = =p e +b [ nδ ( np e ( nk e s i E(p si e p z) P e zd +b +nd e +b =p e p z z d ) P z ] ( P ) nd z e nφ si zd p e P e zd ) 1 = 0. (A5) Accounting for P e and P z fro (13), for zd = nz OPT in (A5), and solving (A5) for z OPT establishes (19). Derivation of the coalition-fringe equilibriu: The coalition axiizes (20) subect to P e (z c,z f ) = a +b + b[z c +(n )z f ], P z (z c,z f ) = [z c +(n )z f ]. (A6) (+b)n n The first-order condition is given by { [ d(w c ) = D e p z (z c z s dz c)pz z c c { [ np e δ (z c +(n )z f ) [ ( np e δ D e ] } Φ s p e +e d i e s i p z Φ sc p e Pz e c ] ) P z (z c Pz n ) ] n (z c +(n )z f ) + a Pe Pe b Inserting the price functions (A6) and rearranging (A7) yields b n(+b) } = 0.(A7) aδn 3 (+b) 2 nz c θ c [z c +(n )z f ] = 0, (A8) where θ c := (+b) 2 (n ) (+b)b+δn 2. Solving (A8) for z c results in the coalition country s reaction function z c = R c (z f,) := aδn 3 θ c +(+b) 2 n θ c θ c +(+b) 2 n n z f. (A9) Making use of zd = z c + (n )z f and of P e and P z fro (A6) in the fringe country s first-order condition (A2), we obtain, after rearrangeent of ters, aδn 3 (+b) 2 nz f θ f [z c +(n )z f ] = 0, (A10) where θ f := ( + b) 2 (n 1) ( + b)b + δn 2. Solving (A10) for z f results in the fringe country s reaction function z f = R f (z c,) := aδn 3 θ f (n )+(+b) 2 n θ f θ f (n )+(+b) 2 n z c. 23 (A11)