Green subsidies as strategic trade policy tools

Abstract

In a third-country market model in which two export countries adopt environmental policies (taxes and subsidies), this article analyses how an abatement (“green”) subsidy can become a potential strategic trade policy tool. When governments set the optimal policy considering their local environmental damages, a rich set of equilibria arises. In contrast to the standard result, it is shown that subsidising pollution abatement can 1) emerge as the unique Pareto-efficient Nash equilibrium of the policy game, 2) be the only feasible environmental policy when environmental awareness is low, irrespective of the efficiency of the cleaning technology, and 3) emerge as the unique Pareto-inefficient Nash equilibrium of the policy game at the end of the ecological transition. The article also tackles some dynamic issues that the policy game implies.

1 Introduction

The provision of cost-reducing subsidies for exporting firms is a keystone of public intervention in several manufacturing sectors. As WTO rules generally forbid subsidies, in recent decades governments have adopted well-designed industrial policies (The Economist 2013) and in recent months (The Economist 2023a; 2023b) environmental policies as pseudo-strategic trade policy tools.

Consider, for instance, the “architecture of subsidies”, included in the Inflation Reduction Act (IRA) of the Biden Administration, in the US, related to clean energy and “green” transition, $400bn for green tech in ten years. On the surface, the official motivation for introducing those subsidies is the need to improve environmental quality and reduce the environmental damage due to manufacturing and services production, often generated by giant companies producing local highly polluting emissions.¹ Deep down, it seems that those measures are mainly designed to harm Chinese exports. Nonetheless, they have also generated harsh reactions in the EU and among US “alleys” Asian countries like Japan and South Korea. French and German ministers have declared that they want “a new green industrial policy”; European Commission president Ursula von der Leyen has called for “our European IRA” (Financial Times, 2023). The Economist (2023a) reports that a senior Asian diplomat in Washington declared that “Free trade is dead. It’s a basic game theory. When one side breaks the rule, the other soon break the rules, too. If you stand still, you will lose the most”.

Indeed, this is the result of the standard model of strategic trade policy due to Brander and Spencer (1985): in the case of quantity competition, providing subsidies creates a competitive advantage when other rival countries do nothing; if the other country counter-reacts with a subsidy policy, the outcome is a prisoner's dilemma in which both countries would have been better off without policy intervention (see Krugman 1986; Helpman and Krugman 1989 and Brander 1995 for earlier surveys of classical issues in this strand of the literature, and Fanti and Buccella 2023 and the works quoted therein for recent developments).

Commentators at The Economist (2023a, 2023b) seem to share those concerns; on the other hand, observers at Financial Times (2023) have a more cautious and optimistic approach because, in their opinion, “[…] a subsidy race in green-tech and carbon-free energy would be a race to the top, not the bottom.”

Since the 1990s, scholars have identified that an environmental policy can work as a “strategic trade policy” to improve competitiveness in international trade models with oligopolistic industries (Conrad 1993; Barrett 1994; Ulph 1996a,b). In a third-country market model with a duopolistic industry, Conrad (1993) develops a two-stage game in which governments at the first stage determine an optimal emission tax in the presence of a global pollutant, and at the second stage exporting firms choose output and abatement levels. In such a context, governments (acting without environmental awareness) have an incentive to grant their exporting firms subsidy programs (for either abatement activities or polluting intensive inputs) whose aim is to increase national benefit from large market shares. Using a similar framework with local pollution, Barrett (1994) builds a two-stage game in which governments set either an environmentally optimal standard (in which the marginal damage equals the marginal abatement cost) or a strategically optimal standard (the marginal damage exceeds the marginal cost of abatement). It is shown that, in a simultaneous move game, the Nash equilibrium of the governments’ game is the adoption of a strategically optimal standard facing, however, a prisoner’s dilemma. However, this result is not robust to changes in market structures and competition mode (price competition). Ulph (1996a) studies the government's incentives in adopting a strategic environmental policy in a Cournot duopoly with homogenous goods when firms can strategically invest in process innovation (cost reduction) R&D. The author reveals that 1) when producers strategically engage in R&D, this tends to reduce the incentive for governments to act strategically; 2) allowing governments to act strategically increases the incentive for producers to act strategically; 3) when both parties act strategically, social welfare decreases; and 4) strategic behaviour by producers and governments is greater when governments use emission taxes than when they use emission standards. Ulph (1996b) extends the analysis to Bertrand competition with differentiated goods.²

The present article offers a threefold contribution to the above-mentioned literature. First, given the increased attention of public opinion (especially in advanced economies) about environmental issues, this work stresses the relevance of environmental awareness in governments’ decisions, an element the previous literature has largely disregarded, pinpointing the Pareto efficiency of the strategic use of the abatement subsidies emerging as a sub-game perfect Nash equilibrium of the policy game. Second, it emphasizes the role technological progress can have on the choice of the optimal environmental policy. Third, abatement subsidies emerge as the unique Pareto-inefficient Nash equilibrium of the policy game at the end of the ecological transition. Fourth, following recent literature studying the dynamics of environmental oligopolies (e.g., Buccella et al. 2023a, b), it takes a simple dynamic view of the problem of using environmental taxes or subsidies by considering the time dependence of the main parameters of the model (i.e., the societal awareness of a clean environment and the efficiency of the cleaning technology) and their historical evolution discussing the emerging sub-game perfect Nash equilibrium of the policy game played by the government of each exporting countries. Finally, the main policy implication of the paper is the use of abatement subsidies as the unique tool that can be applied in a naïve society (not caring for adequately environmental quality) as a public instrument triggering other possible policy intervention.

In such a way, this paper aims to 1) provide additional insights on the use of “green” subsidies (i.e. subsidies to abatement activities) as a tool of strategic trade policy; and 2) launch a discussion on this renewed debate on the use of environmental policies to improve the national welfares of countries involved in international trade.

In doing so, the work develops a basic two-stage, third-country market model based on Cournot-rivalry game, in which there exists a single polluting industry consisting of two firms located in two exporting countries that produce homogeneous goods. These goods are sold to an importing third country. In the first stage, a social welfare maximising government with environmental concerns optimally chooses the environmental policy tool for the exporting polluting firm: either an emissions tax or an abatement subsidy. In the second stage, Cournot duopolists compete in the third market, choosing simultaneously both output and abatement. The key result of the analysis is as follows.

Depending on the societal awareness of the environment and the available abatement technology (an element mainly disregarded by the earlier literature), a rich set of equilibria arises. However, contrary to the standard result with cost-reducing subsidy per unit of output, it is found that to subsidize pollution abatement can emerge as a Pareto-efficient sub-game perfect Nash equilibrium of the policy game. Moreover, an abatement subsidy is the only feasible policy when environmental awareness is low, irrespective of the available technology. Therefore, if governments consider the impact of environmental damage in the design of the environmental policy for exporting sectors, the provision of “green” subsidies can be the only policy option for a transition to use green technology when the societal awareness towards a clean environment is low. Thus, our results offer novel and interesting policy implications.

The remainder of this paper proceeds as follows. Section 2 develops the model and presents the main results. Section 3 provides a dynamic analysis of the static game developed in the previous section. Section 4 closes the paper by launching a discussion about “green” strategic trade policy and outlining potential routes for further investigation.

2 The model and the results

We consider a single polluting industry consisting of two firms, $i$ and $j$ ($i,j=\left\{\mathrm{1,2}\right\},$ $i\ne j$), located in two exporting countries, respectively producing homogeneous goods, ${q}_{i}$ and ${q}_{j}$, and competing à la Cournot. These goods are sold to an importing third country. The generic firm $i$ of the exporting Country $i$ uses a linear technology to produce ${q}_{i}$ units of the goods, leading to constant (marginal) costs set equal to zero for analytical tractability, and without loss of generality.

Production generates ${e}_{i}$ units of pollution, with ${e}_{i}={q}_{i}-{k}_{i}$ (Ulph 1996a), where ${k}_{i}\in [0,{q}_{i})$ is the abatement level to reduce the environment impact, deriving from the adoption of an end-of-pipe cleaning technology available on the market.³ The cost function of the emissions abatement technology is $C{A}_{i}\left({k}_{i}\right)=\frac{z}{2}{k}_{i}^{2},$ with $z>0$ being an exogenous index of technological progress: a lower $z$ reflects a technology improvement which makes abatement less costly. However, to abate emissions, firms sustain costs with decreasing returns to investment.

The index $E{D}_{i}=\frac{g}{2}({e}_{i}{)}^{2}$ measures the environmental damage that the industrial production generates in each country, and it is a convex function of total pollution. The parameter $g>0$, assumed to be the same in the two countries, is the weight the government attributes to the environmental damage, i.e., the society’s awareness towards the environment: increasing values $g$ imply, ceteris paribus, that the society is more concerned about the environment. The (inverse) market demand is linear, whose expression is normalized to $p=1-Q$, where $Q={q}_{i}+{q}_{j}$ is total supply.

2.1 Environmental tax

Consider the case in which the governments of both exporting countries incentivise firms’ abatement activities via an optimal emissions tax per each unit of polluting output, $t\in (\mathrm{0,1}]$, with the aim of maximising social welfare. The tax base of firm $i$ is ${q}_{i}-{k}_{i}$; the government’s tax revenue per firm is $t({q}_{i}-{k}_{i})$. Thus, firm $i$ profit function is:

$${\Pi }_{i}^{ET/ET}=\left(1-{q}_{i}-{q}_{j}\right){q}_{i}-{t}_{i}\left({q}_{i}-{k}_{i}\right)-\frac{z{{k}_{i}}^{2}}{2},$$

(1)

where the upper script $ET/ET$ stands for “emissions tax” in the two exporting countries. At stage two of the game, firms simultaneously choose output and the abatement level. By cutting emissions, firms decrease their costs of an amount equal to the reduced tax burden. Maximisation of (1) with respect to ${q}_{i}$ and ${k}_{i}$ leads to the following first-order conditions:

(i) ${q}_{i}=\frac{1-{q}_{j}-{t}_{i}}{2}$; (ii) ${k}_{i}=\frac{{t}_{i}}{z},$

and from the Hessian matrix, one gets that the successive principal minors are $\left|{H}_{1}\right|<0$ and $\left|{H}_{2}\right|>0$ revealing that it is negative definite, i.e., the stationary point is a maximum. Solving the system of output reaction functions (i), one gets the equilibrium output as a function of the tax rate of Country $i$ and Country $j$, which is given by ${q}_{i}=\frac{1-2{t}_{i}+{t}_{j}}{3},$ with the standard comparative statics $\frac{\partial {q}_{i}}{\partial {t}_{i}}<0$ and $\frac{\partial {q}_{i}}{\partial {t}_{j}}>0.$

Using equilibrium output and the condition in (ii), one obtains the expressions for the producer surplus $PS,$ the government’s budget, $GB,$ and the environmental damage, $ED,$ under the $ET/ET$ regime entering the social welfare expression, $S{W}_{i}^{ET/ET}=P{S}_{i}^{ET/ET}+G{B}_{i}^{ET/ET}-E{D}_{i}^{ET/ET},$ which is given by:

$$S{W}_{i}^{ET/ET}=\frac{-4{z}^{2}({t}_{i}-.5{t}_{j}-.5)[(1+g){t}_{i}-.5(1+{t}_{j})(g-2)]-12z{t}_{i}[(g+.75){t}_{i}-.5(1+{t}_{j})]-9g{t}_{i}^{2}}{18{z}^{2}}.$$

(2)

At stage one, the government sets the emissions tax to maximise the expression in (2), that is:

$$\frac{\partial S{W}_{i}^{ET/ET}}{\partial {t}_{i}}=0\Rightarrow {t}_{i}^{ET/ET}\left({t}_{j}\right)=\frac{z\left[\left(2zg+3g-z\right)\left(1+{t}_{j}\right)\right]}{4{z}^{2}\left(1+g\right)+3z\left(3+4g\right)+9g}.$$

(3)

Equation (3) represents the reaction function of government $i$. Considering the symmetric counterpart of (3) for Country $j$ and solving the system of the reaction functions of the government of Country $i$ and the government of Country $j$ one gets the symmetric equilibrium tax rate, which is given by:

$${t}^{*ET/ET}=\frac{z(2gz+3g-z)}{2g{z}^{2}+9gz+5{z}^{2}+9g+9z}>0\Rightarrow {g}^{ET/ET}\left(z\right)>\frac{z}{2z+3}.$$

Direct inspection of the expression in (3) reveals, for $g>{g}^{ET/ET}\left(z\right),$ that $\frac{\partial {t}_{i}^{ET/ET}}{\partial {t}_{j}^{ET/ET}}>0.$This means that the environmental policy game among governments is played in strategic complements. The second-order condition for a maximum $\frac{{\partial }^{2}S{W}_{i}^{ET/ET}}{\partial {t}_{i}^{2}}<0$ is satisfied. One can also verify that if $g>{g}^{ET/ET}\left(z\right),$ then the conditions ${q}_{i}^{ET/ET}>0,$ ${k}_{i}^{ET/ET}>0,$ and ${e}_{i}^{ET/ET}={q}_{i}^{ET/ET}-{k}_{i}^{ET/ET}>0$ are always satisfied. Making use of (3), after substitutions, the symmetric equilibrium social welfare of the exporting Country $i$ and Country $j$ under the $ET/ET$ regime is given by (see also Table 1):

Table 1 Governments’ payoff matrix

$$S{{W}_{i}}^{*ET/ET}=S{{W}_{j}}^{*ET/ET}=\frac{(g+z)(2+z)[(1+g)4{z}^{2}+12gz+9g+9z]}{2(2g{z}^{2}+9gz+5{z}^{2}+9g+9z{)}^{2}},$$

which is always positive knowing that the inequality $g>{g}^{ET/ET}(z)$ must hold to guarantee the positivity of the environmental tax rate in the two exporting countries.

2.2 Abatement subsidy

This section considers the case in which the social welfare maximising governments incentivise a cutting emission policy by providing firms an optimal subsidy per each unit of pollution abatement, $s\in (\mathrm{0,1}]$ (see, e.g., Lee and Park 2021). Governments of the exporting countries incur an expenditure per firm of ${s}_{i}{k}_{i}$. The profit function of firm $i$ is now:

$${\Pi }_{i}^{AS/AS}=\left(1-{q}_{i}-{q}_{j}\right){q}_{i}+{s}_{i}{k}_{i}-\frac{z{{k}_{i}}^{2}}{2},$$

(4)

where the upper script $AS/AS$ stands for “abatement subsidy” in the two exporting countries. At stage two of the game, firms simultaneously choose output and the abatement level. By cutting emissions, firms now decrease their cost of the cleaning technology. Maximising (4) with respect to ${q}_{i}$ and ${k}_{i}$ yields the following first-order conditions:

(iii) ${q}_{i}=\frac{1-{q}_{j}}{2}$; (iv) ${k}_{i}=\frac{{s}_{i}}{z},$

and from the Hessian matrix, one obtains that the successive principal minors are $\left|{H}_{1}\right|<0$ and $\left|{H}_{2}\right|>0,$ revealing that it is negative definite, i.e., the stationary point is a maximum. The system of output reaction functions in (iii) leads to the equilibrium output in the case of abatement subsidisation, which is given by ${q}_{i}=\frac{1}{3}.$ Using this output together with condition (iv), one gets the producer surplus, the government’s budget, and the environmental damage needed for the expression of social welfare in the $AS/AS$ regime, $S{W}_{i}^{AS/AS}=P{S}_{i}^{AS/AS}+G{B}_{i}^{AS/AS}-E{D}_{i}^{AS/AS},$ which is given by

$$S{W}_{i}^{AS/AS}=\frac{1}{9}-\frac{{s}_{i}^{2}}{2z}-\frac{g}{2}{\left(\frac{1}{3}-\frac{{s}_{i}}{z}\right)}^{2}.$$

(5)

At stage one, the government fixes the subsidy to maximise the expression in (5), that is:

$$\frac{\partial S{W}_{i}^{AS/AS}}{\partial {s}_{i}^{AS/AS}}=0\Rightarrow {s}_{i}^{*AS/AS}=\frac{gz}{3(z+g)}.$$

(6)

Direct inspection of the expression in (6) reveals that, when the environmental policy is an abatement subsidy, its amount depends only on technology and societal awareness, i.e. there is no strategic interaction with the government of the rival exporting country. This is because the abatement decision of firms is not linked to output. The second-order condition for a maximum $\frac{{\partial }^{2}S{W}_{i}^{AS/AS}}{\partial {s}_{i}^{2}}<0$ is satisfied. From (6), one gets that an optimal feasible abatement subsidy exists (i.e., ${s}_{i}^{*AS/AS}\le 1$) if the social environmental awareness is not large, that is, $g < - \frac{3z}{{3 - z}}: = g^{{{AS/{AS}}}} \left( z \right).$ Analytical inspection of the expression in (6) shows that, if $g<{g}^{AS/AS}\left(z\right),$ then ${q}_{i}^{AS/AS}>0,$ ${k}_{i}^{AS/AS}>0$ and ${e}_{i}^{AS/AS}={q}_{i}^{AS/AS}-{k}_{i}^{AS/AS}>0$ are always satisfied. Using (6), after the standard substitutions, the symmetric equilibrium social welfare of the exporting Country $i$ and Country $j$ under the $AS/AS$ regime is given by (see also Table 1):

$$S{{W}_{i}}^{*AS/AS}=S{{W}_{j}}^{*AS/AS}=\frac{2g+2z-gz}{18(g+z)}.$$

2.3 Asymmetric policies

Consider now the asymmetric situation according to which the government of one of the two exporting countries provides an abatement subsidy, e.g., Country $i$, whereas the government of the rival exporting country, e.g., Country $j$, levies an emission tax. The firms profit functions are (4) and (1), respectively, in the two countries from which the first order conditions are (iii) and (iv) for firm in Country $i$ and (i) and (ii) for firm in Country $j$. However, solving the system of reaction function, one gets that the equilibrium output are ${q}_{i}=\frac{1+{t}_{j}}{3}$ and ${q}_{j}=\frac{1-2{t}_{j}}{3}$: the higher the environmental tax levied in Country $j$, the higher the costs of the exporter in that country which leads to output expansion of the firm in the rival Country $i$. Given the equilibrium outputs, together with conditions (ii) and (iv), one gets the producer surplus, the government’s budget, and the environmental damage included into the social welfare in the two countries, that is:

$$S{W}_{i}^{AS/ET}={\left(\frac{1+{t}_{j}}{3}\right)}^{2}-\frac{{s}_{i}^{2}}{2z}-\frac{g}{2}{\left(\frac{1+{t}_{j}}{3}-\frac{{s}_{i}}{z}\right)}^{2},$$

(7)

and

$$S{W}_{j}^{AS/ET}=\frac{8z({t}_{j}-.5{)}^{2}+9{t}_{j}^{2}}{18z}-{t}_{j}\left(\frac{1-2{t}_{j}}{3}-\frac{{t}_{j}}{z}\right)-\frac{g}{2}{\left(\frac{1-2{t}_{j}}{3}-\frac{{t}_{j}}{z}\right)}^{2}.$$

(8)

At stage one, government’s maximization of social welfare leads to:

$$\frac{\partial S{W}_{i}^{AS/ET}}{\partial {s}_{i}^{AS/ET}}=0\Rightarrow {s}_{i}^{*AS/ET}=\frac{(1+{t}_{j})gz}{3(z+g)},$$

(9)

and

$$\frac{\partial S{W}_{j}^{AS/ET}}{\partial {t}_{j}^{AS/ET}}=0\Rightarrow {t}_{j}^{*AS/ET}=\frac{z(2gz+3g-z)}{(1+g)4{z}^{2}+12gz+9g+9z}>0\Rightarrow {g}^{ET/ET}\left(z\right)>\frac{z}{2z+3}.$$

(10)

Direct inspection reveals that $\frac{\partial {s}_{i}^{*AS/ET}}{\partial {t}_{j}^{AS/ET}}>0$: if Country $j$ levies an environmental tax, the competitive advantage of Country $i$ increases, which allows its government to set higher subsidies. Substituting (10) into (9) one gets that the optimal abatement subsidy in the asymmetric regime $AS/ET$ is given by ${s}_{i}^{*AS/ET}=\frac{gz(2g{z}^{2}+5gz+{z}^{2}+3g+3z)}{[(1+g)4{z}^{2}+12gz+9g+9z](z+g)},$ from which it is obtained that the abatement subsidy is feasible if $g < \frac{{z\left( {3z^{2} + 13z + 18 + z\sqrt {41z^{2} + 166z + 169} } \right)}}{{2\left( {2z^{3} + z^{2} - 9z - 9} \right)}}: = g^{{{AS}/{ET}}} \left( z \right).$ Analytical inspection reveals that all non-negativity constraints as well as the second-order conditions for a maximum for both countries are satisfied if $g>{g}^{ET/ET}\left(z\right),$ and $g<{g}^{AS/ET}\left(z\right).$

From (9) and (10), standard substitutions lead to the equilibrium social welfare under the regime $AS/ET$ are given by (see also Table 1):

$$S{{W}_{i}}^{*AS/ET}=\frac{(2g+2z-gz)(2g{z}^{2}+5gz+{z}^{2}+3g+3z{)}^{2}}{2(g+z)[(1+g)4{z}^{2}+12gz+9g+9z{]}^{2}},$$

and

$$S{{W}_{j}}^{*AS/ET}=\frac{\left(g+z\right)\left(2+z\right)}{2[8{z}^{2}\left(1+g\right)+6z\left(4g+3\right)+18g]}.$$

2.4 The strategic game played by national governments

Now we can move to the study of the first decision-making stage and derive the endogenous equilibrium regime of the game among governments. The countries’ benefits of the different environmental policy regimes are summarised in the Governments’ pay-off matrix in Table 1. The couple of strategies available to each government are levying an environmental tax, $ET,$ or abatement subsidy, $AS$. The first element in each entry represents the payoff of Country $i$, while the second element represent the entry of Country $j$. On the top, government $j$’s strategies are listed; on the left, those of government $i$. Preliminary, analytical inspection of ${SW}_{i}^{*AS/AS}$ and ${SW}_{i}^{*AS/ET}$ reveals the results summarised in Lemma 1 and Lemma 2.

Lemma 1

$S{{W}_{i}}^{*AS/AS}>0,$ $S{{W}_{i}}^{*AS/ET}>0$ if $g < \frac{2z}{{z - 2}}: = g^{SW}\left( z \right) .$

Proof

The proof follows from the positivity condition of the numerator of $S{{W}_{i}}^{*AS/AS}$ and $S{{W}_{i}}^{*AS/ET}.$

Lemma 2

${g}^{SW}(z)<{g}^{AS/ET}(z)<{g}^{AS/AS}(z)$.

Proof

The proof follows from direct comparison.

Let us now define the following social welfare differentials of the government of the generic Country $i$ (the social welfare differentials of the government of the generic Country $j$ are symmetric and not reported as they are redundant):

$${\Delta }_{1} : = SW_{i}^{{{*}{ET}/{AS}}} - SW_{i}^{{{*}{AS}/{AS}}} ,$$

$${\Delta }_{2} : = SW_{i}^{{{*}{AS}/{ET}}} - SW_{i}^{{{*}{ET}/{ET}}} ,$$

and

$${\Delta }_{3} : = SW_{i}^{{{*}{AS}/{AS}}} - SW_{i}^{{{*}{ET}/{ET}}} .$$

The first differential shows the incentive of the government of Country $i$ to deviate from levying the environmental tax policy and using the abatement subsidy policy when its sign is negative – and vice versa when its sign is positive –, knowing that the government of Country $j$ is using abatement subsidies. The second differential shows the incentive of the government of Country $i$ to deviate from using an abatement subsidy policy and levying the environmental tax policy when its sign is negative – and vice versa when its sign is positive –, knowing that the government of Country $j$ is levying environmental taxes. The third differential defines the Pareto efficiency properties of the symmetric Nash equilibria. The analysis of the profit differentials allows us to conclude that within the feasible region in the parameter space $\left(g,z\right),$ which is bounded by the set of inequalities ${g}^{ET/ET}\left(z\right)<g<{g}^{SW}\left(z\right),$ ${\Delta }_{1}=0$ if and only if $g={g}_{1}\left(z\right),$ ${\Delta }_{2}=0$ if and only if $g={g}_{2}(z)$ and ${\Delta }_{3}=0$ if and only if $g={g}_{3}(z)$. The feasible region can be interpreted as follows: the societal awareness towards a clean environment ($g$) must be high enough that society is willing to pay environmental taxes to incentivise firms to move towards an ecological transition, allowing them to install a green technology; likewise, the societal awareness $g$ cannot be too high otherwise there would be no resources to finance an abatement subsidy. The feasible parametric space of the policy game played between the government of the exporting Country $i$ and the government of the exporting Country $j$ must consider both thresholds imposed by the two different “green” public incentive systems.

The analytical expressions of (a) the profit differentials (not reported in the paper as they are cumbersome and not economically meaningful), (b) the feasibility condition of the environmental tax rate, and (c) the non-negativity condition on social welfare under subsidisation (both the inequalities in (b) and (c) bounding the feasible region of the policy game) allow us to build on Fig. 1, Panel A, whose graphical and analytical inspection leads to the core result of the paper (Fig. 1, Panel B represent an enlargement view of Panel A to emphasise the outcome of Area $E$). More specifically, the figure represents a rigorous geometrical portray of the analytical outcomes of this non-cooperative game. The green (resp. orange) curve represents the bound $g={g}^{ET/ET}(z)$ (resp. $g={g}^{SW}(z)$). The black solid line is the threshold $g={g}_{1}(z)$. If $g<{g}_{1}(z)$ then ${\Delta }_{1}<0$. If $g>{g}_{1}(z)$ then ${\Delta }_{1}>0$. The black dashed line is the threshold $g={g}_{2}(z)$. If $g<{g}_{2}(z)$ then ${\Delta }_{2}>0$. If $g>{g}_{2}(z)$ then ${\Delta }_{2}<0$. The black dotted line is the threshold $g={g}_{3}(z)$. If $g<{g}_{3}(z)$ then ${\Delta }_{3}>0$. If $g>{g}_{3}(z)$ then ${\Delta }_{3}<0$.

Fig. 1

Nash equilibria of the policy game and their efficiency properties. Panel A: geometrical portray of analytical results in the feasible space $(g,z)$. Panel B: enlargement view of Panel A to emphasise the existence of Area $E$. In this region, the Pareto-efficient SPNE is $(AS,AS)$, so that the policy game is a deadlock  in which self-interest and mutual benefit of providing abatement subsidies do not conflict

The sub-game perfect Nash equilibrium (SPNE) outcomes of the policy game studied in the present paper are summarised in Result 1.

Result 1

The social welfare differentials ${\Delta }_{1}$, ${\Delta }_{2}$, ${\Delta }_{3}$ and the feasibility conditions ${g}^{ET/ET}(z)<g<{g}^{SW}(z)$ generate six regions in Fig. 1 with the following characteristics.

(1) Region $A$: the policy game involving the comparison between strategies $ET$ and $AS$ is economically unfeasible; only the $ET$ policy is feasible in this parameter space.

(2) Region $B$: ${\Delta }_{1}>0$, ${\Delta }_{2}<0$ and ${\Delta }_{3}<0$; the unique Pareto-efficient SPNE is $(ET,ET)$ and the policy game is a deadlock in which self-interest and mutual benefit of levying environmental taxes do not conflict.

(3) Region $C$: ${\Delta }_{1}<0$, ${\Delta }_{2}<0$ and ${\Delta }_{3}<0$; there are multiple symmetric SPNE, $(ET,ET)$ and $(AS,AS)$, and the policy game is a coordination game in which $ET$ payoff dominates $AS$.

(4) Region $D$: ${\Delta }_{1}<0$, ${\Delta }_{2}>0$ and ${\Delta }_{3}<0$; the unique Pareto-inefficient SPNE is $(AS,AS)$ and the policy game is a prisoner’s dilemma in which self-interest and mutual benefit of providing abatement subsidies conflict.

(5) Region $E$: ${\Delta }_{1}<0$, ${\Delta }_{2}>0$ and ${\Delta }_{3}>0$; the unique Pareto-efficient SPNE is $(AS,AS)$ and the policy game is an a deadlock in which self-interest and mutual benefit of providing abatement subsidies do not conflict.

(6) Region $F$: the policy game involving the comparison between strategies $ET$ and $AS$ is economically unfeasible; only the $AS$ policy is feasible in this parameter space.

Thus, if the societal awareness is significantly low, the government can nudge abatement activities only via subsidization; in an international trade context with governments engaged in environmental policies, those subsidies can lead, though in a limited parametric area, to a Pareto-efficient sub-game perfect Nash equilibrium. If the environmental awareness is high enough, the standard result that mutual subsidization leads to a Pareto-inefficient equilibrium appears.

Those results seem to suggest that there is room for the provision of “green” subsidies because these can be beneficial for governments to start pushing the “green” transition.

3 A simple dynamic analysis of the policy game

Following Buccella et al. (2021), it is possible to conjecture the potential historical paths of the changes in the efficiency of the cleaning technology ($z$) and the societal awareness of environmental quality ($g$). For a methodological discussion about the difference between the logical time (order of moves) of the static (timeless) one-shot, non-cooperative game and the historical timing of the events (past, present, and future) that contributes to create a chronological structure of sequences see Buccella et al. (2021, 2024).

Although the model developed in the previous section is timeless, it is possible to consider a chronological linkage of the changes observed in history of $z$ and $g$ with the prevailing SPNE of the policy game, in turn, going beyond the logical narrative detailed so far. The changes in time of $z$ and $g$ and summarised in Fig. 2. In this regard, as time passes, we can reasonably assume that the cleaning technology becomes more efficient, i.e., the index $z$ is decreasing over time, and the societal ecological awareness is increasing or, alternatively, the society becomes increasingly interested in protecting the environment, i.e., the index $g$ is increasing over time.

Fig. 2

Historical trend of societal awareness and technological progress

Our speculation in this section focuses on trying to link the possible historical changes of the two main parameters of the model to the SPNE of the static policy game obtained in a non-cooperative context, in which the government of two exporting countries must strategically choose the optimal environmental policy. When the efficiency of the cleaning technology is low and society cares little about environmental quality (Past), see the north-west region (Area $F$) in Fig. 1, $AS$ is the unique feasible policy that can then be used by the government of each country to begin with caring for the environment. When the efficiency of the cleaning technology is high, and society is highly concerned about environmental quality issues (Future), see Area $D$ in Fig. 1, $(AS,AS)$ is the unique Pareto-inefficient SPNE of the policy game. This implies that governments of developed countries would jointly be better off levying an environmental tax to incentive firms to undertake emission-reduction actions instead of applying abatement subsidies, but no government has the incentive to play $ET$ unilaterally at the end of the ecological transition. Then, following a trajectory in which $z$ and $g$ move south-eastwards from the past to the future (beginning with Area $F$ or Area $E$ ending up in Area $D$) the strategic adoption of green taxes or subsidies changes as the incentive of the governments of the exporting countries modify based on the prevailing values of $z$ or $g$, then passing from Area $C$ (in which the Nash outcome is indeterminate) and Area $B$ (in which the Nash outcome incentivises the adoption of environmental taxes). However, it is important to pinpoint the existence of an area in which subsidising abatement emerges as the unique Pareto-efficient SPNE of the game. This can happen also for a relatively inefficient cleaning technology and a low societal awareness of environmental quality.

To analyse more in depth the dynamics emerging in the model, we assume that the changes over time of $z$ and $g$, which are denoted by $\dot{g}=\frac{dg}{d\tau }$ and $\dot{z}=\frac{dz}{d\tau }$ (where $\tau$ is the time index and the dot stands for time derivative), are captured by the following differential equations:

$$\dot{z}=\alpha z\left({z}_{min}-z\right),$$

(11)

and

$$\dot{g}=\beta g\left(g-{g}_{max}\right),$$

(12)

where $\alpha >0$ and $\beta >0$ capture the speed through which $z$ and $g$ evolve over time, respectively, and ${z}_{min}>0$ and ${g}_{max}>0$ represent the trend values to which $z$ and $g$ converge. To simplify the exposition, the dynamic analysis will focus on studying the changes in the main SPNE results of the model by changing only one parameter at a time, that is, assuming a given value of $g$ (resp. $z$) and studying the effect of changing $z$ (resp. $g$). We pinpoint that reducing $z$ and increasing $g$ have similar consequences on the equilibria of the model and therefore we do not report what happens when both change together ($z$ reduces and $g$ increases).

Figure 3 shows the changes in the social welfare prevailing in Country $i$ corresponding to the relevant SPNE of the policy game when $z$ reduces (Panel A) for a given value of $g$, and the (decreasing) temporal trend of $z$ (Panel B) representing the R&D advancement of the existing cleaning technology that can be observed over time. Unlike this, Fig. 4 shows the changes in the social welfare prevailing in Country $i$ corresponding to the relevant SPNE of the policy game when $g$ increases (Panel A) for a given value of $z$, and the (increasing) temporal trend of $g$ (Panel B) representing the increasing attention to the environment that society has had over time. For comparison purposes between Panel A and Panel B in both figures, the parameters $z$ and $g$ are reported on the vertical axis and the social welfare level and the time index on the horizontal axis of the figure depicted in Panel A and Panel B, respectively.

Fig. 3

Panel A: Social welfare prevailing in the SPNE of the policy game when $z$ varies. Panel B: temporal trend of $z$. Parameter values: ${z}_{min}=0,$ $\alpha =1,$ $g=4,$ initial value of $z$ equal to $5$

Fig. 4

Panel A: Social welfare prevailing in the SPNE of the policy game when $g$ varies. Panel B: temporal trend of $g$. Parameter values: ${g}_{max}=5,$ $\beta =1,$ $z=4,$ initial value of $g$ equal to $0.001$

Assuming a given value of the societal awareness of cleaning the environment ($g=4$) and starting from relatively high values of $z$ (i.e., the cleaning technology is inefficient), Panel A of Fig. 3 shows that the only applicable policy is $ET$ because $AS$ is not available and the prevailing social welfare is described by the black line (see the corresponding Area $A$ in Fig. 1, Panel A). As technological advances are observed ($z$ decreases), the prevailing level of social welfare tends to increase following the Nash equilibrium of the policy game played by the two exporting countries (blue line), in which the Pareto-efficient SPNE is $(ET,ET)$. This occurs in Area $B$ of Fig. 1, Panel A. When the policy game becomes a coordination game (see Area $C$ in Fig. 1, Panel A), the government of generic Country $i$ is in an indeterminate situation as both environmental taxes to incentivise firms to undertake emission-reduction actions and the use of abatement subsidies can be observed in equilibrium. In the first case, social welfare follows the increasing trajectory discussed so far (red line). In the second case, there is a downward jump (grey line) although as $z$ is reduced social welfare increases but follows a lower trajectory than the one implied by the red line. However, a further reduction of $z$, implying another improvement in the green technology of the industry of the two exporting countries, allows society of Country $i$ to increase social welfare following the prevailing Pareto inefficient SPNE $(AS,AS)$. As $z$ continues to decrease due to improvements in the abatement technology, this turns out to be the best scenario overall (although society would be better off under $(ET,ET)$). This is captured by the green line. We pinpoint that a reduction in $z$ allows for an increase in social welfare as better abatement technology reduces the costs of the firms and increases their profits while also reducing environmental damage, in turn, implying that the resources needed to finance ad hoc public environmental programmes are lower.

Assuming now a given value of the efficiency of the green technology ($z=4$). Then, starting from relatively low values of $g$ (representing a naïve society from the point of view of protecting environmental quality), Panel A of Fig. 4 shows that the only feasible policy for environmental protection is $AS$ because $ET$ is not available and social welfare is described by the yellow line (Area $F$ in Fig. 1, Panel A). This means that subsidising firms by incentivising an abatement policy is the first step to trigger policies to protect the environment. As the societal awareness toward a clean environment improves ($g$ increases), the prevailing level of social welfare tends to reduce following the Nash equilibrium of the policy game played by the two exporting countries, where the SPNE is $(AS,AS)$, which is initially Pareto efficient (blood-red line) and then becomes Pareto inefficient (green line) for higher values of $g$. This happens in correspondence with Area $E$ and Area $D$ of Fig. 1, Panel A, respectively. An increase in $g$ means that society is willing to finance larger public programmes to protect environmental quality whose financing takes away the well-being of private individuals, even though the environmental damage is gradually reduced. When the policy game becomes a coordination game (see Area $C$ in Fig. 1, Panel A) due to a further increase in $g$, the $ET$ policy becomes a possible intervention tool. However, the choice of the generic Country $i$ is indeterminate because both collecting taxes to incentivise firms to undertake emission-reduction actions and the use of abatement subsidies can be observed in Nash equilibrium. In the first case, the prevailing level of social welfare would jump upwards compared to the previously prevailing green line, following however a decreasing trajectory (red line). In the second case, social welfare follows the decreasing trend contiguous to the previous one (grey line). However, a further increase in $g$ allows the society of the exporting Country $i$ to follow a higher welfare trajectory because the prevailing SPNE now becomes $(ET,ET)$ which also turns out to be Pareto efficient; however, if $g$ continues to increase, ET becomes the only feasible policy. We pinpoint that an increase in $g$ implies a reduction in the level of social welfare as an increasing awareness towards a cleaner environment implies that society is willing to finance a larger number of resources to reduce pollution, in turn, implying that the financing ad hoc public environmental programmes are higher.

4 Conclusions

Using a basic two-stage game, third-country market model, in which at the first stage, social welfare maximising governments optimally choose the environmental policy tool for exporting polluting firms, and at the second stage, firms compete in quantity (choosing concurrently abatement levels), this article gives a first insight on the use of “green” subsidies as a tool of strategic trade policy. The key result of the analysis is that, depending on the societal awareness toward the environment and the abatement technology efficiency, a rich set of equilibria emerges. Subsidization can emerge as a Pareto-inefficient equilibrium at the end of the ecological transition. However, for low environmental awareness, subsidizing pollution abatement can 1) emerge as the unique Pareto-efficient SPNE of the policy game or 2) be the only feasible environmental policy.

Based on this paper, both the concerns of The Economist and the optimistic views of The Financial Times observers are worth to be considered. Then, this article aims to launch a provocative discussion on the current debate on the use of environmental policies as a tool to improve the national welfare of countries involved in international trade. The article also pinpoints the dynamic outcomes emerging from the policy game by considering the (historical) time evolution of the efficiency of the cleaning technology and the societal awareness towards a clean environment compared to the prevailing SPNE of the game.

Even so, further investigation and more articulated models are needed. For example, extensions with segmented markets/reciprocal trade models in which home and foreign firms supply their goods to the domestic market and the other country’s market, and that embeds consumer welfare when designing the policy, “green” R&D investments that abate emissions and improve production processes, and the case in which environmental pollution may spillover to trading partners (transboundary pollution) may be considered for future research.