Fakultät III Wirtshaftswissenshaften, Wirtshaftsinformatik und Wirtshaftsreht Volkswirtshaftlihe Diskussionsbeiträge Disussion Papers in Eonomis No. 171-14 November 2014 Thomas Eihner Rüdiger Pethig Forging a global environmental agreement through trade santions on free riders?
Universität Siegen Fakultät III Wirtshaftswissenshaften, Wirtshaftsinformatik und Wirtshaftsreht Fahgebiet Volkswirtshaftslehre Hölderlinstraße 3 D-57068 Siegen Germany http://www.wiwi.uni-siegen.de/vwl/ ISSN 1869-0211 Available for free from the University of Siegen website at http://www.wiwi.uni-siegen.de/vwl/researh/diskussionsbeitraege/ Disussion Papers in Eonomis of the University of Siegen are indexed in RePE and an be downloaded free of harge from the following website: http://ideas.repe.org/s/sie/siegen.html
Forging a global environmental agreement through trade santions on free riders? Thomas Eihner Department of Eonomis, University of Hagen Rüdiger Pethig Department of Eonomis, University of Siegen Abstrat This paper studies the formation of self-enforing global environmental agreements in a world eonomy with international trade and two groups of ountries that differ with respet to fuel demand and environmental damage. It investigates whether the signatories threat to embargo (potential) free riders seures all ountries partiipation in the agreement. Resorting to numerial analysis, we find that an embargo may be unneessary, ineffetive or even ounterprodutive - depending on the degree of asymmetry and other parameters. On some subset of parameters, the embargo stabilizes the otherwise unstable global agreement, but the threat of embargo is not redible. However, in some of these ases redibility an be restored by suitable intra-oalition transfers. JEL lassifiation: Key words: F02, Q50, Q58 embargo, trade, asymmetry, free rider, fuel demand, limate damage Eihner: Department of Eonomis, University of Hagen, Universitätsstr. 41, 58097 Hagen, Germany, email: thomas.eihner@fernuni-hagen.de; Pethig: Department of Eonomis, University of Siegen, Hölderlinstr. 3, 57068 Siegen, Germany, pethig@vwl.wiwi.uni-siegen.de. 1
1 The problem The redution of global arbon emissions neessary to stabilize the world limate at safe levels requires a broad and deep international environmental agreement (IEA), i.e. an IEA that seures ooperation of all (major) ountries and strives for maximum world welfare. The first legally binding IEA on limate hange, the Kyoto Protool, aomplished only little more than global non-ooperation. It expired in 2012, and the prospets are unertain for reahing a more effetive follow-up agreement. That alls for further efforts to improve our understanding of how to reah a broad and deep limate agreement. Trade reates interdependene among ountries in addition to the interdependene generated by global limate damage and is therefore important for understanding the (dis)inentives to ooperate. Although no sovereign ountries an be fored to sign an IEA, it is possible to design an IEA that obliges all signatories to impose trade santions on non-signatories. 1 The intention or hope is that the threat of santions suffies to indue partiipation of all ountries. Among the few IEAs with trade santions to inentivize partiipation, is the Montreal Protool. It bans trade between signatories and non-signatories in CFCs and other substanes ontrolled by the treaty as well as imports from non-signatories of produts ontaining these substanes. Interestingly, partiipation in the Montreal Protool turned out to be almost global without the need of atually implementing the ban. Van Slooten (1994), Brak (1996) and Barrett (2003) onlude that the ban had the intended effet of deterring ountries from free riding. The present paper takes up the issue of trade santions to enhane further our understanding of how effetive they are in forging broad and deep IEAs. We will disregard trade restritions like import tariffs or border arbon adjustment 2 but rather assume the strongest form of trade santions, a general embargo or trade ban threatened to be imposed on non-signatories by all signatories. The analytial literature on IEAs with trade santions against free riders is small and offers mixed onlusions. Barrett (1997) studies a partial equilibrium model with symmetri ountries where the ountries play "abate" or "pollute" and imperfetly ompetitive firms sell a homogeneous produt in segmented markets. He investigates how trade poliy may help support self-enforing 3 IEAs and finds that the threat of trade santions is welfare 1 Trade restritions may not be ompatible with WTO rules, Charnovitz (2007). In our paper, we ignore potential onflits between environmentally motivated trade restritions and international trade law. 2 For various trade restritions see Lessmann et al. (2009) and for border arbon adjustment see e.g. Elliott et al. (2010). The goal of this type of trade restritions is primarily to level the playing field of international trade rather than induing ountries to partiipate in the IEA. 3 An IEA is said to be self-enforing or a limate oalition is said to be stable, if no signatory has an inentive to defet from the IEA and no non-signatory has an inentive to sign. The literature on the formation of IEAs has adopted that stability onept from the theory of artels (D Aspremont et al. 1983). 2
enhaning and may foster full partiipation. Chui Ying (2010) extends Barrett s (1997) approah to asymmetri ountries and shows that eonomi santions ould be redible, but annot indue full partiipation of an IEA. In another game model, Barrett (1999) shows that a ban on trade is effetive but not redible. 4 In ontrast to the studies of Barrett and Chui Ying, our point of departure is Eihner and Pethig (2013, 2014a). They expand the basi model of the early literature on limate oalition formation 5 by introduing world markets for fossil fuel and onsumption goods 6 and show for the ase of idential ountries, tax poliy and international trade that the grand oalition is stable and implements the soial optimum on some subset of parameters. Motivated by that remarkable result, Eihner and Pethig (2014b) expand the tax-poliy model of Eihner and Pethig (2014a) by assuming two groups of ountries that differ with respet to limate damage and the demand for energy. 7 They find that asymmetri limate damage tends to destabilize and asymmetri energy demand tends to stabilize the grand oalition. The reason for the stabilizing effet of asymmetri energy demand is as follows. With full symmetry, trade takes plae only between the oalition of all but one ountry and the outsider, but not between the (idential) oalition ountries. With demand asymmetry, trade also takes plae between oalition ountries and thus makes it more attrative for the outsider to join. Asymmetry is also very important for the effetiveness of an embargo, beause, in ontrast to idential signatories, asymmetri signatories still enjoy gains from intra-oalition trade during the embargo, and therefore they suffer under the embargo less than idential signatories. Hene asymmetry promises to strengthen the inentives for full ooperation under the threat of embargo, and that is why the present paper investigates the onsequenes of the threat of embargo in the otherwise unhanged model of Eihner and Pethig (2014b). Having emphasized the relevane of asymmetry for oalition formation we 4 A different strand of the literature, not followed here, employs large-sale simulation models. In suh a model, Kempfert (2004) shows that trade santions do not neessarily indue outsiders to join a oalition. Lessmann et al. (2009) find a signifiant potential to raise partiipation and global welfare through import tariffs. 5 Here we refer to the basi model introdued by Barrett (1994) and rigorously haraterized by Diamantoudi and Sartzetakis (2006) and by Rubio and Ulph (2006). We onsider orner solutions (e.g. zero emissions) an implausible artefat of the parametri approah and therefore follow Diamantoudi and Sartzetakis (2006) who restrit their fous on interior solutions. 6 Eihner and Pethig (2013, 2014a, 2014b) plae a game model on top of a simple general ompetitive equilibrium of the world eonomy, whih inreases analytial omplexity onsiderably. The subsequent analysis also has to ope with this problem and does so by resorting to numerial alulations in ases of intratability. 7 Sine Barrett (1997) many asymmetri models (without trade) of self-enforing IEAs have been studied with various simplifying assumptions and degrees of omplexity, e.g. Carraro and Sinisalo (1998), Barrett (2001), MGinty (2007), Fuentes-Albero and Rubio (2010), Pavlova and de Zeeuw (2013). 3
need to add that, from the viewpoint of theory, the downside of asymmetry is that it boosts omplexity. The prie to be paid is that we need to resort to numerial analysis. In the present paper, we fous on the situation in whih all ountries but one have already signed a limate agreement that implements the soial optimum, if all ountries sign, and that obliges all signatories to impose a trade ban on free riders. The deision problem of the last and only outsider is then to sign or to stay outside. The outsider determines its positive or negative net benefit of signing assuming that all other ountries stay in the oalition. 8 It does sign the agreement, if it is better off signing than suffering under the embargo and if the oalition s threat of embargo is redible, i.e. if no signatory is worse off with than without imposing the embargo. If the threat of embargo is not redible and the outsider prefers free riding to joining in the absene of an embargo, then it will enjoy its free-rider position knowing that out of self-interest the signatories will not fulfill their obligation to embargo the free rider. In our subsequent analysis, we distinguish three different regimes. The free-trade regime, in whih no non-signatory is embargoed; the embargo regime, in whih non-signatories fae an embargo whether or not the threat of embargo is redible; and the threat-of-embargo regime, in whih non-signatories are embargoed only, if the threat of embargo is redible. Ultimately, we are interested in the threat-of-embargo regime, of ourse. However, in order to obtain informative results about that regime we need to analyze and ompare the other regimes first. Table 1 displays the possible outomes of the transition from free trade to the embargo regime. Clearly, an effetive embargo (box [2] in Table 1) is what we want an embargo to aomplish. However, somewhat unexpetedly we will have to deal with all boxes [1] - [4] of Table 1. Obviously, the redibility of the threat of embargo is not an issue when an embargo is unneessary, ounterprodutive or ineffetive (boxes [1], [3] or [4] in Table 1), beause it is lear that in these ases the threat of embargo makes no sense in the first plae.... in the embargo regime: The grand oalition is stable... in the free-trade regime: yes no yes [1] embargo unneessary [2] embargo effetive no [3] embargo ounterprodutive [4] embargo ineffetive Table 1: Comparison of outomes in the senario of free trade and embargo 8 This ruial assumption is an impliation of the stability onept (footnote 3). It portrays free riders as shortsighted and thus puts them in a favorable position. 4
So we restrit the redibility hek to those ases in whih imposing an embargo stabilizes the otherwise unstable grand oalition (box [2] in Table 1). It turns out that one group of oalition ountries is always worse off in the embargo regime than in the free-trade regime. We do not find onditions under whih the embargo renders stable an otherwise unstable grand oalition and is redible, no matter how low or high the degree of asymmetry is. Given this negative result, we investigate whether it is possible through intra-oalition transfers to make all oalition ountries better off in the embargo regime than in the freetrade regime. We find that suh transfers an restore redibility, in fat, on a subset of the set of parameters that leads to the outome of box [2]. In the following Setion 2, we introdue some neessary notation and develop the analytial framework. Setion 3 derives the ountries equilibrium welfares depending on parameters and asymmetries in the grand oalition and in the regimes of free trade and embargo. The entral part of the paper is Setion 4 that studies the onditions for the (in)stability of the grand oalition in five samples plaing the fous on variations in the degree of asymmetry of limate damage (Samples 1-2) and of energy demand (Samples 3-5). Some parameters that are uniform aross ountries are also varied to improve the understanding of the (dis)inentives to ooperate. Setion 6 investigates the possibility to make the threat of embargo redible through intra-oalition transfers. Setion 7 onludes with an emphasis on the aveat onerning the robustness of the results. 2 Analytial framework Following Eihner and Pethig (2014b), we onsider a world eonomy with two groups of ountries, group M := {1,...,m} and group N := {1,...,n} desribed by the following equations (1), (2) and (3): 9,10 x s i = X (e s i) := x ξ 2 (es i) 2 for i = 1,...,m+n, (1) V m( e d ) ( m+n ) i +x d i D m j=1 ed j = a m e d i b ( ) ( 2 e d 2 m+n 2 i +x d i δm 2 j=1 j) ed if i M, V n( e d ) ( m+n ) i +x d i D n j=1 ed j = a n e d i b ( ) ( 2 e d 2 m+n 2 (2) i +x d i δn 2 j=1 j) ed if i N, m+n j=1 x d j = m+n j=1 x s j and m+n j=1 e d j = m+n j=1 e s j, (3) 9 The supersripts s and d indiate quantities supplied and demanded, respetively. Upper-ase letters denote funtions. Subsripts attahed to them indiate partial derivatives. 10 We use general funtional forms suh as X in equation (1) only for onveniene of notation. For reasons of tratability, we will make use of the linear-quadrati funtional forms in (1) and (2) throughout the paper. 5
where the parameters in (1) and (2) satisfy ξ, x, a m, a n, b, δ m, δ n > 0. Aording to the transformation funtion (1), eah ountry i = 1,..., m + n produes two goods, a standard omposite onsumption good (quantity x s i ) and fossil energy (quantity es i ), alled fuel. The funtion (1) is the same aross ountries and implies that both goods are produed by means of domesti produtive fators with given endowments. To interpret the parameter ξ, observe that the osts (in terms of the onsumption good) of extrating the amount e s i are x X (e s i ) = x [ x ξ 2 (es i )2 ] = ξ 2 (es i )2, of fossil fuel beause X(e s i) = x for e s i = 0 and x s i = X (e s i) < x for e s i > 0. Therefore, ξ is a measure of fuel extration osts. On the maro level, it measures fossil fuel abundane or sarity beause for given pries total fuel output is stritly dereasing in ξ. In eah ountry i, a representative onsumer demands the onsumption good (quantity x d i ) and fossil energy (quantity ed i ) and suffers from limate damage. Her utility, also referred to as ountry i s welfare, is speified in equation (2) and depends on whether ountry i belongs to the group of ountries M or N. For i M, V m( ei) d + x d ( i is the utility from m+n ) onsuming fuel and the onsumption good. D m is the disutility or damage from j=1 ed j limate hange aused by aggregate arbon emissions. Carbon emissions are proportional to fuel onsumption, and we therefore simply take e d i to be both fuel demand and emissions. Aording to (2), onsumers in both groups of ountries may differ with respet to the parameters a m and a n or with respet to the parameters δ m and δ n. For analytial onveniene, we define a m := a, a n := a+, R and δ m = δ, δ n = δ +ρ, ρ R and plae our main attention on exogenous variations of the asymmetry parameters and ρ in what follows. Aggregate demand is required to math aggregate supply for fuel and the onsumption good in the equations (3). Eihner and Pethig (2014b) show that there exists a unique general ompetitive equilibrium with world markets for the onsumption food (prie p x 1) and for fuel (produer prie p), when eah ountry regulates domesti emissions by means of an emission tax t i. For the time being that tax is arbitrarily hosen. Defining t := (t 1,...,t m+n ), the equilibrium welfare of ountry i reads W m (t,,ρ) := V m( e d i) +X(e s i )+P(t,) ( e s i ed i) D m W n (t,,ρ) := V n( e d i) +X(e s i )+P(t,) ( e s i e d i) D n ( m+n j=1 ed j ( m+n ) j=1 ed j ) if i M, if i N, (4) where the equilibrium fuel prie is p = P(t,) := ξ [ (m+n)a+n ] m+n j=1 t j, (5) (m+n)(b+ξ) 6
and where e s i and e d i satisfy e s i = P(t,) for i M N, e d ξ i = [a P(t,) t i] b e d i = [a+ P(t,) t i] for i N. b for i M and Note that due to the additivity of the utility funtion (2) the equilibrium alloation ( e d i,e s i,xd i i),xs depends on the fuel-demand asymmetry parameter, but not on the i M N damage asymmetry parameter ρ. The parameter ρ affets the equilibrium welfare (4), however. Central to our subsequent analysis is the onept of self-enforing IEAs or stable environmental oalitions introdued by D Aspremont et al. (1983), 11 whih requires that no signatory has an inentive to defet and no non-signatory has an inentive to sign. As pointed out in the Introdution, we restrit our attention to the stability of the grand oalition. It therefore suffies to ompare the situation, in whih a grand oalition exists, with situations with or without embargo onsisting of a oalition of all ountries but one, i.e. a oalition of m + n 1 ountries, and a single ountry of group M or N outside the oalition. The outsider has to deide whether to join the oalition under the threat of embargo. Obviously, the outome is a stable grand oalition, if and only if it is in the outsider s self-interest to join. We denote as f-ountry (with f = m,n) the ountry of group F = M,N outside the oalition of size m + n 1, and we all hf-ountry (with h,f = m,n) a ountry of group H = M,N inside the oalition of size m+n 1 whih faes an f-ountry of group F = M,N. When the f-ountry alulates its benefits from free riding, it antiipates whether the oalition will deliver on its threat of embargo. The f-ountry rightly expets an embargo, if and only if the oalition s threat is redible, i.e. if and only if all oalition ountries are not worse off implementing the embargo than when they let the free rider go unpunished. If oalition ountries are worse off, they will not live up to their threat of embargo, sine there is no supranational enforement ageny to prevent them from following their self-interest. Hene, a threat that is not redible fails to deter free riding and renders unstable the grand oalition. The omplexity of the stability issue with the threat of embargo suggests distinguishing three different regimes: the free-trade regime, the embargo regime and the threat-of-embargo regime. The free-trade regime is the regime that prevails when the oalition refrains from imposing an embargo on the f-ountry. In the embargo regime, the f-ountry is embargoed, if it hooses to free ride, irrespetive of whether the embargo makes oalition ountries worse off. Finally, in the threat-of-embargo regime, the free-riding f-ountry is embargoed, if and only if the oalition ountries are at least as well off after imposing the embargo as in the free- 11 We use the terms "stable (environmental) oalition" and "self-enforing IEA" synonymously. 7
trade regime. Although our fous is on the threat-of-embargo regime, the thorough analysis of the regimes of free trade and embargo is a preondition for assessing the redibility of the threat of embargo.... if the f-ountry Welfare of the...... does not join the oalition in the... joins the oalition embargo regime free-trade regime in either regime f-ountry,... ŵ f = Ŵf (,ρ) w f = W f (,ρ) wf = w h = W h (,ρ) hf-ountry,... ŵ hf = Ŵhf (,ρ) w hf = W hf (,ρ) wf = w h = W h (,ρ) Table 2: Notation for the equilibrium welfares of the f-ountry and the hf-ountries (h,f = m,n) depending on regimes, on the f-ountry s deision to join or not to join the oalition, and on the asymmetry parameters and ρ Table 2 introdues some notation we will use for the welfare of the f-ountry and the hf-ountries in the regimes of free trade and embargo, when the f-ountry does or does not free ride. The funtions W h, Wf, Whf,Ŵ f and Ŵhf in Table 2 desribe the dependene of equilibrium welfares on the degree of asymmetry that is measured by the asymmetry parameters 12 and ρ. Taking advantage of that notation, the following statements hold: The grand oalition is stable in the free-trade regime, if and only if wf w f for f = m and f = n; in the embargo regime, if and only if wf ŵ f for f = m and f = n; in the threat-of-embargo regime, if and only if wf ŵ f for f = m and f = n and ŵ hf w hf for hf = mm,mn,nm,nn (i.e., if and only if the grand oalition is stable in the embargo regime and the threat of embargo is redible). 3 Equilibrium welfares 3.1 Welfares in the grand oalition and in the free-trade regime Eihner and Pethig (2014b) have derived the welfare funtions of the seond and third olumn of Table 2. It therefore suffies here to sketh the proedure. Obviously, the f-ountry s welfare in the grand oalition is independent of whether the free-trade regime or the embargo regime prevails. To derive the welfare funtion W h, reall the welfare W h (t,,ρ) in (4) that represents the welfare ountries of group H = M, N attain in the ompetitive equilibrium 12 We suppress all parameters other than the asymmetry parameters as arguments in these welfare funtions, beause our fous will be on systemati variations of the latter. 8
with the tax profile t = (t 1,...,t m+n ). An obvious neessary ondition for maximizing the aggregate welfare of the grand oalition, as of all other oalitions, is that all members tax rates be equal. Therefore, we an assign to all oalition ountries the same tax rate, denoted t z, and write the welfare of ountries of group H = M,N in the grand oalition as W h (t,,ρ) = W h (t z,,ρ), with t = (t z,...,t z ). Eihner and Pethig (2014b) show that the }{{} (m+n) times equilibrium welfare of ountries of group H is W h (t z,,ρ) := V h( e d h) +X(e s h )+P(t z,) ( e s h e d h) D h [(m+n)e s h] for h = m,n, (6) where P(t z,) := ξ[(m+n)(a tz)+n], e d (m+n)(b+ξ) h = a h P(t z,) t z and e s b m = es n = P(tz,). Maximization of ξ the grand oalition s aggregate welfare yields the soially optimal tax rate t z = T(,ρ) := [(m+n)a+n][mδ +n(δ +ρ)] b+ξ +(m+n)[mδ +n(δ +ρ)]. (7) Insertion of t z from (7) in (6) finally yields w h := Wh (t z,,ρ) = Wh [T(,ρ),,ρ] =: W h (,ρ) for h = m,n. (8) Equation (8) speifies the funtion W h from Table 2. Consider next the ountries welfare in the free-trade regime with a oalition of size m + n 1 and a free rider, Wf (,ρ) and W hf (,ρ). We assign to eah oalition ountry the tax rate t z and denote by t f the tax rate of the f-ountry, suh that the f-ountry s equilibrium welfare is W f (t f,t z,,ρ) := V f ( e d f and the hf-ountries equilibrium welfare is W hf (t f,t z,,ρ) := V h( e d hf where P(t f,t z,) := ξ[(m+n)a+n] [t f (m+n 1)t z] P(t f,t z,) ξ ) +X(e s )+ P(t f,t z,) ( ) e s e d f D f [(m+n 1)e s ], (9) ) +X(e s )+ P(t f,t z,) ( ) e s e d hf D h [(m+n 1)e s ], (10) (m+n)(b+ξ) =: e s, and e d hf = a h P(t f,t z,) t z b., e d f = a f P(t f,t z,) t f b, e s f = es mf = es nf = It follows that the aggregate welfare of the oalition of size m+n 1 is W zf (t f,t z,,ρ) := { (m 1) Wmf (t f,t z,,ρ)+n W nf (t f,t z,,ρ) if f = m, m W mf (t f,t z,,ρ)+(n 1) W nf (t f,t z,,ρ) if f = n. (11) The oalition and the f-ountry are players in a non-ooperative game with payoffs (t f,t z,,ρ), Wf (t f,t z,,ρ) and strategies t z andt f. Our solution onept is the Nash equilibrium. That equilibrium is defined as a tuple of tax rates [ t f = T f (,ρ), t zf = T zf (,ρ) ] satisfying W f ( t f, t zf,,ρ) W f (t f, t zf,,ρ) for all t f and W zf ( t f, t zf,,ρ) W zf ( t f,t z,,ρ) 9 W zf
for allt z. Eihner and Pethig (2014b) alulate the Nash equilibrium tax rates and determine the Nash equilibrium welfares as w f : = W f ( t f, t zf,,ρ) = W f [ Tf (,ρ), T zf (,ρ),,ρ ] =: Wf (,ρ), w hf := W hf ( t f, t zf,,ρ) = W hf [ Tf (,ρ), T zf (,ρ),,ρ ] =: Whf (,ρ). (12) Thus we have substantiated the funtions W f and W hf in Table 2. 3.2 Welfares in the embargo regime with a free rider Coneptually, we follow the proedure of Setion 3.1 to speify the welfare funtions Ŵ f and Ŵhf introdued in Table 2. As before, we denote the oalition ountries tax rate by t z and the f-ountry s tax rate by t f. Aordingly, in the non-ooperative ompetitive equilibrium with tax rates t z and t f the f-ountry s welfare now is Ŵf (t f,t z,,ρ) and the oalition ountries welfare isŵhf (t f,t z,,ρ). To speifyŵ(t f,t z,,ρ), we onsider the trade embargo and readily derive for the f-ountry s autarki eonomy, p f = ξ(a f t f ), e s b+ξ f = p f e d f = a f p f t f, and e s b f = ed f = a f t f. Hene, b+ξ Ŵ f (t f,t z,,ρ) = V f ( e d f) +X ( e s f ) D f [ e s f +(m+n 1)e s zf], (13) where e s zf is the oalition ountries fuel supply, when the outside ountry belongs to group F. To speify that supply, we proeed as follows. In view of e s hf = p zf =: e s ξ zf for h,f = m,n, e d hf = a h p zf t z for h = m,n and the ondition for learing the intra-oalition fuel market b we alulate the equilibrium fuel prie as { ξ[(m+n 1)(a tz)+n] p zf = ˆP if f = m, f (m+n 1)(b+ξ) (t z,) := ξ[(m+n 1)(a t z)+(n 1)] if f = n. (m+n 1)(b+ξ) Plugging ˆP f (t z,) into the oalition ountries fuel demands and supplies yields e d hf = a h ˆP f (t z,) t z b and e s zf = ˆP f (t z,). (14) ξ This information allows speifying the individual and aggregate welfares in the oalition as Ŵ hf (t f,t z,,ρ) := V h( ( ) ehf) d +X e s zf + ˆPf (t z,) ( e s zf ehf) [ d D h e s f +(m+n 1)ezf] s, { (m 1) Ŵ zf Ŵ mf (t f,t z (t f,t z,,ρ) :=,,ρ)+nŵnf (t f,t z,,ρ) if f = m, (15) mŵmf (t f,t z,,ρ)+(n 1)Ŵnf (t f,t z,,ρ) if f = n. As in the free-trade regime, the oalition and the f-ountry are players in a non-ooperative game. Their payoffs are Ŵzf (t f,t z,,ρ) and Ŵf (t f,t z,,ρ) from (13) and (15) and their ξ, 10
strategies are t z and t f, respetively. In the Appendix A we alulate the Nash equilibrium tax rates. Inserting these tax rates in (13) and (15) yields the Nash equilibrium welfares, ŵ f := (ˆt Ŵf f,ˆt zf,,ρ ) [ˆTf = Ŵf (), ˆT ] zf (),,ρ := Ŵf (,ρ), ŵ hf := (ˆt Ŵhf f,ˆt zf,,ρ ) [ˆTf = Ŵhf (), ˆT ] zf (),,ρ := Ŵhf (,ρ). (16) The equations (16) speify the funtions Ŵf and Ŵhf in Table 2. 4 Size and asymmetry of limate damage and the threat of embargo (δ,ρ, = 0) Throughout this setion, we assume that onsumer preferenes for fuel are the same in all ountries ( = 0), whereas the limate damage may differ aross the groups of ountries (ρ 0). The first step towards assessing the impat of the threat of embargo on free riding is to investigate the onditions under whih the grand oalition is stable in the embargo regime. 4.1 Stability of the grand oalition in the embargo regime The grand oalition is stable [instable] in the embargo regime, if the welfare differene ˆD f (ρ) := W h (ρ) Ŵf (ρ) is non-negative [negative] for f = h = m,n. 13 The question we are interested in is whether in the embargo regime the onditions for the stability of the grand oalition improve, when the limate damage differs aross groups (ρ 0). Sine analytial omplexity prevents the derivation of informative general results, we turn to numerial analysis and investigate the stability of the grand oalition in the Samples 1 and 2 of Table 3. These samples differ only with respet to the size of the parameter δ and inlude the ontinuous variation of the damage parameter δ in the interval 14 [ρ min,ρ max ], whih is the set of all values of δ, for whih the equilibrium demands and supplies of fuel are positive. 15 13 To avoid lutter, we write ˆD f (ρ) short for ˆD f ( = 0,ρ) et. in the present setion. 14 For details see Appendix B. We keep our analysis within that interval, beause negative quantities are an artefat of the linear-quadrati funtional forms (1) and (2), and zero onsumption of fuel is highly unrealisti. Positive values of the demand and supply of the onsumption good are seured by hoosing a suffiiently high value of the parameter x. To avoid lutter, we write[ρ min,ρ max ] instead of[ρ min (δ),ρ max (δ)]. Also, we set ρ min (δ) = δ and thus avoid dealing with limate hange benefits (= negative limate damage). 15 We use the term sample rather than example beause eah sample haraterizes the outome along the asymmetry dimension ρ and hene onsists of a ontinuum of examples. 11
δ m = δ a m = a m = n b ξ ρ = δ n δ = a n a Sample 1 1,600 100 5 2,000 100,000 [ρ min,ρ max ] 0 Sample 2 3 100 5 2,000 100,000 [ρ min,ρ max ] 0 Table 3: Degree of asymmetry and level of limate damage: Samples 1 and 2 Figure 1 determines for Sample 1 the sign of the welfare differene ˆD f (ρ) = W h (ρ) Ŵ f (ρ) < 0 for f = h = m,n and for all ρ [ρ min,ρ max ], where ρ min = 1,600 and ρ max = 1,596. The straightforward result is that a ountry of either group prefers being embargoed to joining the oalition on the entire domain of asymmetry, [ρ min,ρ max ]. Hene, under the onditions of Sample 1 an embargo fails to forge a stable grand oalition. 1500 1000 500 500 1000 1500 ρ 1500 1000 500 500 1000 1500 ρ 0.005 0.005 0.010 0.010 0.015 0.020 m W Ŵm 0.015 n W Ŵn Figure 1: Welfare differene funtions ˆD m (ρ) and ˆD n (ρ) in Sample 1 (δ = 1,600) In Sample 2 the boundary points of the feasibility interval [ρ min,ρ max ] are ρ min = 3 and ρ max = 4,429. Figure 2 shows that in Sample 2 we get the same qualitative result as in Sample 1: ˆDf (ρ) < 0 for all f = m,n and for all ρ [ρ min,ρ max ]. Hene, under the onditions of Sample 2 an embargo also fails to forge a stable grand oalition. 4.2 Credibility of the threat of embargo The negative result of Setion 4.1 learly disqualifies the embargo poliy as an instrument to stabilize the grand limate oalition in the Samples 1 and 2 that fous on asymmetri limate damage. In partiular, there is no sense in examining the redibility of the threat of embargo, sine the desired result of an embargo, namely the stabilization of the grand oalition, annot be seured - irrespetive of whether the threat of embargo is redible. Nonetheless, we will briefly investigate by means of the Tables 4 and 5 how the embargo 12
0.005 1000 2000 3000 4000 ρ 0.002 1000 2000 3000 4000 ρ 0.010 0.015 0.020 m W Ŵm 0.004 0.006 0.008 0.010 n W Ŵn Figure 2: Welfare differene funtions ˆD m (ρ) and ˆD n (ρ) in Sample 2 (δ = 3) regime ompares with the free-trade regime in ase of the Samples 1 and 2. The first row of these tables presents the results from Setion 4.1 and the third row ontains the orresponding information "imported" from Eihner and Pethig (2014b). 16 Embargo regime unstable Free-trade regime unstable Parameter ρ ρ min ρ = 0 ρ max Table 4: Stability in the regimes of free trade and embargo in Sample 1 (δ = 1,600) Embargo regime Sub-interval no.: unstable 1 2 3 Free-trade regime unstable stable unstable Parameter ρ ρ min ρ m ρ = 0 ρ n ρ max Table 5: Stability in the regimes of free trade and embargo in Sample 2 (δ = 3) For the ase of high limate damage (Sample 1), the omparison of regimes in Table 16 Eihner and Pethig (2014b) study the Samples 1 and 2 as speified in Table 3 in the free-trade regime. Here we only present their results and refer the reader to Eihner and Pethig (2014b) for further disussion and interpretation of these results. We will apply the same "import" proedure below for the Samples 3, 4 and 5 of Table 4. 13
4 shows that an embargo is ineffetive (box [4] in Table 1) with and without asymmetri limate damage. If the limate damage is low (Sample 2), an embargo is also ineffetive in the sub-intervals 1 and 3 of Table 5 with high limate damage asymmetry ρ. However, there is an interval [ ρ n, ρ m ] ontaining ρ = 0 in whih the grand oalition is stable in the free-trade regime but unstable in the embargo regime. In that ase implementing an embargo would be ounterprodutive (box [3] in Table 1), beause it would destabilize the otherwise stable grand oalition. The explanation for the puzzle of Table 5 that in the interval [ ρ m, ρ n ] an embargo destabilizes the otherwise stable grand oalition is as follows. Aording to Eihner and Pethig (2014a) the grand oalition is stable in the free-trade regime when the parameters of Sample 2 are given and all ountries are alike ( = 0). If the oalition implements an embargo in that ase of full symmetry, not only the free rider is pushed into the state of autarky, but international trade also eases within the oalition of size m+n 1 beause all ountries in that oalition are alike. Hene, the embargo turns the world eonomy from trade between the free rider and the oalition into full autarky in whih the grand oalition is known to be unstable (Eihner and Pethig 2014a). As the third row of Table 5 shows, the inentives for ooperation tend to deline with growing asymmetry in the free-trade regime, 17 and this is also true in the embargo regime. Sine the grand oalition is unstable for = 0 in the embargo regime of the Samples 1 and 2, inreasing asymmetry fails to turn that result around. One an show that the negative results of the Samples 1 and 2 not only hold for the parameter values δ = 1,600 (Sample 1) and δ = 3 (Sample 2), but also for all δ > 0. If we vary the damage parameter δ > 0 ontinuously and keep unhanged all other parameters in Table 3, we find that in qualitative terms the outome is the same as in the Figures 1 and 2 for all δ > 0. We summarize these findings in Result 1. (Embargo and size and asymmetry of limate damage) Set the parameters a = 100,b = 2,000, = 0,m = n = 5 and ξ = 100,000 that are ommon to the Samples 1 and 2 and onsider all feasible pairs (δ,ρ). Threatening to embargo free riders is not suitable as a poliy to forge the grand limate oalition for any pair (δ,ρ), beause for all δ > 0, the grand oalition is unstable in the entire interval [ρ min (δ),ρ max (δ)] of feasible limate damage asymmetries. 17 For more details see Eihner and Pethig (2014b) 14
5 Size and asymmetry of fuel demand, size of extration osts and the threat of embargo (a,, ρ = 0, ξ ) Now we assume that the limate damage hits all ountries in the same way (ρ = 0), whereas the preferenes for fuel may differ aross ountries ( 0). As in Setion 4, the omplexity of the asymmetry analysis fores us into numerial analysis. Speifially, we will explore the impat on the stability of the grand oalition of ontinuous variations of the fuel-demand asymmetry parameter by means of the Samples 3, 4 and 5 speified in Table 6. These samples differ with respet to the parameter ξ only and in eah sample, the parameter will be varied in the interval 18 [ min, max ], the set of all values of, for whih the equilibrium demands and supplies of fuel are positive. Sample 5 equals Sample 1 exept that we turn the asymmetry ρ 0 and = 0 from Sample 1 into the asymmetry 0 and ρ = 0 in Sample 5. δ m = δ a m = a m = n b ξ ρ = δ n δ = a n a Sample 3 3 100 ) 5 2,000 5,000 0 [ min, max ] Sample 4 3 100 5 2,000 500 0 [ min, max ] Sample 5 3 100 5 2,000 100,000 0 [ min, max ] ) For the ase of Sample 3, Setion 5.1 also studies variations of parameter α Table 6: Fuel preferene asymmetry and extration osts: Sample 3, 4 and 5 Setion 5 is organized as follows. Setion 5.1 investigates Sample 3 and determines ˆD f ( ) first for all fuel-demand asymmetry parameters [ min, max ] and then for the set of all feasible tuples (a,). The ontinuous variation of the parameter a serves to study the interdependene of the impats of the size and asymmetry of fuel demand. For the Samples 3, 4 and 5, the first part of Setion 5.2 determines the sign of the welfare differene ˆD f (), f = m,n, on the interval [ min, max ] and examines the redibility of the threat of embargo. Here we keep the parameter a onstant at a = 100, beause oneptually the effets of its variations are as in Sample 3. However, we expand the Samples 3, 4 and 5 along the extration osts dimension, ξ, that is the only dimension in whih the Samples 3, 4 and 5 differ. 18 The feasibility interval [ min, max ] is the analogue to the interval [ρ min,ρ max ] in Setion 4. To avoid lutter, we write [ min, max ] instead of [ min (ξ), max (ξ)]. 15
5.1 Size and asymmetry of fuel demand (,a,ρ = 0) In the Figures 3 and 4 we determine for Sample 3 the sign of the welfare differenes ˆD m () and ˆD n () for all [ min, max ]. The right-hand-side panels of these figures depit enlarged segments of the welfare differene urves, whih enables us to identify the (sign of the) intersetion points ĉ m1 and ĉ m2, respetively. 0.14 0.12 0.10 0.08 0.06 m W Ŵm 0.0005 ĉ m1 2 1 1 2 0.0005 0.04 0.02 ĉ m2 40 20 20 40 60 0.0010 0.0015 0.0020 m W Ŵm Figure 3: Welfare differene funtion ˆD m in Sample 3 (ξ = 5,000) 0.25 0.20 0.15 n W Ŵn 0.0005 ĉ n2 2 1 1 2 0.0005 0.10 0.05 ĉ n1 40 20 20 40 60 n W Ŵn 0.0010 0.0015 0.0020 Figure 4: Welfare differene funtion ˆD n in Sample 3 (ξ = 5,000) In Figure 3 we find ĉ m1 = 0.99 and ĉ m2 = 19.10 satisfying ˆD m (ĉ m1 ) = ˆD m (ĉ m2 ) = 0, ˆD m (ĉ m1) < 0 and ˆD m (ĉ m2) > 0. In Figure 4 there exist ĉ n1 = 16.03 and ĉ n2 = 0.99 satisfying ˆD n (ĉ n1 ) = ˆD n (ĉ n2 ) = 0, ˆDn (ĉ n1 ) < 0 and ˆD n (ĉ n2 ) > 0. Sine min = 40 and max = 68, the ranking is 19 min < ĉ n1 < ĉ m1 < 0 < ĉ n2 < ĉ m2 < max. Table 7 illustrates the 19 For ountries belonging to the groups M and N the results are not mirror-symmetri, beause the preferenes for fuel of a free-riding m-ountry are invariant in, while the preferene parameter a n = 100+ of a free-riding n-ountry obviously depends on. 16
onlusion regarding the stability of the grand oalition. m-ountry free rides: no yes no n-ountry free rides: no yes no Grand oalition is: stable unstable stable Parameter : min ĉ m1 = 0 ĉ n2 ĉ n1 ĉ m2 max Table 7: Embargo and stability of the grand oalition in Sample 3 (ξ = 5,000) Aording to Table 7 the grand oalition is unstable in Sample 3 in the interval]ĉ n1,ĉ m2 [ of zero, low and medium fuel-demand asymmetry and eventually beomes stable when is suffiiently large. This learly suggests that asymmetri fuel demand improves the inentives to ooperate in the embargo regime, beause inreasing asymmetry raises the gains from trade among oalition ountries, whih in turn redue the advantage of the autarki free-riding ountry. Embargo regime stable unstable stable Sub-interval no.: 1 2 3 4 5 Free-trade regime stable unstable stable n1 Parameter : min = 0 ĉ m2 ĉ n1 m2 max Table 8: Stability of the grand oalition in the regimes of free trade and embargo in Sample 3 (ξ = 5,000) The next step towards examining the redibility of the threat of embargo in Sample 3 is to ompare the intervals of stability and instability of the grand oalition in the regimes of free trade and embargo. The first row of Table 8 reprodues the last row of Table 7, and the third row ontains the outome of Sample 3 in the free-trade regime "imported" from Eihner and Pethig (2014b, Table 5). 20 The ommon feature of both regimes is that instability prevails in ases of zero and small to moderate asymmetry. If the asymmetry gets suffiiently large, the grand oalition stabilizes in both regimes, but the swith ours at smaller degrees of asymmetry under embargo than under free trade. Although the embargo does not sueed in turning the grand oalition from instable to stable in all areas 20 See also footnote 16. 17
of asymmetry, in Sample 3 the embargo has the expeted impat, to some extent at least, in ontrast to the embargo in the Samples 1 and 2 above. More speifially, Table 8 shows that an embargo is ineffetive at low levels of asymmetry (sub-interval 3; box [4] in Table 1), is unneessary at very high levels of asymmetry (sub-intervals 1 and 5; box [1] of Table 1), and is effetive at intermediate levels of asymmetry (sub-intervals 2 and 4; box [2] of Table 1). It is lear that the redibility of threatening to embargo free riders is not an issue in the eonomies belonging to the sub-intervals 1, 3 and 5, beause in those eonomies an embargo makes no sense in the first plae. The sub-intervals 2 and 4 are most interesting, beause in these ases the embargo will do the job it is expeted to do, if the threat of embargo turns out to be redible. To examine the redibility in those sub-intervals, we reall from Table 2 the notation ŵ hf = Ŵhf () and w hf = W hf (), aording to whih an hf-ountry (with h,f = m,n) is a ountry of group H = M,N inside the oalition that is of size m + n 1 and faes an f-ountry, f = m,n, outside the oalition. Applying that notation, the threat of embargo is said to be redible, if (i) ŵ mm w mm and ŵ nm w nm and (ii) ŵ mn w mn and ŵ nn w nn. Sine redibility requires satisfying onditions (i) and (ii), the threat of embargo fails to be redible if either the onditions (i) or the onditions (ii) or both onditions fail to hold. 0.06 0.04 Ŵ mm W mm 0.02 40 20 20 40 60 0.02 0.04 0.06 Ŵ nm Wnm Figure 5: Credibility hek in Sample 3 (ξ = 5,000) Figure 5 depits the welfare differenes Ŵ hm () W hm () on [ min, max ] for h = m,n. The shaded areas in that figure mark the intervals [ n1,ĉ n1 ] = [ 32.36, 16.03] and [ĉ m2, m2 ] = [19.10,47.86] on the -axis that orrespond to the sub-intervals 2 and 4 of Table 8 in whih the transition from free trade to embargo stabilizes the grand oalition. A neessary ondition for redibility is that Ŵmm () W mm () and Ŵnm () W nm () for 18
some [ n1,ĉ n1 ] [ĉ m2, m2 ]. Figure 5 shows, however, that this ondition is not satisfied for any [ n1,ĉ n1 ] [ĉ m2, m2 ]. Hene in all eonomies of Sample 3 in whih an embargo ould be useful it fails to be redible. In Sample 3 the parameter a is fixed at the level a = 100. We wish to generalize the insight of Sample 3 - in a modest way - by investigating how the outome of an embargo and its redibility hange when we onsider ontinuous variations of the parameters and a while keeping unhanged all other parameters of Sample 3. To that end, we first onsider the embargo regime. It an be shown that the points min, ĉ n1 and ĉ m1 are linearly dereasing in a and ĉ n2, ĉ m2 and max are linearly inreasing in a. The impliation for the (in)stability of the grand oalition in the (a,) spae is readily illustrated in Figure 6. The vertial line in Figure 6 illustrates the intervals of stability and instability of Sample 3 known from Table 7. Essentially, inreasing the parameter a amounts to linear expansions of the intervals of asymmetry in whih the grand oalition is stable or instable leaving the order of these intervals unhanged. 21 For any given value of a, the impat of variations of is as shown in Table 7 with the qualifiation that the asymmetry neessary to turn instability into stability is inreasing in the parameter a. If we start with a tuple (a,) for whih the grand oalition is stable and inrease a while keeping onstant, we find some value ã suh that the grand oalition is unstable for all feasible (a,) satisfying a > ã. Sample 3 max 200 100 ĉ m2 100 200 300 ĉ 400 n1 a 100 Figure 6: Stability of the grand oalition in the (a, ) parameter spae, when all other parameters are as in Sample 3 (ξ = 5,000) min Eihner and Pethig (2014b, Figure 7) derive a figure similar to Figure 6 for Sample 3 in the free-trade regime. Rather than reproduing that figure here, we integrate Figure 7 from Eihner and Pethig (2014b) and Figure 6 of the present paper to obtain Figure 7. In that figure, the ones shaded in grey give us the intervals [ n1 (a),ĉ n1 (a)] and [ĉ m2 (a), m2 (a)] for 21 This is also true for the Samples 4 and 5 we study below whih is why we will not go through the exerise arried out in Figure 6 again in the subsequent analysis. 19
all parameters a for whih an embargo is effetive. The small stripe in red around the a-axis is the area of redibility. Sine that stripe does not overlap with the grey ones anywhere the onlusion is max 200 m2 100 100 ĉ m2 100 200 300 400 ĉ n1 n1 a Figure 7: Chek of redibility in the (a,)-spae, when all other parameters are as in Sample 3 (ξ = 5,000) Result 2. (Embargo and the size and asymmetry of fuel demand) Set the parameters b = 2,000,δ = 3,m = n = 5,ρ = 0 and ξ = 5,000 as in Sample 3 and onsider all feasible pairs (a,). Threatening to embargo free riders is not suitable as a poliy to forge the grand limate oalition for any pair (a, ), beause the embargo is either ineffetive or unneessary or it is effetive but not redible. 5.2 Size and asymmetry of fuel demand and size of extration osts The Sample 3 we disussed above is haraterized by medium-level extration osts. Now we turn to the ases of lower (Sample 4) and higher (Sample 5) extration osts. 1.5 1.0 0.5 m W Ŵm 0.010 0.005 ĉ m1 ĉ m2 20 20 40 60 80 100 0.005 0.010 0.015 ĉ m1 ĉ m2 100 200 300 400 0.020 0.025 m W Ŵm Figure 8: Welfare differene funtion ˆD m in Sample 4 (ξ = 500) 20
3.5 3.0 2.5 n W Ŵn ĉ n1 ĉ n2 50 40 30 20 10 10 20 2.0 0.005 1.5 1.0 0.5 ĉ n1 ĉ n2 100 200 300 400 n W Ŵn 0.010 0.015 Figure 9: Welfare differene funtion ˆD n in Sample 4 (ξ = 500) The Figures 8 and 9 orrespond to Sample 4. In Figure 8 we find ĉ m1 = 17.70 and ĉ m2 = 90.45 satisfying ˆD m (ĉ m1 ) = ˆD m (ĉ m2 ) = 0, ˆD m(ĉ m1) < 0 and ˆD m(ĉ m2) > 0. In Figure 9 there exist ĉ n1 = 47.5 and ĉ n2 = 21.51 satisfying ˆD n (ĉ n1 ) = ˆD n (ĉ n2 ) = 0, ˆDn (ĉ n1 ) < 0 and ˆD n(ĉ n2) > 0. Sine min = 83 and max = 479, the ranking is 22 min < ĉ n1 < ĉ m1 < 0 < ĉ n2 < ĉ m2 < max. We onlude that in Sample 4 the pattern of stability and instability of the grand oalition is the same as in Table 7 for Sample 3, whih is why there is no need to reprodue that table here for Sample 4. An embargo sueeds to stabilize the grand oalition, if the fuel-demand asymmetry is suffiiently large. Embargo regime: stable unstable stable Sub-interval no.: Free-trade regime: 1 2 3 unstable Parameter : min ĉ n1 = 0 ĉ m2 max Table 9: Embargo and stability of the grand oalition in Sample 4 (ξ = 500) The first row of Table 9 shows the stability pattern of Sample 4 in the embargo regime, and the third row of this table, taken from Eihner and Pethig (2014b, Table 7), desribes the outome of Sample 4 in the free-trade regime. Aording to Table 9 an embargo is either 22 The results for m- and n-ountries are not mirror-symmetri, beause the preferenes for fuel of a freeriding m-ountry are invariant in, while the preferene parameter a n = 100+ of a free-riding n-ountry obviously depends on. 21
ineffetive (sub-interval 2) or effetive (sub-intervals 1 and 3) whih requires examining the redibility of the threat of embargo in eonomies belonging to the sub-intervals 1 and 3. 0.6 0.4 Ŵ mm W mm 0.03 0.2 0.02 0.2 0.4 0.6 100 200 300 400 Ŵ nm W nm Ŵ mm 80 60 40 20 Ŵ nm W mm W nm 0.01 0.01 0.02 Figure 10: Credibility hek in Sample 4 (ξ = 500) Figure 10 depits the welfare differenes Ŵhm () W hm () on [ min, max ] for h = m,n. The shaded area in the left and right panel of Figure 10 marks the sub-interval 4 and 2 of Table 8, respetively, in whih the transition from free trade to embargo stabilizes the grand oalition. We onlude that there is no in the shaded intervals for whih both urves are positive valued. Hene in all eonomies of Sample 4 in whih an embargo ould be useful it fails to be redible. Finally, we turn to Sample 5 that represents the ase of high extration osts, muh higher than in the Samples 3 and 4. The welfare differene urves of Sample 5 are plotted in Figures 11 and 12. In Figure 11 we find ĉ m1 = 0.004 and ĉ m2 = 1.18 satisfying ˆD m (ĉ m1 ) = ˆD m (ĉ m2 ) = 0, ˆDm (ĉ m1 ) < 0 and ˆD m (ĉ m2) < 0. In Figure 12 there exist ĉ n1 = 1.17 and ĉ n2 = 0.004 satisfying ˆD n (ĉ n1 ) = ˆD n (ĉ n2 ) = 0, ˆDn (ĉ n1 ) < 0 and ˆD n (ĉ n2) > 0. Sine min = 3.5 and max = 3.6, the ranking is min < ĉ n1 < ĉ m1 < 0 < ĉ n2 < ĉ m2 < max. The Figures 11 and 12 show that in Sample 5 the pattern of stability and instability of the grand oalition is the same as in Table 7 for Sample 3, whih is why we need not reprodue that table for Sample 5. Interestingly, in the embargo regime it is the ommon feature of the Samples 3, 4 and 5 that in ase of suffiiently large asymmetry the grand oalition turns from instable to stable. This pattern does not hold in the free-trade regime, 22
0.0010 0.0008 0.0006 0.0004 0.0002 ĉ m2 m W Ŵm 3 2 1 1 2 3 W m Ŵm 4. 10 7 2. 10 7 ĉ m1 0.010 0.005 0.005 0.010 2. 10 7 4. 10 7 6. 10 7 8. 10 7 1. 10 6 Figure 11: Welfare differene funtion ˆD m in Sample 5 (ξ = 100,000) 0.0010 n W Ŵn 0.0008 4. 10 7 3. 10 7 n W Ŵn 0.0006 2. 10 7 0.0004 0.0002 3 2 ĉ n1 1 1 2 3 1. 10 7 1. 10 7 2. 10 7 ĉ n2 0.002 0.004 0.006 0.008 0.010 Figure 12: Welfare differene funtion ˆD n in Sample 5 (ξ = 100,000) however, as the omparison of the last rows of the Tables 8, 9 and 10 shows. 23 In the free-trade regime, the ommon feature of the Samples 2 and 5 is that the grand oalition is stable in ases of symmetry and small asymmetries ( ρ 0 in Sample 2 and 0 in Sample 5), beause a low damage parameter δ as well as a high extration ost parameter ρ keep limate damage low. The Samples 2 and 5 differ (in the free-trade regime), however, beause large asymmetries restore stability in Sample 5 but not in Sample 2. Observe also that under free trade, the effet of asymmetry on stability is "non-linear" in Sample 5. The grand oalition is stable in ase of full symmetry, it gets unstable at intermediate levels of fuel-demand asymmetry, and it stabilizes again when the asymmetry beomes suffiiently large. Inspetion of Table 10 reveals that the set of feasible asymmetries [ min, max ] is partitioned into seven sub-intervals that over all possible ombinations, listed in Table 1, between stability and instability in the transition from free trade to embargo. 24 As above, we restrit 23 The last row in Table 10 is taken from Table 8 in Eihner and Pethig (2014b). 24 The explanation of the feature that an embargo destabilizes the otherwise stable grand oalition in the 23
Embargo regime stable unstable stable Sub-interval no.: 1 2 3 4 5 6 7 Free-trade regime: stable unstable stable unstable stable Parameter : min n1 n2 = 0 m1 ĉ n1 ĉ m2 m2 max Table 10: Stability of the grand oalition in the regimes of free trade and embargo in Sample 5 (ξ = 100,000) our attention to the sub-intervals in whih an embargo stabilizes the otherwise unstable grand oalition, if the threat of embargo turns out to be redible. 0.0008 0.0006 0.0004 0.0002 Ŵ mm W mm 3 2 1 1 2 3 0.0002 0.0004 0.0006 Ŵ nm W nm Figure 13: Credibility hek in Sample 5 (ξ = 100,000) Figure 13 depits the welfare differenes Ŵhm () W hm () on [ min, max ] for h = m,n. The shaded areas in Figure 13 mark the sub-intervals 2 and 6 of Table 10, in whih the transition from free trade to embargo stabilizes the grand oalition. Aording to Figure 13, there is no in the shaded intervals for whih both urves are positive valued. Hene in all eonomies of Sample 5 in whih an embargo ould be useful it fails to be redible. In the preeding analysis, we showed for three different values of the extration ost parameter ξ that there is no subset of parameters in the Samples 3, 4 and 5, for whih the threat of embargo is redible in ases where the imposition of the embargo would stabilize the otherwise unstable grand oalition. In the sequel, we generalize by showing that this result holds not only for the values ξ = 500,ξ = 5,000 and ξ = 100,000 of the Samples 4, 3 and 5, respetively, but also for all positive ξ. Speifially, we will haraterize the parameter sub-interval 4 of Table 10 is the same as in Sample 2 (sub-interval 2 of Table 5). 24