Carbon tariffs and cooperative outcomes

Terry Eyland a,b, Georges Zaccour a,n

a GERAD, HEC Montréal, Canadab Bishop's University, Canada

H I G H L I G H T S

� One of the first studies to consider border-tax adjustment in a strategic context.� Border-tax adjustment can lead to an optimal outcome, in cooperative sense.� Optimal outcome is achieved with partial tax adjustment.

a r t i c l e i n f o

Article history:Received 21 August 2012Received in revised form9 October 2013Accepted 14 October 2013Available online 5 November 2013

Keywords:Game theoryBorder tax adjustmentInternational environmental agreementsCompetitivenessCarbon leakage

a b s t r a c t

In the absence of an international environmental agreement (IEA) on climate change, a country may bereluctant to unilaterally implement environmental actions, as this may lead to the relocation of firms toother, lax-on-pollution countries. To avoid this problem, while still taking care of the environment, acountry may impose a carbon tariff that adjusts for the differences between its own carbon tax and theother country's tax. We consider two countries with a representative firm in each one, and characterizeand contrast the equilibrium strategies and outcomes in three scenarios. In the first (benchmark)scenario, in a first stage the regulators in the two countries determine the carbon taxes noncooperatively,and in a second stage, the firms compete à la Cournot. In the second scenario, the regulators cooperate indetermining the carbon taxes, while the firms still play a noncooperative Cournot game. In the thirdscenario, we add another player, e.g., the World Trade Organization, which announced a border tax in aprior stage; the game is then played as in the first scenario. Our two major results are (i) a border-taxadjustment (BTA) mimics quite well the cooperative solution in setting the carbon taxes as in scenariotwo. This means that a BTA may be a way around the lack of enthusiasm for an IEA. (ii) All of oursimulations show that a partial correction of the difference in taxes is sufficient to maximize totalwelfare. In short, the conclusion is that a BTA may be used as a credible threat to achieve an outcome thatis very close to the cooperative outcome.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

A challenging problem for a country contemplating the intro-duction of a unilateral environmental policy, e.g., taxing pollutantsor imposing emissions standard, is how to keep its local firmscompetitive. Indeed, since any environmental policy may increaseproduction costs, at least in the short term, firms operating inenvironmentally lax countries gain a competitive advantage, andlocal firms are tempted to relocate to such countries. Thisphenomenon is referred to in the literature as the pollution-haven hypothesis (PHH), see, e.g., Copeland and Taylor (1994),Sheldon (2006) and Levinson and Taylor (2008).

A more troubling outcome would be that the emissions fromthe production going abroad would cancel out the reduction incarbon emissions in the abating country because of the lessenvironmentally friendly technologies being used in the laxcountry.1 For example, a firm moves to a country that uses coalfor energy instead of hydroelectricity. Leakage rates have beenwidely studied and some find results close to 2%, while moststudies find leakage rates between 5% and 20%.2 Carbon leakage istypically separated in multiple channels, where the two mainchannels are the energy prices channel and the competitivenesschannel. The energy prices channel relates to an increase in theforeign demand of polluting products following the decrease inthe demand of the countries adopting an environmental policy,

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Energy Policy

0301-4215/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enpol.2013.10.043

n Corresponding author. Tel.: þ 1 514 340 6053x6050; fax: þ 1 514 340 5665.E-mail addresses: teyland@ubishops.ca (T. Eyland),

georges.zaccour@gerad.ca (G. Zaccour).

1 For carbon leakage to occur, the emissions reduction does not need to becancelled out but rather emissions abroad increasing due to this environmentalpolicy is carbon leakage.

2 For more on this, see Zhou et al. (2010).

Energy Policy 65 (2014) 718–728

and thus a decrease in its world price. The competitivenesschannel relates to an increase in foreign emissions becausedomestic firms are shifting its production to a country with lessenvironmental stringency. The bleak dual outcome for abatingcountries is then a loss of competitiveness and a large increase inforeign emissions. In an extreme carbon leakage context, very fewcountries would be tempted to adopt an environmental policy.3

Even if the other countries also engage in setting carbon prices,there may still be opportunities for arbitrage due to differences intheir levels.4 One proposal that has been discussed over the yearsis the introduction of a carbon tariff, also known as a carbon-motivated border-tax adjustment (BTA), which would impose atariff to compensate for the difference in taxes and give a subsidyon exports going to a country with a less stringent environmentalpolicy. As a BTA may potentially be viewed as a protectionistmeasure, a requirement for its implementation is its acceptance bythe World Trade Organization (WTO). There is a significantliterature advancing reasons why a BTA should be allowed underthe WTO (see, e.g., Ismer and Neuhoff, 2007; Cendra, 2006;Pauwelyn, 2007; Weber and Peters, 2009). For instance, Ismerand Neuhoff (2007) suggest using a best-available-technology(BAT) rule whereby a unit of product would be taxed in accordancewith the emissions released in the country with the lowestemissions ratio in place. Similarly Mattoo et al. (2009), look atimplementing BTAs with respect to carbon content in importsversus using carbon content in domestic production. They believeit would seriously address competitiveness concerns in high-income countries without significantly hurting developing-country trade. They suggest that WTO rules may prohibit BTAbased on embodied carbon content but allow for domestic carboncontent BTA. Monjon and Quirion (2010) discuss the design of aborder adjustment (BA) applied to European Union. The authorsbelieve that we must be wary of using the BAT because we maynot have an appropriate tax level. Certain technologies such asproducing metals with hydropower should be excluded; otherwisethe level of the BA may be too low. They propose that the easiestway to define the BAT is to use the product-specific benchmarksfor goods at risk of carbon leakage, which are determined by theEuropean Commission. These benchmarks are computed based onthe average emissions of the 10 percent least carbon-intensiveEuropean plants.

This paper is a follow-up to Eyland and Zaccour (2012), wherewe assessed the impact of an exogenous BTA on welfare in a two-country model. Contrary to the literature using computable gen-eral equilibrium (CGE) models (e.g., Dissou and Eyland, 2011;Fischer and Fox, 2009), where one country adopts a BTA and onlylooks at its impacts, Eyland and Zaccour (2012) allow for astrategic reaction from the other country, as advised by Ludemaand Wooton (1994). Further, we found that a partial adjustmentmay lead to higher welfare than a full adjustment.

In a two-country framework, our objectives are to endogenizethe border-adjustment tax and to answer the following researchquestions:

1. What is the BTA value that maximizes total welfare?2. Is it always in the best interest of the abating country to see a

BTA imposed?3. Can a BTA mimic an environmental agreement in which the

two countries cooperatively set their carbon taxes?

The answer to the first question will offer a hint to internationalagencies (e.g., WTO) on what would be a suitable interval for aBTA. The answer to our second question will provide a guidelinefor an abating country on when to lobby for a BTA, and when it isbetter to keep quiet. Finally, the third question addresses theissue of the decentralization of a collectively optimal policythrough BTA.

To deal with these questions, we shall compare the outcomes ofthree games, namely, a noncooperative game (benchmark), acooperative game under taxation, and a noncooperative gamewith a BTA.

The rest of the paper is structured as follows: In Section 2, weintroduce the different games. In Section 3, we characterize theirequilibria; and in Section 4, we run some simulations to comparethe outcomes of the three considered scenarios. Section 5 dis-cusses the robustness of the results and Section 6 concludes.

2. Duopoly model5

To evaluate the impact of a border tax on welfare, wedeveloped a model similar to that of Brander and Spencer(1985), to which we add an environmental damage cost andconsumer surplus.6 As mentioned above, this paper builds onEyland and Zaccour (2012) and mainly adds a stage to the game inwhich an international body chooses a BTA. As in Brander andSpencer (1985), we have two firms producing a homogeneousgood and located in two countries, referred to as the home andforeign countries. Each country seeks a taxation policy, i.e., adomestic tax or subsidy that may lead to a certain tariff or subsidyon imports, which maximizes its own welfare. Note that through-out the text, the term domestic tax or import tariff may refer to itspositive or negative value (subsidy). For the sake of simplicity,without much loss in qualitative insights and still allowing forreplication of the cases with a carbon tax only, or a carbon tax witha border-tax adjustment (BTA), we assume in the sequel that thereis only a consuming market in home.7

We subscript with F the foreign firm's variables and with H thehome firm's variables. Denote by qH the quantity produced by thehome firm and by qF the quantity produced by foreign. We adoptthe following inverse-linear demand:

PðqH ; qF Þ ¼ α�βðqHþqF Þ; ð1Þwhere Pð�Þ is the price of the good and α and β are strictly positiveparameters.

Let cjðqjÞ be the production cost function of firm j, given by

cjðqjÞ ¼ 12 cjq

2j ; j¼ F;H

with cj40, that is, a convex increasing function satisfying cjð0Þ ¼ 0.As consumption takes place only at home and to save on notation,we suppose that the transportation cost is embedded in cjðqjÞ.Further, we assume that the production cost of the foreign firmis not higher than that of the home firm, i.e., cF rcH . This is inline with the idea that foreign represents a low production-costcountry (e.g., China or India), whereas home is a high production-cost country. Note that this assumption is not necessary tocharacterize the equilibria, but is made only for the sake ofinterpreting and discussing the results in a realistic context.

3 As Böbringer et al. (2010) highlight even though energy intensive tradeexposed sectors make up for less than 6% of United States emissions and only 10–20% of their total emissions, they are taken seriously because they are very wellorganized and vocal.

4 For more on strategic environmental policies see Barrett (1994) andMarkusen et al. (1992).

5 This section draws heavily on Eyland and Zaccour (2012). As mentionedbefore, the basic ingredients of the model are the same.

6 In Brander and Spencer (1985), there are two firms from different countriescompeting à la Cournot in a third country.

7 Having only one consumer market abstracts from the decision of whetherexports from a country with a carbon tax should have a rebate and only focuses onstrategic effects of BTAs on taxation policies.

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728 719

Denote by tj the domestic per-unit carbon tax in countryj; jAfH; Fg.

The profit functions of firms H and F are given by

πHðqH ; qF ; tHÞ ¼ α�βðqHþqF Þ�cH2qH�tH

� �qH ; ð2Þ

πF ðqH ; qF ; tF Þ ¼ α�βðqHþqF Þ�cF2qF�tF

� �qF : ð3Þ

The welfare functions of home and foreign are as follows:

Wj ¼ CSjþPSjþTRj�EDj;

where CSj, PSj, TRj, and EDj, jAfH; Fg; represent the consumersurplus, producer surplus, tax revenue and environmentaldamage, respectively. Given the linear specification for the inversedemand, it can be easily established that the consumer surplus incountry H is

CSH ¼ βðqHþqF Þ22

:

The producers' surpluses in the two countries are equal to theprofits in (2) and (3). The tax revenues, when a BTA is not allowed,are given straightforwardly by

TRH ¼ tHqH ;TRF ¼ tFqF :

Remark 1. The carbon tax, which is normally applied to emis-sions, is based here on quantities. This simplifying formulationrests on the two following assumptions: (i) Emissions and outputare monotonically related, i.e., ej ¼ f jðqjÞ; jAfH; Fg, where ej are theemissions and f jð�Þ is an increasing function. This assumption iscommon in the literature, which actually assumed that f jð�Þ islinear, i.e., ej ¼ αjqj; with αj being a scaling parameter. (ii) Bothcountries use the same technology, that is, αH ¼ αL, and thereforeany difference in emissions are only due to a difference in outputsin the two countries. Whereas the first assumption is by no meanssevere and has the advantage of saving on the number of variables,the second assumption is clearly restrictive. However, as ourmodel is static and does not include technological improvement,we believe that this assumption would not much alter ourqualitative message. Of course, the quantitative results wouldchange if we account for technological difference among the twocountries. This could be done in a future research by assuming thatemissions and output are related as follows: ej ¼ αjðKjÞqj, where Kj

represents abatement capacity (see, e.g., Jørgensen and Zaccour,2001).

Regarding the environmental damage costs, we are interestedin looking at the situation where the two countries are highlyasymmetric. This is meant to represent, in a figurative manner, thecontext where foreign is a developing country for which environ-mental issues are not a top priority in the short run, compared togrowth, and home is a developed country whose citizens insist onfully accounting for environmental damage. Within this setting,we normalize the environmental damage cost to zero in foreign.For home, we assume that the environmental damage cost isconvex and increasing in total production. We adopt the followingsimple quadratic functional specification:

EDH ¼ γðqHþqF Þ22

;

where γ is a strictly positive scaling parameter.Next, we characterize and compare the equilibrium strategies

and payoffs of the following three games (or scenarios):

Benchmarkscenario:

In this scenario, the game is played in two stages.In the first stage, the regulator in each country

sets the domestic per-unit carbon tax in its coun-try, and in the second stage, the firms compete àla Cournot. The resulting equilibrium strategiesand outcomes will be superscripted by NC (non-cooperative solution).

Cooperation intaxes:

The game is also played in two stages. In the first,the two regulators determine the tax rates coop-eratively, by maximizing their joint welfare. Thesecond stage and the computation of equilibriaare as in the first scenario. Equilibrium strategiesand outcomes will be superscripted by C (coop-eration in taxes).

Border tax: In this scenario, we add a prior stage to the twoinvolved in the benchmark scenario, in which,WTO or another international authority, choosesthe BTA level that maximizes total welfare. Equili-brium strategies and outcomes will be super-scripted by B (border tax).

3. Equilibria

In this section, we characterize the equilibria in three scenarios.As many of the formulas are extremely long and do not provideany qualitative insights, we only show, for the sake of readability,those that can be written in a compact manner.

3.1. Benchmark scenario

To compute a subgame-perfect Nash equilibrium, we first solvethe second-stage game. Assuming an interior solution, the max-imization of the firms' profits yields the following reaction func-tions to the taxes set by the regulators:8

qNCH ¼ cF ðα�tHÞþβðα�2tHþtF ÞcHcFþβð2cFþ3βÞ ; ð4Þ

qNCF ¼ cHðα�tF ÞþβðαþtH�2tF ÞcHðcFþ2βÞþβð2cFþ3βÞ : ð5Þ

A simple analysis of the above reaction functions leads to thefollowing characterization:

∂qi∂tj

is40 for ia j ði¼H; F; j¼H; FÞ;o0 for i¼ j ði¼H; F; j¼H; FÞ:

(

Inserting the above functions into the regulators' problems andsolving for equilibrium, we obtain the following taxes:

tNCH ¼ N H

D ; tNCF ¼ �αβ2½cF ðcHþγÞþβð2cHþγÞ�D ;

where

N H ¼ �αβðcHþβÞ½ð3βþcHÞðβ�γÞþβ2��αcF ½ð5βðcHþβÞþc2HÞðβ�γÞþðcHþ2βÞðβ2þcF ðβ�γÞÞ�;

D¼ c2F ðcHþ2βÞðcHþβþγÞþcFβð4c2Hþ11cHβþ7β2þ2cHγþ3βγÞþβ2ð4c2Hþβð4βþγÞþcHð9βþγÞÞ

Independent of the parameter values, the tax in foreign isalways negative, i.e., it is a subsidy. As foreign does not suffer frompollution (there is no environmental damage cost), this result is

8 The second-order conditions for a maximum are satisfied with∂2πj=∂ðqjÞ2 ¼ �2β�cjo0 and ∂2πj=∂qH∂qF ¼ �βo0, jAfH; Fg leading to a positivedefinite Hessian matrix.

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728720

intuitive. The sign of tNCH cannot be analytically determined as itdepends in a complex way on all the model parameters. However,if we consider the extreme case, where the production cost inforeign is zero, then the tax would be given by

tNCH ¼ �αβðcHþβÞ½βð4β�3γÞþcHðβ�γÞ�β2ð4c2Hþβð4βþγÞþcHð9βþγÞÞ

;

and

signðtNCH Þ ¼ signðγ½3βþcH ��β½4βþcH�Þ;

implying that a necessary condition for a positive tax is γ beingsufficiently higher than β. Otherwise, tNCH would be a subsidy.

To obtain the equilibrium profits, consumer surplus and wel-fares, it suffices to insert the taxes and quantities into thesefunctions.

3.2. Cooperation in taxes scenario

In this scenario, the two regulators cooperatively set the taxrates in the first stage and the firms compete à la Cournot in thesecond stage. Since the latter stage is played as in the benchmarkscenario, the maximization of the firms' profits leads to the samereaction functions as in benchmark scenario ((4)–(5)). Insertingthese quantities into the total welfare given by

TW ¼ α� cH2qH

� �qHþ α� cF

2qF

� �qF�

βðqHþqF Þ22

� γðqHþqF Þ22

;

ð6Þ

and maximizing yields the following taxes:

tCH ¼ αððcHþcF Þγ�βcF ÞcHðβþγÞþcF ðcHþβþγÞ ;

tCF ¼αððcHþcF Þγ�βcHÞ

cHðβþγÞþcF ðcHþβþγÞ ;

tCH�tCF ¼βðcH�cF Þ

cHðβþγÞþcF ðcHþβþγÞ Z0:

Recalling our assumption that cHZcF , we have the followingcharacterization of the taxation policies:

If γ4βcH

cHþcF; then tCF and tCH are positive;

IfβcF

ðcHþcF Þoγo βcH

ðcHþcF Þ; then tCF is negative and tCH is positive;

If γo βcFðcHþcF Þ

; then tCF and tCH are negative:

Clearly, if the two firms face the same costs, then the taxes will beequal. Otherwise, the equilibrium tax is always higher at home.Further, the above characterization shows that depending on theparameter values, three situations can occur, namely: (i) if thedamage cost parameter γ is high enough, then both countries willtax their firms; (ii) for some intermediate values of γ, foreign willsubsidize its firm, whereas home will tax its own; and (iii) whenthe damage cost is low enough, that is, when there are not manyenvironmental externalities to correct for, then both countriessubsidize their firms. The main reason is simply to gain to increaseconsumer surplus in home.

The intuition behind the above results is straightforward.Looking at the total welfare function, it is clear that whether aunit is produced by home or foreign, it has the same impact on theconsumer surplus and environmental damage. As well, becausethe taxation revenue paid is cancelled by the amount received bythe government, taxation is only useful in influencing the firms'production decisions. Further, the equilibrium quantities, which

are given by

qCH ¼ cFαcHðβþγÞþcF ðcHþβþγÞ ; ð7Þ

qCF ¼cHα

cHðβþγÞþcF ðcHþβþγÞ ; ð8Þ

are determined by the familiar rule that marginal costs must beequal in both countries. Indeed, we have

qCHqCF

¼ cFcH

3cHqCH ¼ cFqCF :

Inserting these quantities into the total welfare yields

TWC ¼ α2ðcHþcF Þ2ððcHþcF ÞðβþγÞþcFcHÞ

:

As one might expect, the total welfare is decreasing in the costparameters (cH ; cF and γ) as well as in consumer-sensitivity para-meter β, and increasing in the maximum willingness-to-pay α.

3.3. Border-tax scenario

In this scenario, the foreign firm is subject to a per-unit BTA,which is given by

BTA¼ δðtH�tF Þ;where δA ½0;1�. As an illustration of this idea, we can think of δ asa decision variable whose value is set by an international environ-mental treaty or by the WTO. The choice of δ depends on thesupranational entity's objective. Here, we assume that its goal is tomaximize the total welfare, but it could just as well be to minimizepollution emissions or a combination of these objectives. Clearly,the extreme case δ¼ 0 corresponds to the benchmark scenarioanalyzed above.9 The scenario δ¼ 1 represents a border tax thatfully adjusts for the difference in tax rates between the twocountries. This range of possibilities between no BTA and fulladjustment of the difference in taxation was first introduced inEyland and Zaccour (2012) and we keep the same idea here.However, in the previous reference, the actual value of δ wasexogenously given whereas here, it is endogenous and is the resultof an optimization process.

After inserting a BTA, the profit function of foreign and taxrevenue of home needs to be adjusted. The profit functions of firmsH and F and the tax-revenue functions are given by

πHðqH ; qF ; tHÞ ¼ α�βðqHþqF Þ�cH2qH�tH

� �qH ; ð9Þ

πF ðqH ; qF ; tH ; tF Þ ¼ α�βðqHþqF Þ�cF2qF�tF

� �qF�δðtH�tF ÞqF :

ð10Þ

TRH ¼ tHqHþδðtH�tF ÞqF ; ð11Þ

TRF ¼ tFqF : ð12ÞMaximizing profits in the last stage yields the following

reaction functions for the firms, which include the BTA effect:10

qBH ¼ cF ðα�tHÞþβððδ�2ÞtHþtF ð1�δÞþαÞcHðcFþ2βÞþβð2cFþ3βÞ ; ð13Þ

9 Throughout the following analysis it is assumed that home will impose a BTAequal to the level allowed by the WTO. However, it may be that home offers asubsidy to foreign if foreign taxes its emissions more heavily, which would beequivalent to foreign taxing home.

10 Obviously, if δ¼ 0, then we revert back to the reaction functions found in thetwo cases discussed above.

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728 721

qBF ¼cHðα�tFþδðtF�tHÞÞþβðtHð1�2δÞþ2ðδ�1ÞtFþαÞ

cHðcFþ2βÞþβð2cFþ3βÞ : ð14Þ

Next, we insert the above quantities into the second stage andmaximize individual welfare levels to determine the noncoopera-tive tax levels. Finally, these taxes are entered into the totalwelfare-maximizing problem and yield the optimal BTA.

4. Numerical results

Since it is not possible to fully analytically investigate theequilibrium results in the general case, we turn to numericalanalysis. Our model has 5 parameters, namely,

production cost : cH ; cF ;

damage cost : γ;

demand : α;β:

To keep the number of simulations manageable, we have to definea numerical grid by setting some bounds on the parameter values.First, without any loss of qualitative insight, we normalize thedemand parameters α and β and set them, in all simulations, equalto 1. Second, as we wish to concentrate on a setting where foreignrepresents an exporting, low-production-cost developing country,whereas home is a developed high-production-cost country, weimpose cFrcHoα¼ 1. The last inequality simply states that theunit-production cost in home is lower than the consumer's will-ingness-to-pay; otherwise, home would never produce. Third, asthe relative values of β and γ played an important role in thescenarios analyzed above, we keep all options open and letγA ½0:5;1:5�. Recalling that β has been set to 1, this range for γallows us to consider cases where the damage-cost parameter is(up to 50%) lower, or (up to 50%) higher, or equal to β.

4.1. Symmetric production cost

The two countries differ essentially in terms of environmentaldamage and (possibly) production costs. To isolate the impact ofthe asymmetrical damage cost on the results, we first run a seriesof simulations where the production costs are taken as equal. In asecond series of simulations, we consider both damage- andproduction-cost asymmetries. We set cH ¼ cF ¼ 0:1 in this section,and note that increasing or decreasing the value of the equal costdoes not qualitatively change the conclusions. Table 1 summarizesthe welfare results in the symmetric cost case for five values of theenvironmental damage parameter γ. For each value of γ, weprovide the optimal value for the border tax adjustment δ. Thedetailed results are given in Tables 2–4.11

Before directly addressing our research questions, we commenton the results obtained in the three scenarios. We make thefollowing observations:

Impact of γ on total output: In all scenarios, increasing theenvironmental cost parameter γ leads to a lower total quantityavailable on the market. Consequently, total profits, consumersurplus and environmental damage are lower.

Impact of γ on total welfare: In all scenarios, increasing γ leads toa lower total welfare. This means that the gain resulting fromdecreased environmental damage is outweighed by the loss in theother components of welfare (i.e., consumer surplus, profits andtax revenues).

Impact of γ on the BTA: In the BTA scenario, increasing γ leads toa quicker rise in home taxes than foreign taxes, resulting in a largerper-unit BTA as γ rises.

Impact of an agreement: From Table 1, we observe that the totalwelfare is higher when the countries cooperate in setting theircarbon taxes and under a BTA than in the benchmark scenario.This is intuitive since any form of policy coordination is better thannone. The main source of the improvement in the total welfare isthe reduction in environmental cost, which is due to a lower totaloutput, and by the same token, to a loss in consumer surplus andprofits.

Dividend of an agreement: Let us measure the dividend of anagreement by

Dividend of cooperation in taxes DCCðγÞ ¼ TWCðγÞ�TWNCðγÞ;Dividend of a BTA DCBðγÞ ¼ TWBðγÞ�TWNCðγÞ;

that is, by the difference in total welfare. Based on Table 1, it iseasy to see that DCCðγÞ and DCBðγÞ are increasing in γ. This showsthat an environmental agreement is especially needed when thedamages caused by pollution are high. To illustrate this in relativeterms, whereas the improvement in total welfare with a BTA isaround 11.8% when γ ¼ 0:5 (0.3220/0.2879), this improvementjumps to 149.6% for γ ¼ 1:5. The percentages are very similarwhen we consider the cooperation-in-taxes scenario instead of aBTA.

Taxes versus subsidies: For all considered parameter values,foreign subsidizes its firm in the noncooperative scenario. How-ever, home only subsidizes when environmental damage is notsufficiently high.

Let us now look at country-specific results. First, whereas homesuffers from a higher γ in the benchmark scenario, foreign benefitsfrom it. To explain this result, let us recall that, in this scenario,home receives the consumer surplus and suffers environmentaldamage. These two components solely depend on the totalquantity produced and on the parameters β (normalized here to1) and γ. The sum of consumer surplus and the (negative)environmental damage will always be positive when γoβ; andnegative when γ4β. So for γ4β; homewill have a smaller welfarelevel than foreign, and the opposite is true when γoβ. If γ is muchsmaller than β, home favors high production levels because the

Table 1Welfare in different scenarios, with symmetric cost.

Result Benchmark Cooperation in taxes Border tax

γ ¼ 0:5-δ¼ 0:470915Total welfare 0.2879 0.3226 0.3220Home welfare 0.2533 0.2133 0.2008Foreign welfare 0.03462 0.1093 0.1212γ ¼ 0:75-δ¼ 0:472579

Total welfare 0.2223 0.2778 0.2777Home welfare 0.1646 0.1582 0.1560Foreign welfare 0.0576 0.1196 0.1217γ ¼ 1-δ¼ 0:47619

Total welfare 0.1667 0.2439 0.2439Home welfare 0.0833 0.1220 0.1220Foreign welfare 0.0833 0.1220 0.1220γ ¼ 1:25-δ¼ 0:480907

Total welfare 0.1193 0.2174 0.2173Home welfare 0.0086 0.0969 0.0956Foreign welfare 0.1107 0.1205 0.1217γ ¼ 1:5-δ¼ 0:486276

Total welfare 0.0785 0.1961 0.1959Home welfare �0.0604 0.0788 0.0748Foreign welfare 0.1389 0.1173 0.1210

11 The results for γ ¼ 0:5 and γ ¼ 1:5 are qualitatively similar to those ofγ ¼ 0:75 and γ ¼ 1:25, respectively. Results for any parameter values are availablefrom the authors upon request.

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728722

gains to consumers outweigh the losses in environmental damage.There is an incentive for home to subsidize production more thanforeign which makes it harder for foreign's firm to compete. By thedesign of the BTA, if home taxes less than foreign, which isequivalent to home subsidizing more the BTA automaticallybecomes a subsidy. This process may be viewed in a similar wayas the clean development mechanism whereby foreign firms thatdo more for the environment receive a subsidy. Additionally, for aBTA to be accepted by an international organization it must be fairfor whomever is doing the most effort. On the other hand, if γ ismuch larger than β, home favors small production levels becausethe negative impact of production on environmental damageoutweighs the positive impact of production on consumer surplus.In this case, home would like to tax production, but if it does so, itwill lose a lot of competitiveness to foreign and suffer carbonleakage. Remember that whereas we were able to analyticallyestablish that foreign always subsidizes its firm, the sign of the taxin home was ambiguous. We see from the numerical results thatthis tax is positive only for high values of γ, e.g., γ ¼ 1:5. In thiscase, home has a negative welfare overall, and some might arguethat home should prohibit the importation of that good under suchcircumstances.

The specific case where β¼ γ is a situation where theconsumer-surplus and environmental-damage levels cancel each

other out for home, thereby leaving the two countries in identicalcircumstances, that is, where their welfare solely depends on thefirm's profits and on tax revenue. This is like the result seen inBrander and Spencer (1985), where the two countries compete fora third market. The result is the same as under noncooperation, inwhich each country subsidizes its firms to gain market share.Additionally, they also found that when both countries cooperate,they end up restricting output and taxing their own firms to gainlarger welfare levels, which may also be seen here.

In the cooperation-in-taxes scenario, we showed that

tCH�tCF ¼βðcH�cF Þ

cHðβþγÞþcF ðcHþβþγÞ Z0;

cHqCH ¼ cFqCF :

Therefore, whenever cH ¼ cF ¼ c, and regardless of the values of βand γ, we always have tCH ¼ tCF and qCH ¼ qCF . As the total output islower in this scenario than in its benchmark counterpart, whoeverwas producing most will then see the largest reduction inproduction. Having the same production and tax in both countriesalso means that they have the same profits and tax revenues. Thus,the only way in which they differ is that only home receives theconsumer surplus and suffers the environmental damage. Fromthe noncooperative benchmark, we already know how the rela-tionship between γ and β influences these two components ofhome's welfare, and there is no need to repeat the analysis.

Table 3Results for symmetric cost for γ ¼ 1:00 and γ ¼ 1:25.

Benchmark Cooperation intaxes

Border tax

γ ¼ 0:50 γ ¼ 0:75 γ ¼ 0:50 γ ¼ 0:75 γ ¼ 0:50 γ ¼ 0:75

Total welfare 0.1667 0.1193 0.2439 0.2174 0.2439 0.2173Home welfare 0.0833 0.0086 0.1220 0.0969 0.1220 0.0956Foreign welfare 0.0833 0.1107 0.1220 0.1205 0.1220 0.1217Home quantity 0.3811 0.2868 0.2439 0.2174 0.2439 0.1919Foreign quantity 0.3811 0.4392 0.2439 0.2174 0.2439 0.2420Home tax �0.1815 �0.0415 0.2439 0.3261 0.2439 0.3551Foreign tax �0.1815 �0.2091 0.2439 0.3261 0.2439 0.2488BTA 0 0 0 0 0 0.0511Home profit 0.1525 0.0864 0.0625 0.0496 0.0625 0.0386Foreign profit 0.1525 0.2026 0.0625 0.0496 0.0625 0.0615Home C.S. 0.2905 0.2635 0.1190 0.0945 0.1190 0.0941Home env. dam. 0.2905 0.3294 0.1190 0.1181 0.1190 0.1176Home tax revenue �0.0692 �0.0119 0.0595 0.0709 0.0595 0.0681Foreign tax revenue �0.0692 �0.0919 0.0595 0.0709 0.0595 0.0602Home tariff revenue 0 0 0 0 0 0.0124

Table 4Results for symmetric cost and γ ¼ 1:50.

Benchmark Cooperation in taxes Border tax

Total welfare 0.0785 0.1961 0.1959Home welfare �0.0604 0.0788 0.0748Foreign welfare 0.1389 0.1173 0.1210Home quantity 0.2010 0.1961 0.1506Foreign quantity 0.4920 0.1961 0.2295Home tax 0.0858 0.3922 0.4444Foreign tax �0.2343 0.3922 0.2540BTA 0 0 0.0926Home profit 0.0424 0.0404 0.0238Foreign profit 0.2542 0.0404 0.0602Home C.S. 0.2402 0.0769 0.0761Home env. dam. 0.3603 0.1153 0.1141Home tax revenue 0.0172 0.0769 0.0669Foreign tax revenue �0.1153 0.0769 0.0608Home tariff revenue 0 0 0.0212

Table 2Results for symmetric cost for γ ¼ 0:50 and γ ¼ 0:75.

Benchmark Cooperation in taxes Border tax

γ ¼ 0:50 γ ¼ 0:75 γ ¼ 0:50 γ ¼ 0:75 γ ¼ 0:50 γ ¼ 0:75

Total welfare 0.2879 0.2223 0.3226 0.2778 0.3220 0.2777home welfare 0.2533 0.1646 0.2133 0.1582 0.2008 0.1560foreign welfare 0.03462 0.0576 0.1093 0.1196 0.1212 0.1217home quantity 0.6011 0.4854 0.3226 0.2778 0.3985 0.3109foreign quantity 0.2456 0.3169 0.3226 0.2778 0.2450 0.2451home tax �0.5080 �0.3362 0 0.1389 �0.0818 0.1021foreign tax �0.1170 �0.1509 0 0.1389 0.2374 0.2391BTA 0 0 0 0 �0.1503 �0.0647home profit 0.3794 0.2473 0.1093 0.0810 0.1667 0.1015foreign profit 0.0634 0.1055 0.1093 0.0810 0.0630 0.0631home C.S. 0.3585 0.3218 0.2081 0.1543 0.2070 0.1546home env. damage 0.1793 0.2414 0.1041 0.1157 0.1035 0.1160home tax revenue �0.3054 �0.1632 0 0.0386 �0.0326 0.0317foreign tax revenue �0.0287 �0.0478 0 0.0386 0.0582 0.0586home tariff revenue 0 0 0 0 �0.0368 �0.0159

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728 723

In the BTA scenario (as in the benchmark scenario), it can beestablished that tBH ¼ tBF when β¼ γ. Therefore, the border-taxterm, that is, δðtBH�tBF Þ, is equal to zero. This means that this taxonly serves as a threat, and does not actually have an impact onthe rest of the results when β¼ γ. Additionally, we have tBH4tNCHand tBF 4tNCF , that is, both countries tax at a higher level than in thebenchmark scenario. (Recall that tH

NC and tFNC were subsidies.)

Now consider the more general situation where βaγ. When γ4β,home suffers more from having higher levels of productionbecause its impact on the environmental damage is greater thanon the consumer surplus. Thus, home wishes to limit productionby foreign, but in the benchmark scenario, it cannot do anythingabout it. However, as a partial BTA is imposed home sees thatimports coming from foreign will now suffer a tariff, which makesit easier for it to increase taxation without suffering a significantloss in competitiveness. In response to this BTA, foreign has anincentive to increase taxation to face a smaller tariff. Foreign'sability to respond as home adopts a unilateral environmentalpolicy is, as mentioned earlier, an important feature in ourframework, and a shortcoming of most computable generalequilibrium type papers. Independently of the BTA level, if foreignsuffers a smaller total production cost (including taxes) than home,it can still produce larger quantities, which was not a possibility inthe cooperative scenario. Similarly to the cooperative scenario, whenthe difference between β and γ is large, there is also one country thatgains in welfare compared to the benchmark and one that loses. Insuch circumstances, the WTO could determine a reallocation schemeto ensure that if one country loses compared to the benchmark, thenthat country would gain from a proper side payment.

In summary, moving from the noncooperative benchmark toeither the cooperation-in-taxes scenario or the BTA scenarioreduced the quantities being produced. This reduction was simplyachieved by imposing a higher tax on the firms (often going from asubsidy to a tax), because the rest of the parameters thatdetermine the firms' production levels remained unchanged.Profits for the firm fall and tax revenue rises. Lastly, consumersurplus and environmental damage, being purely dependent onthe total quantity produced, both fall as total quantity falls.

Given the above analysis, the answers to our research questionsare now straightforward. Figs. 1 and 2 show that BTA andcooperation in taxes lead to higher welfare for foreign for a γlower than 1.3464 (for BTA) and 1.3296 (for coop), and to higherwelfare for home for a γ higher than 0.7969 (for BTA) and 0.7887(for coop). The implication is that for a low enough damage cost,home would not push for a BTA. As mentioned above, the reasonfor this is that the benefits in terms of consumer surplus and

profits are greater than the environmental cost when γ is low.Interestingly, for a large interval of values of γ, i.e.,γA ½0:7969;1:3464�, the BTA is Pareto improving. This result is amain takeaway of this paper. Indeed, in the debate surroundingthe design of an international environmental agreement, it hasalways been assumed that any policy aiming at reducing pollutionwill end up with some countries losing a lot and others gaining abit, with a global loss. Our results show that there are situationswhere a BTA benefits all parties, assuming of course that ourmodel is capturing the essence of the pollution-reduction pro-blem. This win–win scenario, obtained admittedly in a greatlysimplified setting, is a clear invitation to seriously assess thepotential of BTA as policy tool that could rally a significantly largenumber of countries, including main players.

Now, if a BTA is on the agenda, then the natural ensuingquestion is what its optimal level would be. From Table 1, weobserve that all computed values for δ lie in the very narrowinterval [0.4709, 0.4863]. This seems to imply that δ is insensitiveto changes in γ, at least in this symmetric-cost scenario. Indeed,even when we triple γ from 0.5 to 1.5, we obtain an increase of δ ofonly 3.27% (see Fig. 3). This answers our second research question.

Fig. 4 shows the ratio of total welfare under BTA over totalwelfare under cooperation in taxes, as function of γ (i.e.,TWBðγÞ=TWCðγÞ). Clearly, this ratio is very close to 1; morespecifically, all values lie in the interval [0.9982, 1]. This showsthat a BTA pretty well mimics the welfares that would result fromcooperation in taxes. Further, we also see from Figs. 1 and 2 that

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

γ

WF

BenchmarkCooperationBTA

Fig. 1. Foreign welfare under different scenarios.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

−0.05

0

0.05

0.1

0.15

0.2

0.25

γ

WH

BenchmarkCooperationBTA

Fig. 2. Home welfare under different scenarios.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0.472

0.474

0.476

0.478

0.48

0.482

0.484

0.486

γ

δ

Fig. 3. The tax adjustment as function of environmental damage parameter.

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728724

the individual total welfares obtained in the BTA game are veryclose to their cooperation-in-taxes counterpart. The policy impli-cation is that not only a BTA is welfare-improving with respect tothe benchmark case, it also implements in a decentralized waywhat regulators would like to do if they could jointly optimize thewelfare of both countries. As mentioned above, the only pendingissue would be to compensate any country that loses fromimplementing a BTA when compared to the benchmark case.

To wrap up, we found in this symmetric-production costsetting that (i) the optimal BTA is never full, but partial, andhovers around 48% for all considered cases of damage cost; (ii)home should lobby for a BTA, only if the damage cost parameter isabove a certain threshold. Moreover, a BTA is a Pareto-welfare-improving mechanism for a large interval of γ; and (iii) a BTA leadsto almost the same welfare levels as cooperation in carbon taxesbetween the two countries.

4.2. Asymmetric costs

In this subsection we check the extent to which the answers toour research questions, given in a symmetric production-costsetting, carry over to an asymmetric cost setting. To do so, we varythe production-cost parameter in home, while keeping all otherparameters at their previous values. More specifically, we let cH takeits values in the interval ½cF ;3cF �; at the lower bound, both firmsface the same production cost, and at the upper bound, home's costis three times foreign's one. We believe that this range of values islarge enough to encompass most, if not all, realistic situations.

Fig. 5 exhibits the optimal BTA for γA ½0:5;1:5� and cost ratiocH=cFA ½1;3�. From this figure, we see that δ is monotonicallyincreasing in γ and decreasing in cH=cF , with δmin � 0:403 andδmax � 0:486. The message from our simulations is thereforetwofold, namely: (i) the border-tax adjustment is always partial,with the optimal values of δ belonging to the interval½0:403;0:486�; and (ii) the optimal δ is quite insensitive to changesin γ and cH=cF . Indeed, even when we triple the values of γ andcH=cF , the value δ decreases by less than 15%. This confirms thatallowing for asymmetric production costs does not alter thequalitative conclusion reached with equal costs.

From Fig. 6, we note that for all parameter values, the totalwelfare under BTA is higher than its benchmark counterpart.Again, this result is expected, as a BTA is somehow a policy-coordinating mechanism. The crucial issue is whether a BTAis welfare Pareto-improving with respect to a noncooperativemode of play. In the symmetric scenario, we obtained that it isthe case whenever γ is neither too low nor too high, i.e.,γA ½0:7969;1:3464�. More specifically, we found that home prefers

noncooperation to BTA when γ is below the lower bound of theabove interval, and that foreign prefers noncooperation to a BTAwhen γ is larger than the upper bound. This conclusion isunaltered in this asymmetric setting. Indeed, Fig. 7 shows thathome is interested in seeing a BTA imposed only if γ is larger than acertain threshold value ~γ ðcH=cF Þ. We observe that ~γ ðcH=cF Þ is veryslightly decreasing in cH=cF ; with ~γ ð1Þ ¼ 0:7969 and ~γ ð3Þ ¼ 0:7789.In fact, qualitatively speaking, we can claim that ~γ ðcH=cF Þ isinvariant in the cost ratio cH=cF : Similarly, Fig. 8 shows thatforeign's welfare is larger under BTA than under noncooperation

11.522.530.51

1.5

0.41

0.42

0.43

0.44

0.45

0.46

0.47

0.48

cH / cFγ

δ

Fig. 5. Optimal δ for various parameter values.

11.522.53

0.51

1.5

1.2

1.4

1.6

1.8

2

2.2

2.4

γcH / cF

TWB −

TW

NC

Fig. 6. TWB=TWNC for various parameter values.

12

3

0.5 1 1.5

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

γ

cH / c

F

B W

H−

WHN

C

Fig. 7. WBH�WNC

H for various parameter values.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.9982

0.9984

0.9986

0.9988

0.999

0.9992

0.9994

0.9996

0.9998

1

γ

TWB /

TWC

Fig. 4. Ratio total welfare under BTA over total welfare under cooperation in taxes.

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728 725

for γ larger than a threshold value γ ðcH=cF Þ. The lowest threshold isγ ð3Þ ¼ 1:3423, and the highest is γ ð1Þ ¼ 1:3464, that is, the thresh-old value is almost independent of the value of the cost ratio.

In Fig. 9, we plot the ratio of the total welfare under BTA to thetotal welfare under cooperation in taxes, for γA ½0:5;1:5� andcH=cFA ½1;3�. The clear result is that a border tax pretty wellmimics an environmental agreement in which both countriescooperatively set their taxes. As in the symmetric production-cost case, we observe that the ratio TWBðγ; cH=cF Þ=TWCðγ; cH=cF Þ isvery close to one for all admissible parameter values. Once more,we conclude that the results in the asymmetric cost context arequalitatively the same as in the symmetric cost scenario. We musthowever note an important difference here with the equal costcase. In the previous symmetric cost setting, both firms producedthe same quantity under cooperation in order to maximize thejoint welfare. Once an asymmetry in production cost is introduced,home will necessarily produce a lesser amount than foreign as itsproduction costs are greater to equalize the marginal productioncost of the last unit. However, in the case where home can imposea BTA, it would rather produce more than the small cooperative-scenario quantity, to generate greater profits, tax revenue andtariff revenue. Hence, in a situation where home suffers largeenvironmental costs and large production costs, it may see its totalwelfare roughly triple, when going from the cooperative scenarioto a BTA (see Fig. 10). For foreign, imposing a BTA is notadvantageous compared to the cooperative-in-taxes scenario, forthe mirror reason of the one mentioned for home. Still, at the endof the day, what really matters is the comparison of welfares undera BTA and noncooperation. If cooperation in taxes were possible,

then it could be accompanied by a side-payment mechanism thatwould address this issue.

5. Robustness of results

In any modeling effort, the results depend, at least partially, onthe assumptions made. We reasonably expect this statement toalso apply in our case. The three main assumptions whose impactis worth discussing are the following: (i) consumption only takesplace in home; (ii) foreign does not suffer from pollution; and (iii)the market structure in the product-market is oligopolistic. Deal-ing precisely with the effect of these assumptions on the results,requires, in each case, to modify the model and a full consequentanalysis. We leave such work for future research and contentourselves here with some conjectures regarding the direction ofchange. Before doing so, let us recall that our assumptions wereessentially motivated by the wish to cover a situation where thetwo countries are highly asymmetric, which is the case in practice(think of European Union and China as the two players), but wasnot yet fully addressed in a strategic BTA setting.

Consumption in thetwo markets:

If consumption also takes place in foreign,then consumer's surplus will also conse-quently matter in the computations. If wemaintain the same assumption of zerodamage cost in foreign, then we conjecturethat foreign will be even less inclined to taxto avoid harming their consumers. In theBTA scenario, the correction could behigher. More generally, adding a secondmarket requires thinking about some addi-tional economic questions. First, wouldlocally produced goods be taxed in thesame way if they are domestically con-sumed or exported? Second, are there anyexport rebates or domestically producedrebates? Third, if a country adopts only atax on exported goods but not on locallyproduced goods do they still suffer a BTA?At first glance, we believe that if foreignexports a portion of its production andimposes the same tax on its domesticallyconsumed goods, the taxation revenue mayrepresent a lower fraction of their welfareand they will not want to hurt their con-sumers too much leading to a reduction inthe tax level. Clearly, this is simply a

11.5

22.5

3

0.5

1

1.5

0.98

0.985

0.99

0.995

1

γcH/cF

TWB /

TWC

Fig. 9. TWB=TWNC for various parameter values.

11.5

22.5

3

0.5

1

1.5

1

1.5

2

2.5

3

γcH / cF

WH /

WH

BC

Fig. 10. WBH=W

CH for various parameter values.

1

2

3

0.51 1.5

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

c H / c F

γ

B W

F− W

FNC

Fig. 8. WBF �WNC

F for various parameter values.

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728726

conjecture that is far from being proved yet.Other questions that must be answered,when looking at two markets are whetherarbitrage will make it that goods have to beconsumed at the same price in both coun-tries adjusting for additional costs as inFerrara et al. (2009)? What would thisimply if the goods sold in foreign endedup being sold to consumers cheaper than inhome due to smaller taxes because of envir-onmental damage asymmetry. Couldhome's consumers import final goods fromforeign at a lower price than at which it issold in domestic market? If this couldhappen, then we would need to take careof an additional modeling item, namely, ano-arbitrage condition. Lastly, it would beinteresting to determine what size is thehome market relative to the foreign market.

Foreign also suffersfrom pollution:

If foreign suffered just as much as home andhad the same size consuming market, thenwe would have perfect symmetry. Otherwise,if foreign progressively suffers a little more,they will progressively care more about theenvironment, and in all three consideredscenarios, foreign will slowly move towardstaxing more. However, because of the oligo-polistic structure it will not necessarily meanthat they will not subsidize.

Perfect competition Under perfect competition, firms in eachcountry would be price takers and sell atmarginal cost of production including thecarbon tax amount. In such context, strategicinteraction would be completely lost andthere will be no need to a game-theoreticapproach in the last stage of the model.

6. Concluding remarks

The paper is based on a two-country trade model similar toBrander and Spencer (1985) and Eyland and Zaccour (2012), thatallows for possible asymmetries in environmental damage andproduction costs. Each country has one firm producing a homo-geneous product. The pitfall in the previous literature is that a BTAwas treated as exogenous or adjusted for the complete difference intaxation. However, it is possible that an organization such as theWTO would endogenously search for the optimal BTA level as atool to limit free riding, carbon leakage and competitivenessconcerns. In this paper, for various parameter values, an endogen-ous BTA is determined and its value is bounded between 0 and 100percent. To evaluate its ability to increase total welfare comparedto the benchmark noncooperative case, the scenario of coopera-tion in taxes was introduced.

Overall, through a wide range of environmental and pro-duction-cost asymmetries, the optimal BTA hovers between 0.40and 0.48. Consequently, it is important to note that because of thestrategic distortions involved, it may not be best for the sake oftotal welfare to have either no BTA or a complete BTA. Once thisoptimal BTA is introduced, it is clear that total welfare is alwaysgreater for all parameter values. However, it is only when theenvironmental damage parameter is high enough (γ � 0:78 andhigher) that the abating country's own welfare will increasefollowing a BTA. Thus, a country will only lobby the WTO to allowa BTA if it cares sufficiently about the environment. If it obtained

the right to administer a BTA, this would be a credible threat thatwould induce the other country to change its taxation policy. Asfor foreign, which is portrayed in a simplified manner as sufferingno environmental damage, its own welfare will increase followinga BTA if home's environmental damage is not too great (γ � 1:35and smaller). Consequently, if there are no over-large environ-mental damage asymmetries, foreign also gains from a BTA. Thus, ifthe WTO determined and allowed a BTA to be imposed, it wouldbe Pareto-improving for a large range of parameter values. It isinteresting to compare the levels of BTA obtained here to the onesin Eyland and Zaccour (2012), where it is assumed that homeselects the BTA. In Eyland and Zaccour (2012), the range of realizedvalues covers entirely the interval of admissible ones, that is, theinterval ½0;1�. This difference is due to the fact that here theorganization in charge of BTA includes both countries' welfare inthe optimization problem, whereas home would only take care ofits own interest. This observation is a strong argument for lettingan independent entity determine the level of BTA to increase thelikelihood of its acceptance by all parties, rather than leaving thedecision to individual countries.

In a symmetric cost setting, it is interesting to note that the BTAalmost completely mimics a situation where both countriescooperatively set their carbon taxes. The simulations showed thatthe BTA scenario had a total welfare that was less than 0.2 percentlower than the cooperative ideal. This result addresses the goal ofobtaining a cooperative-type outcome through noncooperation.However, even if the total welfare and the individual welfare levelsare very similar between both scenarios, the stories are quitedifferent. In the cooperation-in-taxes scenario, there is a require-ment that the last unit produced by both countries have the samemarginal cost of production. Contrarily, the BTA scenario may havedifferent taxes and different production levels.

Even though the total welfare is still very similar whenasymmetric production costs are introduced, the taxes and quan-tities are now quite different. This difference means that underlarge production-cost asymmetries, one country may win more (orless) going from the benchmark to the BTA scenario versus thecooperation-in-taxes scenario.

A BTA may be successful in practice by looking at real worldestimates. Rubin and Tal (2008) estimate that if the United Statesimposed a tariff of $45 per tonne of carbon dioxide on Chineseimports, this tariff would lead to $55 billion a year in tariffrevenues. If the United States had an environmental policy andChina did not, a BTA parameter of 50 percent would lead to $27.5billion in annual tariff revenues, assuming that trade flows did notchange. The money raised could fund projects in developingcountries to aid in its legality. Additionally, this outcome couldgive China an incentive to tax more locally to keep taxationrevenues within its borders. In essence, a BTA may be used as athreat to incite countries with no reduction commitments to startdoing something about emissions or indirectly using their carbontaxation revenues to fund projects. Either way, the environmentwill benefit from such a policy.

Finally, a possible extension to our work would be to set up anappropriate side-payment scheme that would ensure that bothcountries obtain more under the BTA scenario than in the non-cooperative benchmark. With such a side payment scheme, a BTAcould be a credible threat that would lead to a Pareto-optimaloutcome for any parameter value.

Acknowledgments

We would like to thank the two anonymous reviewers and theeditor for their very helpful comments. Research supported byNSERC and SSHRC, Canada.

T. Eyland, G. Zaccour / Energy Policy 65 (2014) 718–728 727

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