Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-07T12:44:42.312Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal pollution tax under imperfect competition and international trade: the small country case

Published online by Cambridge University Press:  25 August 2010

ALEJANDRO SAMPAOLESI
Rights & Permissions [Opens in a new window]

Abstract

This work depicts the possibility of setting up an optimal pollution tax under non-competitive markets and international trade in a small country. The model employed describes a situation of partial equilibrium characterized by imperfect competition among domestic producers, where the domestic good is a substitute for an imported polluting commodity. In this framework, we also bring in the possibility that the domestic firms can introduce innovation offsets via their investment in R&D. From the results, the optimal pollution tax under domestic distortions can be expressed as a function of a ‘domestic production effect’ and a ‘pollution effect’. Furthermore, when the firms execute R&D expenditures, the optimal policy adds an ‘innovation effect’, which captures the change in welfare coming from a decrease in total costs and can lead our results to a win–win situation.

Information

Type
Research Article
Information
Environment and Development Economics , Volume 15 , Issue 5 , October 2010 , pp. 505 - 514
Copyright
Copyright © Cambridge University Press 2010

1. Introduction

During the last years most economic studies have analysed the impact of environmental policies on international trade by means of the use of at least two-country general equilibrium models. However, because of their enormous simplifications of reality, their conclusions could lead policy makers to a misunderstanding of the true trade-offs between domestic and international competitiveness. In general, when we study the environmental issues associated with determined sectors of the economy, we often see that this kind of models fails to explain them. This emphasizes the need to work on partial equilibrium models to better understand such trade-offs. In particular, the latter are very useful when the polluting industries not only have the power to determine the domestic prices but also compete with some substitute goods which are imported from abroad.Footnote 1

In this context, the aim of this paper is to set up the theoretical framework that allows us to study the characteristics of environmental policy under these conditions. To accomplish this, we work in a two-good partial equilibrium model to design the environmental tax that maximizes the social welfare.Footnote 2 Furthermore, we assume that one of the goods is produced at home under non-competitive conditions, whereas another one, which is an imperfect substitute for the first, is imported from a foreign country. In addition, we assume that the price of the imported good is determined by the world market and that the distortion in production coexists with an environmental externality, where the latter comes from the pollutant emissions associated with the domestic production process. Finally, we rule out the possibility of trans-boundary environmental issues since they are not related to the small open economy condition. In a second extension to the literature, we allow for the possibility of innovation offsets and analyse how these can affect the level of the optimal environmental tax, where the strategic variable for the domestic firms is their investment in R&D.

Our results show that the optimal pollution tax can be expressed as the sum of a ‘domestic production effect’ and a ‘pollution effect’, where the first one stands for a decrease in social welfare because of the drop in domestic sales, and the second one constitutes an increase in social welfare as a result of the decrease in pollution damage. Therefore, depending on whether or not the ‘pollution effect’ surpasses the ‘domestic production effect’, the optimal policy represents a tax-cum-subsidy on pollution. In addition, when the domestic firms have the possibility of introducing innovation offsets via their investment in R&D, the optimal policy tax incorporates an ‘innovation effect’, whose impact on welfare depends on whether the new industry equilibrium (after the tax) is associated with higher or lower levels of emissions. Moreover, the introduction of innovation offsets can lead the economy to a win–win situation, implying that the sign of the optimal policy turns positive (i.e., we must introduce a pollution tax) and that there is a drop in the quantity imported of the foreign good. Finally, we conclude that, besides this situation, a comparison between the levels of this tax and the previous one (without innovation offsets) as well as their effects on the level of imports is not possible.

Turning to the analysis of the economic literature, we found no research addressing these concerns. As mentioned before, most analytical studies are based on the classical/neoclassical models of trade; besides that, non-competitive conditions respond to the use of environmental policy as strategic trade policy.Footnote 3

The remainder of this paper is organized as follows. Section 2 describes the basic model and establishes the optimal pollution policy that maximizes the social welfare. Section 3 sets out the pollution tax level when firms carry out endogenous R&D investments. The last section provides a summing-up and suggests some directions for further research.

2. The model

We place a two-stage game with two players to solve our regulation problem. Hence, working backward from the firms’ decisions to the government's tax decision, in the second stage, the producers choose their outputs and abatement levels under a Nash–Cournot behavioral assumption and, in the first stage, the government sets the tax on pollution to maximize social welfare, recognizing that both the equilibrium behavior of firms and the imports of the substitute commodity depend on the tax.

It should be noted that in the present context of a small open economy, the pollution (production) tax represents a first-best policy. However, we rule out the use of industrial policy on the assumption that environmental policy is politically more feasible than the previous one. Moreover, we assume that there is no interaction with other sectors of the economy, that the economy acts as a net-importer of the foreign good, and that the factor prices are given.Footnote 4, Footnote 5 Before proceeding, some general comments are in order. First, the paper is concerned with the effects of a specific pollution tax on emissions in a static context (i.e., a particular period of time), in which market structure, cost conditions and entry barriers are given. Second, we focus on industries where domestic firms sell in domestic markets but do not export the product. Third, working in a first-best policy leaves out the possibility of trade balance problems in the long run (i.e., the internalization of the environmental damage should improve the trade patterns and, therefore, the gains from trade). Finally, we work in a complete information model, where the government is assumed to know the demand structure of the firms’ output as well as their cost functions. Thus, it correctly anticipates the domestic firms’ output decisions given the imposed emission tax.

2.1 Domestic firms

The industry of the domestic good, x, consists of n identical firms, where the producing process generates a pollutant whose quantity depends on the level of production and abatement activities. Therefore, we can express the cost function for the firm as Cj(xj, aj), where xj and aj are the levels of production and abatement effort respectively. Also, we assume that Cj is increasing and strictly convex in its arguments, i.e., Cjx > 0, Cja > 0, Cjxx > 0, and Cjaa > 0 for all xj and aj, and that the level of emissions, ej, takes the following functional form: ej = ej(xj, aj), with ejx > 0, eja < 0, ejxa < 0, ejxx > 0, and ejaa > 0. Then, if Px(x, y, I) denotes the inverse demand function for x, with y and I representing the imported good and the monetary income respectively, in the second-stage game the representative firm chooses its output, xj, and abatement, aj, levels, recognizing that the rivals’ output and abatement levels as well as the environmental tax placed by the government, τ, are given, to maximize the following profit function:Footnote 6

(1)
\begin{equation} \pi ^j (x^j ,a^j ) = P^x (x,y,I)x^j - C^j (x^j ,a^j ) - \tau e^j (x^j ,a^j ),\quad j = 1, \ldots \ldots ,n,\!\!\!\end{equation}

which yields the first-order conditions

(2a)
\begin{equation} P^x (x,y,I) + \frac{{\partial P^x }}{{\partial x^j }}x^j - C_x^j (x^j ,a^j ) - \tau e_x^j (x^j ,a^j ) = 0,\end{equation}
(2b)
\begin{equation} - C_a^j (x^j ,a^j ) - \tau e_a^j (x^j ,a^j ) = 0.\end{equation}

Aggregating, taking into account that the aggregate level of production of the domestic industry, x, is equal to x = nxj; of abatement, a, is equal to a = naj; and of emissions, e, is equal to e = nej; we can express the first-order conditions for the maximization of the profits at the industry level as:

(3a)
\begin{equation} P^x (x,y.I) - (C_x (x,a) + \tau e_x (x,a)) = - x\frac{{V_x }}{n},\end{equation}
(3b)
\begin{equation} \tau = - \frac{{C_a (x,a)}}{{e_a (x,a)}},\end{equation}

where $V_x = \frac{{\partial P^x }}{{\partial x}}$.Footnote 7 Expression (3a) is a variant of the well-known equilibrium condition in Cournot models, stating that the Lerner index of any individual firm must be equal to that firm's market share divided by the absolute value of total-market-demand elasticity, whereas condition (3b) implies that firms abate pollution to the point where their marginal cost of reducing emissions equals the pollution tax.Footnote 8

2.2 Market equilibrium

Using (3a), we can express the equilibrium output for the domestic market as

(4)
\begin{equation} x = - [P_x (x,y,I) - (C_x (x,a) + \tau e_x (x,a))]\frac{n}{{V_x }}.\end{equation}

Therefore, from (4), the response of the domestic output to a change in τ is given by

(5)
\begin{equation} \frac{{\partial x}}{{\partial \tau }} = \frac{{e_x + (C_{xa} + \tau e_{xa} )\frac{{\partial a}}{{\partial \tau }}}}{{V_x \frac{{1 + n}}{n} - (C_{xx} + \tau e_{xx} ) - \frac{{V_{xx} }}{{V_x }}(P^x - (C_x + \tau e_x ))}}.\end{equation}

Note that as exa < 0, the sign of the second term in the numerator is determined by the effect of an increase in the level of abatement efforts on production costs, Cxa, which could be positive, zero, or negative, depending on the relation between these activities. In other words, the degree of complementarity between these processes will define the sign of the cross-partial derivative. Also, in the case of linear demand functions, Vxx = 0, the third term of the denominator, disappears from the expression. However, since $\frac{{\partial a}}{{\partial \tau }} > 0$ and primary effects (first derivatives) generally dominate secondary effects (second derivatives), the sign of (5) is assumed negative.Footnote 9

2.3 Social welfare and optimal policy

From the above, we can express the government revenues coming from the pollution tax on domestic emissions as τe. Therefore, if D(e) denotes the environmental damage resulting from any aggregate level of pollution in monetary terms, it is possible to define the social welfare function, SW, as the sum of (i) the consumer surpluses, (ii) the domestic industry profits, and (iii) the government revenues, less (iv) the pollution damage.

(6)
\begin{eqnarray} &&SW = \left( {\int_0^{x = nx^j } {P^x (x,y,I)dx - P^x x} } \right)\nonumber\\ && + \left( {\int_0^{y = y(nx^j )} {P^y (x,y,I)dy - P^y y} } \right) + \pi (x,a) + \tau e - D(e),\end{eqnarray}

where Py(x, y, I) denotes the inverse demand function for y, Px, and Py represent the price of the domestic and imported good, respectively, and D(e) is assumed to be increasing and strictly convex, i.e., De > 0 and Dee > 0 for all e. This specification of aggregate social welfare avoids the issue of income distribution effects by weighting each welfare component equally; a way to modify it is to introduce an alternative weighting system. Hence, replacing in π(x.a) and e, we can rewrite (6) as

(7)
\begin{eqnarray} &&SW = \int_0^{x = nx^j } P^x (x,y,I)\,dx \nonumber\\ && + \int_0^{y = y(nx^j )} {P^y (x,y,I)\,dy} - C(x,a) - P^y y - D(e(x,a)).\end{eqnarray}

This provides a simple interpretation of the social welfare as the total benefits from consuming x and y less the private cost of producing x, the social cost of acquiring y (its domestic or international price), and the loss in consumer utility generated by the level of pollution. Then, turning to the analysis of the pollution tax that maximizes the social welfare, we find that in the first-stage game the government chooses the value of τ that maximizes (7), recognizing that y is a function of x and that x depends on τ. From (7), the effect on SW of a small change in τ is given by

(8)
\begin{equation} \frac{{\partial SW}}{{\partial \tau }} = ((P_x - C_x ) - D_e e_x )\frac{{\partial x}}{{\partial \tau }} - (C_a + D_e e_a )\frac{{\partial a}}{{\partial \tau }}.\end{equation}

Then, substituting in (8) for (3a) and (3b), we obtain the result that $\frac{{\partial SW}}{{\partial \tau }} = 0$ when τ = τ*, where

(9)
\begin{equation} \tau ^* = x\frac{{V_x }}{n}\frac{{\partial x}}{{\partial \tau }}\frac{1}{h} + D_e ,\end{equation}

with

\[ h = e_x \frac{{\partial x}}{{\partial \tau }} + e_a \frac{{\partial a}}{{\partial \tau }} < 0. \]

The intuition behind this expression is as follows: The first term denotes the ‘domestic production effect’ and represents a decrease in the welfare of the society. That is, as x is a good whose marginal benefit to consumers (Px) exceeds its marginal cost (apart from the pollution cost), a higher τ decreases the amount of sales of the domestic firms and, therefore, the social welfare. On the other hand, the second term stands for the ‘pollution effect’ and constitutes an improvement in social welfare. Here, a higher τ results in a lower level of emissions, which improves the social welfare because of the decrease in the pollution damage. Also, note that as y is a negative function of x, $\frac{{\partial y}}{{\partial x}} < 0$, a drop in the sales of the domestic firms augments the amount imported of the good y. Therefore, depending on whether or not the ‘pollution effect’ exceeds the ‘domestic production effect’, the optimal policy consists of a tax-cum-subsidy on pollution.

3. Endogenous R&D investments

The model described above provides a tractable framework to allow for the possibility of private actions to counteract the environmental tax effects. Here, we assume that the domestic producers can neutralize such effects through the introduction of some innovation offsets, where the strategic variable for the firms is the investment in R&D.Footnote 10 Hence, we need to focus on a three-stage game, where in the second-stage the producers choose their R&D expenditures required to employ a particular technology, and in the third-stage they choose their outputs and abatement levels. Hence, assuming that the total, average, and marginal costs are decreasing and convex in innovation expenditures, φj, and that the new technology reduces the production as well as the abatement costs, we can express the firm's total cost function as Cj(xj, aj, φj), with Cj φ < 0 and Cj φφ > 0 for all φj.Footnote 11, Footnote 12 Now, at the third-stage game the jth firm chooses its own output, xj, and abatement level, aj, recognizing that the emission tax, τ, set by the government in stage one, the level of φj set in stage two, φj*, and the output and abatement level of its rivals are given. This leads to the following first-order conditions for the domestic industry:

(10a)
\begin{equation} P^x (x,y,I) - (C_x (x,a,\phi ^* ) + \tau e_x (x,a)) = - x\frac{{V_x }}{n},\end{equation}\vskip-12pt
(10b)
\begin{equation} \tau = - \frac{{C_a (x,a,\phi ^* )}}{{e_a (x.a)}}.\end{equation}

In the second-stage game, the representative firm maximizes its profits with respect to φj, assuming that the rivals’ expenditures on R&D are given. However, it figures out that its output and abatement level and the rivals’ output and abatement level in the next stage depend on φj. Therefore, it chooses φj to maximize

(11)
\begin{eqnarray} &&\pi ^j (x^j (\phi ^j ),a^j (\phi ^j ),\phi ^j ) = P^x (x(\phi ^j ),y,I)x^j (\phi ^j ) - C^j (x^j (\phi ^j ),a^j (\phi ^j ),\phi ^j )\nonumber\\ && - \tau e^j (x^j (\phi ^j ),a^j (\phi ^j )),\end{eqnarray}

where the first-order condition at the industry level is given by

(12)
\begin{equation} P^x - \left( {C_x + C_a \frac{{\partial a/\partial \phi }}{{\partial x/\partial \phi }} + \tau \left( {e_x + e_a \frac{{\partial a/\partial \phi }}{{\partial x/\partial \phi }}} \right) + \frac{{C_\phi }}{{\partial x/\partial \phi }}} \right) = - x\frac{{V_x }}{n},\end{equation}

where φ and C φ are the level of innovation expenditures and the innovation marginal cost for the domestic industry respectively. Furthermore, the third term in the brackets represents the change in the market power of the domestic firms, an increase in φ decreases the cost of production per unit of output, which, since $\frac{{\partial x}}{{\partial \phi }} > 0,$ increases the sales of x.

Since the derivation of an optimal value of innovation, φ*, in explicit form is impossible, we can obtain additional insights by taking the second-order condition for a maximum. Then, from (12) we obtain

(13)
\begin{eqnarray} &&\frac{{\partial \left( {\frac{{C_\phi }}{{\partial x/\partial \phi }}} \right)}}{{\partial \phi }} > \left[\left( {V_x \frac{{1 + n}}{n} + x\frac{{V_{xx} }}{n}} \right)\right.\nonumber\\ && \quad- \left.\left( \begin{array}{l} C_{xx} + 2C_{xa} \displaystyle\frac{{\partial a/\partial \phi }}{{\partial x/\partial \phi }} + C_{aa} \left( {\displaystyle\frac{{\partial a/\partial \phi }}{{\partial x/\partial \phi }}} \right)^2 + \displaystyle\frac{{C_{x\phi } + C_{a\phi } }}{{\partial x/\partial \phi }} \\ +\tau \left( {e_{xx} + 2e_{xa} \displaystyle\frac{{\partial a/\partial \phi }}{{\partial x/\partial \phi }} + e_{aa} \left( {\displaystyle\frac{{\partial a/\partial \phi }}{{\partial x/\partial \phi }}} \right)^2 } \right) \\ \end{array} \right) \right]\displaystyle\frac{{\partial x}}{{\partial \phi }},\!\!\!\!\qquad\quad\end{eqnarray}

where $\frac{{\partial x}}{{\partial \phi }}$ is positive and C xφ and C aφ are negative by definition. Thus, as the terms in brackets above denote the demand and supply sides of the market, the effect of a change in φ on the market power of the domestic industry will be greater under linear demand functions (i.e., Vxx = 0) and complementary activities, Cxa > 0.Footnote 13

Finally, in the first-stage game, the government maximizes SW(τ) recognizing that x, y and φ all depend on τ. Therefore, the first-order condition for the government problem is

(14)
\begin{eqnarray} &&0 = ((P_x - C_x ) - D_e e_x )\left( {\frac{{\partial x}}{{\partial \tau }} + \frac{{\partial x}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right)\nonumber\\ && - (C_a + D_e e_a )\left( {\frac{{\partial a}}{{\partial \tau }} + \frac{{\partial a}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right) - C_\phi \frac{{\partial \phi }}{{\partial \tau }},\end{eqnarray}

with $\frac{{\partial \phi }}{{\partial \tau }} > 0$. Hence, using (10a) and (10b), the optimal tax pollution, τ**, can be written as

(15)
\begin{equation} \tau ^{**} = x\frac{{V_x }}{n}\left( {\frac{{\partial x}}{{\partial \tau }} + \frac{{\partial x}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right)\frac{1}{\rho } + C_\phi \frac{{\partial \phi }}{{\partial \tau }}\frac{1}{\rho } + D_e ,\end{equation}

with

\begin{equation*} \[ \rho = e_x \left( {\frac{{\partial x}}{{\partial \tau }} + \frac{{\partial x}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right) + e_a \left( {\frac{{\partial a}}{{\partial \tau }} + \frac{{\partial a}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right). \] \end{equation*}

Comparing (9) with (15), we observe that the introduction of innovation offsets generate some distinctive characteristics in the expression for τ. Now, it is possible to reverse the conclusion that under non-competitive conditions the optimal policy should be a tax-cum-subsidy on pollution. To see this, note that when such offsets are added, the signs of the numerator and denominator of the ‘domestic production effect’ are undetermined, which implies the possibility that it can turn positive. In other words, this will happen when

\begin{equation*} \[ \rho < 0 < \left( {\frac{{\partial x}}{{\partial \tau }} + \frac{{\partial x}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right), \end{equation*} \]

or

\begin{equation*} \[ \frac{{e_x }}{{ - e_a }} < \left( {\frac{{\partial a}}{{\partial \tau }} + \frac{{\partial a}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right)\bigg/\left( {\frac{{\partial x}}{{\partial \tau }} + \frac{{\partial x}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right) \] \end{equation*}

with

\begin{equation*} \[ \left( {\frac{{\partial x}}{{\partial \tau }} + \frac{{\partial x}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}} \right) > 0. \]\end{equation*}

The rationale behind this result is as follows: when the indirect effect generated by the innovation process surpasses the direct effect of τ on x and the denominator still remains negative, since the abatement effect dominates the production effect of τ on e, the introduction of innovation offsets not only increases the sales of x but also decreases the level of emissions, which, therefore, improves the social welfare. Also, note that as the domestic sales of x increase, there will be a drop in the quantity imported of good y. In contrast, if the direct effect dominates the indirect effect of τ on x (i.e., ρ < 0 with $( {\frac{{\partial x}}{{\partial \tau }} + \frac{{\partial x}}{{\partial \phi }}\frac{{\partial \phi }}{{\partial \tau }}}) < 0$), the ‘domestic production effect’ maintains its negative sign. In addition, the second term in (15) describes what we call the ‘innovation effect’: an increase in τ diminishes the production costs, which is welfare increasing when the new equilibrium for x is associated with a lower level of emissions, ρ < 0, or welfare decreasing when the contrary happens, ρ > 0. Hence, we observe that under a win–win situation (i.e., when the firms can reduce their emissions level and increase their domestic sales), the optimal policy represents a tax on pollution and has a higher level than the previous one (without innovation offsets), i.e., τ** > τ*, with τ** > 0, and τ* > = < 0.Footnote 14 Otherwise, if the innovation offsets are positively correlated with higher emissions (i.e., ρ > 0), we obtain that τ** could be lower or greater than τ*.

4. Conclusions

This paper focuses on the design of optimal environmental policy when non-competitive conditions exist in a small economy. To accomplish this, we work in a two-good partial equilibrium model, where one of the goods is imported from a foreign country. As the preceding analysis made clear, the optimal pollution policy under domestic distortions can be decomposed into a ‘domestic production effect’, which describes the change in welfare coming from a variation in the level of domestic firms’ sales, and a ‘pollution effect’, capturing the change in welfare coming from a variation in pollution damage. Furthermore, since these two effects have opposite signs, the optimal policy will be a tax-cum-subsidy on pollution, depending on whether or not the ‘pollution effect’ dominates the ‘domestic production effect’.

Interesting highlights appear when the firms have the possibility of introducing innovation offsets through their investment in R&D. In this case, the optimal pollution tax adds an ‘innovation effect’, which captures the change in welfare coming from a decrease in production costs. From the analysis, its effect on welfare will depend on whether the new equilibrium (after the tax) for the domestic industry is associated with a higher or lower level of emissions, creating the possibility that we can obtain a win-win situation when the innovation offsets generate more abatement than emissions and the domestic firms increase their sales. Finally, we conclude that only under a win-win situation does the optimal environmental policy represent a tax and it is higher than the previous one (without innovation offsets). Otherwise, a comparison between them is impossible.

There are many additional areas of research that could be pursued. A natural extension would be to admit the presence of foreign direct investment in the form of local production of the imported good. Another development would be to introduce stochastic elements.

Footnotes

1 Some examples of these conditions can be found in the paper industry in Argentina or in the white goods industry in Chile.

2 Note that since there is not a best policy instrument to deal with environmental damages, it will be a function of pollutant characteristics (i.e., global or local, stock or fund, etc.).

3 See Conrad (Reference Conrad1993), Barrett (Reference Barrett1994), and Kennedy (Reference Kennedy1994) for an initial discussion of these issues. Some extensions of these studies are Simpson and Bradford (Reference Simpson and Bradford1996), Ulph (Reference Ulph, Carraro and Siniscalco1994, Reference Ulph1996), Nannerup (Reference Nannerup1998), and others.

4 See, for example, Dixit (Reference Dixit and Feenstra1988).

5 It is assumed that wage rates and other factor prices reflect social opportunity costs. Furthermore, the policy issues associated with factor market distortions are well understood (see Bovenberg and Mooij, Reference Bovenberg and de Mooij1994; Bovenberg and van der Ploeg, Reference Bovenberg and van der Ploeg1994; Corden, Reference Corden1997), and do not need further treatment here.

6 We assume that the pollution damage resulting from domestic emissions does not affect the relative attractiveness of the goods. Formally, the representative consumer's maximization problem can be expressed as: maximize U = (x, y, z, e)= u(x, y) + z − d(e), where z, the numeraire, represents the consumption of all other goods in the economy and d(e) the pollution damage, subject to his budget constraint.

7 It should be noted that there is no difference between $\frac{{\partial P^x }}{{\partial x^j }}$ and $\frac{{\partial P^x }}{{\partial x}}$ when we work on the demand side of the market.

8 The aggregate cost function C(x, a) is defined as the ∑j Cj (xj ,aj), or nCj(xj, aj) given the assumption of symmetry. Then, from the first-order necessary and sufficient condition for the minimization of costs, we have that Cix = Cjx and that Cia = Cja for all i and j, which implies that Cx = Cjx and that Ca = Cja for any j. The same procedure applies to ej(xj, aj).

9 Decreasing marginal costs introduce problems for the sign of the comparative static results only if the degree of decreasing costs (as measured by the second derivative of the cost function) is ‘sufficiently large’ (Tirole, Reference Tirole1988). It can easily be seen that under independent processes and increasing marginal costs $\frac{{\partial x}}{{\partial \tau }} < 0$.

10 It should be noted that for developing countries, as they do not generate technological change, such expenditures should be associated with the licensing of some international patent.

11 Note that our assumption of symmetry on production rules out the possibility of spillovers in innovation at the firm level.

12 We assume that there are a large number of potential technologies, so many that the technological space can be represented as continuous.

13 Note that Cxa = Cax and exa = eax for the theorem on the second-order cross partial derivatives.

14 See, for example, Porter (Reference Porter1990) and Porter and van der Linde (Reference Porter and van der Linde1995) for a discussion of win–win situations.

References

Barrett, S. (1994), ‘Strategic environmental policy and international trade’, Journal of Public Economics 54: 325–338.CrossRefGoogle Scholar
Bovenberg, A.L. and de Mooij, R.A. (1994), ‘Environmental taxation and labor market distortions’, European Journal of Political Economy 10: 655–683.CrossRefGoogle Scholar
Bovenberg, A.L. and van der Ploeg, F. (1994), ‘Environmental policy, public finance, and the labour market in second-best world’, Journal of Public Economics 55: 349–370.CrossRefGoogle Scholar
Conrad, K. (1993), ‘Taxes and subsidies for pollution-intensive industries as trade policy’, Journal of Environmental Economics and Management 25: 121–135.CrossRefGoogle Scholar
Corden, W. (1997), Trade Policy and Economic Welfare, 2nd edn, Oxford: Clarendon Press.CrossRefGoogle Scholar
Dixit, A.K. (1988), ‘Optimal trade and industrial policies for the U.S. automobile industry’, in Feenstra, R. (ed.), Empirical Methods for International Trade, Cambridge, MA: The MIT Press.Google Scholar
Kennedy, P.W. (1994), ‘Equilibrium pollution taxes in open economies with imperfect competition’, Journal of Environmental Economics and Management 27: 49–63.CrossRefGoogle Scholar
Nannerup, N. (1998), ‘Strategic environmental policy under incomplete information’, Environmental and Resource Economics 11: 61–78.CrossRefGoogle Scholar
Porter, M. (1990), ‘The Competitive Advantage of the Nations’, New York: Free Press.CrossRefGoogle Scholar
Porter, M. and van der Linde, C. (1995), ‘Toward a new conception of the environment-competitiveness relationship’, Journal of Economic Perspectives 9: 97–118.CrossRefGoogle Scholar
Simpson, D.R. and Bradford, R.L. (1996), ‘Taxing variable cost: environmental regulation as industrial policy’, Journal of Environmental Economics and Management 30: 282–300.CrossRefGoogle Scholar
Tirole, J. (1988), The Theory of Industrial Organization, Cambridge, MA: The MIT Press.Google Scholar
Ulph, A. (1994), ‘Environmental policy, plant location and government protection’, in Carraro, C. and Siniscalco, D. (eds), Trade, Innovation, Environment, Dordrecht: Kluwer.Google Scholar
Ulph, A. (1996), ‘Environmental policy and international trade when governments and producers act strategically’, Journal of Environmental Economics and Management 30: 256–281.CrossRefGoogle Scholar