1. Introduction

Two significant trends in the international trade arena and some outstanding strategic trade reforms followed by several advanced and emerging countries have shaped nowadays international trade’s architecture and its dynamism.

On the one hand, since the end of the Second World War, countries have engaged in major global trade negotiations that in subsequent trade rounds have resumed under the Doha Round, promoting under the most favored nation principle (MFN), several reductions on multilateral taxes and subsidies.

On the other hand, episodes of high volatility observed in the international financial markets associated with an unfavorable evolution of financial and economic conjunctural indicators, have had significant spillover effects on the pace of expansion of international trade. To compensate for fluctuations in trade flows, policy makers have managed trade protection granting in some cases, even more safety, than otherwise it would have been observed, if strategic protection could have been acknowledged as a result of a non-cooperative equilibrium among trade partners.

In this context, however, it is not sufficiently clear if the extra protection granted based on less dynamic international trade flows is more distortionary than that awarded in episodes of a significant pace of expansion of the global economic activity. The former argument calls for a counter-cyclical protectionism, while the latter argument, calls for a pro-cyclical protectionism, both forms being well known by their welfare-loss consequences.¹

The effects of protectionism on welfare must be analyzed in the light of the number of strategic trade reforms we have witnessed during the last two decades that in general have taken two broad approaches: i) unilateral, bilateral or multilateral reforms, some of them yet to be implemented; and ii) second and even third best reforms to partially correct trade distortions or some other externalities in production and consumption in specific sectors.

In this paper, I present a duopolistic competition model where a domestic and a foreign firm compete in the domestic market with homogeneous products and differentiated production technologies. The domestic firm has a pollutant technology, while the foreign firm is assumed to have an environmental-friendly technology. In this context, I design a mechanism that provides incentives for the domestic firm to adopt a cleaner technology with the aim to reduce domestic pollution. In doing so, I investigate if administered protection, as a trade policy, partially corrects the production externality in a second-best fashion, where the domestic government has a limited commitment to provide the proposed administered protection, and if domestic firms are willing to adopt the cleaner technology in the absence of an explicit environmental policy designed with a first best approach. I analyze this assumption finding that there is an optimal trade tax that credibly provides incentives for domestic firms to adopt the cleaner technology of production. Though the administered protection clearly generates some welfare losses, the expected reduction of the production externality compensates these losses via welfare gains.²

In this context, I examine the theoretical relationship between administered trade through a trade tax and an environmental policy designed to adopt a cleaner technology in a polluted open economy with endogenous pollution levels, assuming that the government actually has a very limited commitment credibility. In so doing, I propose a three-stage game: i) during the first stage, the domestic firm decides whether to adopt or not the cleaner technology, ii) in the second stage the domestic government chooses the degree of administered trade protection, and iii) in the third stage domestic and foreign firms compete à la Cournot in the domestic market.

The basic insight of the model relies upon the fact that unless the government credibly threatens granting administered protection, the domestic firm would not adopt the cleaner technology. Therefore, the objective is twofold: on the one hand, the domestic government has a clear incentive to protect a cleaner firm, than to protect a pollutant one; and on the other hand, the firm would adopt the cleaner technology if it has enough confidence about the government’s commitment. In this context, a free trade policy would be unfavorable because it would provide no elements to make credible the government’s threat, whereas an autarky situation will not contribute to switch on the mechanism linking pollution and trade.

Following Regibeau and Gallegos (2004), Brander and Spencer (1985), Eaton and Grossman (1986), Dixit (1983) and Spencer and Brander (1983), this paper considers a duopolistic competition between firms combined with strategic interaction between domestic and foreign governments in imposing optimal trade and environmental policies. The distinction between the previous works on strategic interaction is that the model developed here, considers that the production of the final tradeable good generates certain amount of pollution, which is assumed to be proportional to the output levels; and it only harms consumers, not neighboring firms or countries. Therefore, no transboundary pollution is considered. In that sense, environmental authorities strategically design an optimal environmental policy to deal only with domestic pollution.

In a related paper, Ludema and Takeno (2007), propose a model where unilateral tariffs are designed to induce foreign firms to adopt more environmental-friendly technologies assuming there is a negative cross-border externality on production coming from the foreign country. Despite the non-environmental purpose of several international examples of this type of policy intervention, the implication is that unilateral tariffs can be partially effective environmental policies.³

As in Regibeau and Gallegos (2004), the model is analyzed formally in a two-country partial equilibrium framework. The emphasis is on the domestic market of one of the two countries. This market can be served by n domestic firms and 𝑚 foreign firms. Initially, I will take these numbers as exogenously determined, starting with 𝑛=1=𝑚. Later on, I will endogenize them. Domestic production creates an amount of pollution proportional to domestic output: the cleaner the technology, the lower these pollution levels will be. As foreign firms serve the market through exports, they do not generate any local pollution.

However, unlike Spencer and Brander (1983)), Brander and Spencer (1985) and Eaton and Grossman (1986), to analyze the strategic interaction between a credible threat and possible improvements in social welfare through commitments granted by the government, the timing of the granted protection is crucial. In this paper, I assume that the domestic government has a limited commitment. In so doing, I suppose that firms choose their output levels in the third stage as is usual, i.e., just after the government chooses its trade policy. The main difference is that I allow the domestic firm to choose the kind of technology before trade policies are set up.

In a three-stage model with no transboundary pollution, Xing (2006) examines the strategic effects that lenient environmental policies on exporting countries have on the design of environmental policies in importing countries, and finds that the strategic behavior of the exporting country leads to the application of optimal environmental tariffs on imports from countries with lax environmental regulations.⁴ Iida and Takeuchi (2011) propose a four-stage model to influence a domestic-polluting firm to adopt a cleaner technology of production from the foreign, depending on the concern the domestic country has on the environmental damage, if the domestic firm does not use the cleaner technology. Iida and Takeuchi (2011) propose that if the country cares about the environmental damage, a policy of free trade is better compared to a tariff policy with the aim to achieve the technological transfer: the cost of free trade is that there would be no tariff revenue, but the gain is a lower license fee to use the cleaner technology.

The plan of this paper is the following. In the second section I develop a duopolistic model with two firms competing in the domestic market with a homogeneous product. The domestic country faces domestic pollution and chooses the mechanism to credible threaten its limited commitment to protect cleaner production technologies. In the third section, the model is extended to include 𝑛 domestic and 𝑚 foreign firms to determine endogenously the optimal number of adopting firms. In the fourth section I present the main conclusions and some comments on further research.

2. The Model

The framework for the analysis I build consists on a domestic country assumed to be a small open economy and a net importer of the final homogenous good initially produced by two firms competing each other in a Cournot-Nash fashion only in the domestic country. The domestic firm produces the homogeneous good with a pollutant technology whereas the foreign firm already produces it with an environment-friendly technology. Because the domestic country faces domestic pollution, only the domestic government is assumed to choose the mechanism to credibly threaten its commitment to protect cleaner production technologies. This is done by maximizing a social welfare function that accounts for the effects of the trade tax on the consumer surplus, the benefits of the domestic firms, plus the tax revenue net of pollution costs.

The domestic country is assumed to consume the final good and initially, is modelled using a general specification for the inverse demand function P=Q, where

The foreign firm’s export-oriented production, constitutes the domestic country’s imports. Trade policy takes the form of a specific trade tax (t). The home country is the only one with an active trade policy. The case for one domestic firm competing with one foreign firm will show some of the basic insights of this model. Later, a more general case where n domestic and m foreign firms interact with each other, will be shown. The home firm is indexed as firm 1, while the foreign firm is indexed as firm 2. The foreign firm does not pollute in the domestic country, because no transboundary pollution is considered. In this context, the “polluting” technology generates local pollution, while the “clean” technology does not.

A continuum of technology adoption decisions is available, so that I index the adoption choice. A technology adoption choice θ is associated with each point on the interval [0, 1]. Two benchmark cases can be characterized: a firm that does not adopt the cleaner technology, and a firm that does adopt the cleaner technology.⁶ Therefore, the social welfare cost of pollution is directly proportional to local output in the domestic country. In this context, the credible threat that the government makes, influences the decision the domestic firm takes to fully or partially adopt the cleaner technology, or not adopt at all.

As previously mentioned, the parameter θ belongs to the interval [0, 1]. If the domestic firm fully adopts the cleaner technology θ=0, and pollution emissions are

I also assume that the home firm is initially endowed with the pollutant technology but it can adopt the cleaner technology at a fixed cost F. Likewise, I assume that the choice of technology does not affect the marginal costs of production.⁸

In this context, the home country’s government is free to set its tariff at any level it wishes, whereas the domestic firm must decide whether to keep its current polluting technology or to adopt the new cleaner one at a cost F, in the first stage. In the second stage the domestic government decides the level of protection to grant through a specific trade tax t. In the third stage firms simultaneously choose their output levels in a Cournot-Nash fashion. Once the game is set up, it is solved for its unique sub-game perfect equilibrium.⁹

3. Third Stage: firms compete à la Cournot

Like in the general case, I assume that all domestic firms are symmetric and the choice of technology does not affect marginal costs. In fact, without loss of generality, I will assume that the marginal costs are constant and equal to zero for the sake of simplicity. Additionally, I will assume a specific inverse demand function of the linear type where P (Q) = a - bQ, where a = 1 =b. Then, the profit functions of every representative firm take the following form: Domestic representative adopting firm:

Foreign representative firm:

where the specific inverse demand function is:

Again, at this stage of the game, conjectures are of the Cournot type. In order to get the reaction functions, I solve for the first order conditions considering that domestic and foreign firms are symmetric.²² Then for the non-pollutant domestic firms and after solving simultaneously the reaction functions I obtain the output levels in equilibrium for each type of firm:

It is clear from eqs. (26), (27) and (28) that the effect of the trade tax in each of the output levels affects positively the output of domestic firms and negatively the output of the foreign firm.²³ With this information, I obtain:

Similarly, substituting those output values in each profit function we have for the non-pollutant domestic firm:

for the pollutant domestic firm:

and for the foreign representative firm:

3.1 Second stage: optimal trade tax

At this stage of the game, government chooses the optimal trade tax maximizing a social welfare function that includes, as is usual, the consumer surplus, profits of the domestic firms, the trade tax revenue and the costs associated with pollution emissions. It is important to recall that if domestic firms adopt the cleaner technology, it has been assumed that pollution emissions are reduced to zero, i.e., θq_i = 0 for any i = 1,…, δ. Then the social welfare function takes the following functional form:

[Formula ID: e40]

<mml:mi>W</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>θ</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:msub> <mml:mrow> <mml:mo>∫</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> </mml:msup> <mml:mi>P</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> </mml:mfenced> <mml:mi>d</mml:mi> <mml:mi>Q</mml:mi> <mml:mo>-</mml:mo> <mml:mi>P</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> </mml:mfenced> <mml:mi>Q</mml:mi> <mml:mo>+</mml:mo> <mml:mi>δ</mml:mi> <mml:msub> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>+</mml:mo> <mml:mfenced> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mi>δ</mml:mi> </mml:mrow> </mml:mfenced> <mml:msub> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>j</mml:mi> </mml:mrow> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>+</mml:mo> <mml:mi>t</mml:mi> <mml:mi>m</mml:mi> <mml:msub> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> <mml:mo>-</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mi>δ</mml:mi> <mml:mo>)</mml:mo> <mml:msup> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> </mml:msup>

(34).

After totally differentiating eq. (34) with respect to t for a given θ, i.e., Dw (t, θ) / dt = 0, we obtain:

[Formula ID: e41]

<mml:msup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> <mml:mi>p</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mo>(</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>-</mml:mo> <mml:mi>θ</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mi>δ</mml:mi> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>)</mml:mo>

(35).

Aiming at having an interior solution the degree of adoption must take the value

<mml:mi>θ</mml:mi> <mml:mo><</mml:mo> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mi>δ</mml:mi> <mml:mo>)</mml:mo> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo>

, which naturally occurs because

<mml:mi>θ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0,1</mml:mn> <mml:mo>]</mml:mo>

. Therefore, the optimal tax is clearly positive.

Proposition 3: The larger the number of adopting firms δ, the higher the level of the optimal trade tax will be.

Proof: By taking the partial derivative of the optimal trade tax with respect to parameter δ:

[Formula ID: e42]

<mml:mrow> <mml:mrow> <mml:mo>∂</mml:mo> <mml:msup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> <mml:mi>p</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:mo>∂</mml:mo> <mml:mi>δ</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mo>[</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>]</mml:mo> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo>

Proposition 4: The larger the number of not adopting firms (n - δ), the lower the level of the optimal trade tax will be.

Proof: By taking the partial derivative of the optimal trade tax with respect to parameter (n - δ):

[Formula ID: e43]

<mml:mrow> <mml:mrow> <mml:mo>∂</mml:mo> <mml:msup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>o</mml:mi> <mml:mi>p</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:mo>∂</mml:mo> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mi>δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mo>[</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>]</mml:mo> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo>

On the other hand, comparing the domestic firm’s incentives to invest in the non-polluting technology, any single domestic firm compares the net benefit of full adoption versus not adopting at all the cleaner technology:

[Formula ID: e44]

<mml:msub> <mml:mrow> <mml:mi>Φ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>-</mml:mo> <mml:msub> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>≥</mml:mo> <mml:mi>F</mml:mi> <mml:mo>,</mml:mo> <mml:mi> </mml:mi> <mml:mi>f</mml:mi> <mml:mi>o</mml:mi> <mml:mi>r</mml:mi> <mml:mi> </mml:mi> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> <mml:mi>y</mml:mi> <mml:mi> </mml:mi> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi> </mml:mi> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi> </mml:mi> <mml:mi>n</mml:mi> <mml:mo>.</mml:mo>

(36).

Therefore, when comparing this private benefit with the sunk cost F, there is a threshold for adoption: the lower the sunk cost F is, the higher the degree of adoption the domestic firm will take. Naturally, the i-th firm will invest in the cleaner technology if and only if

<mml:mi>F</mml:mi> <mml:mo><</mml:mo> <mml:msub> <mml:mrow> <mml:mi>∅</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo>

Comparing the change in the domestic welfare net of the net producer surplus from adopting versus not adopting the cleaner technology:

[Formula ID: e45]

<mml:mo>∆</mml:mo> <mml:mi>W</mml:mi> <mml:mo>-</mml:mo> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Φ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>-</mml:mo> <mml:mi>F</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mi>Δ</mml:mi> <mml:mi>C</mml:mi> <mml:mi>S</mml:mi> <mml:mo>+</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mi>R</mml:mi> <mml:mo>-</mml:mo> <mml:mi>P</mml:mi> <mml:mi>C</mml:mi> <mml:mo>)</mml:mo>

(37).

Equation (37) for the specific case where n = 1 = m allows us to see the expected result:

[Formula ID: e46]

<mml:mi>Δ</mml:mi> <mml:mi>W</mml:mi> <mml:mo>-</mml:mo> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Φ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>-</mml:mo> <mml:mi>F</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mn>7</mml:mn> <mml:mi>θ</mml:mi> <mml:mo>(</mml:mo> <mml:mn>8</mml:mn> <mml:mo>-</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mn>162</mml:mn>

(38).

which is no negative given that

<mml:mi>θ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0,1</mml:mn> <mml:mo>]</mml:mo>

.

Proposition 5: Private incentives are insufficient to adopt the cleaner technology from the point of view of the domestic welfare, specifically when the sunk cost of adoption F lies in the range

<mml:mo>(</mml:mo> <mml:mi>Φ</mml:mi> <mml:mi>i</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Δ</mml:mi> <mml:mi>W</mml:mi> <mml:mo>)</mml:mo>

for a given ϑ.

[Figure ID: ch1]

Social Benefits.

Finally, assuming free entry to get the endogenous number of adopting firms, I analyze the benefits of any adopting firm net of sunk costs for a given indexed value of θ, when benefits for this firm are equal to zero to get the maximum number of adopting firms, i.e.,

[Formula ID: e47]

<mml:msub> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mfenced> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>-</mml:mo> <mml:mi>θ</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mi>δ</mml:mi> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:mfenced> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>-</mml:mo> <mml:mi>F</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi> </mml:mi> <mml:mi> </mml:mi> <mml:mi>f</mml:mi> <mml:mi>o</mml:mi> <mml:mi>r</mml:mi> <mml:mi> </mml:mi> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> <mml:mi>y</mml:mi> <mml:mi> </mml:mi> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1,2</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi>δ</mml:mi> <mml:mo>.</mml:mo>

(39).

which implies that the number of adopting firms obtained is:

[Formula ID: e48]

<mml:mi>δ</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> <mml:msqrt> <mml:mi>F</mml:mi> </mml:msqrt> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>-</mml:mo> <mml:mi>m</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mi>θ</mml:mi> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> <mml:mo>)</mml:mo> <mml:mo>/</mml:mo> <mml:mi>θ</mml:mi> <mml:mi>m</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> <mml:mo>,</mml:mo> <mml:mi> </mml:mi> <mml:mi>f</mml:mi> <mml:mi>o</mml:mi> <mml:mi>r</mml:mi> <mml:mi> </mml:mi> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> <mml:mi>y</mml:mi> <mml:mi> </mml:mi> <mml:mi>θ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0,1</mml:mn> <mml:mo>)</mml:mo> <mml:mo>.</mml:mo>

(40).

4. Conclusion

The mechanism that allows domestic firms to adopt the cleaner technology, is strongly linked with the credibility that the limited commitment the domestic government sets up. The managed trade regime grants protection aiming at abating pollution from the production externality. In this context, liberalizing international trade could be counterproductive since a minimum rate of protection is needed to make that threat credible for the domestic producer to adopt, in certain degree, the cleaner technology, as long as the sunk cost F does not exceed the producer surplus.

Notably, even though the model can be thought of for a small open economy -as in this paper-, the tariff that is obtained from the managed trade protection regime in the presence of production externalities is different from zero, as is usual when modelling small open economies in a context of imperfect competition. Precisely, the government’s threat to be credible, requires a positive level of protection, otherwise, it would not be credible and the alleged managed protection will not have the expected adoption results. However, even in the case of a big open economy, the level of protection must be higher than that obtained from a non-cooperative solution as long as the domestic government needs to keep its limited commitment to grant extra protection to adopt the cleaner technology.

The domestic welfare behaves as expected when the domestic pollution parameter takes some values to favor interior solutions for the output levels and the specific trade tax. In those cases, it is clear that even though the effects of the managed protection are well known as distortionary, those are clearly compensated as long as the sunk costs do not exceed the gross benefits from adopting the cleaner technology. For the policy maker, to maintain credibility on the level of protection granted, is crucial to avoid negative effects that may exacerbate opening trade processes upon the environment: a free-trade policy could be counterproductive for the domestic firm to adopt, since the incentives to adopt are null.

This model clearly can be extended if I allow pollutant technologies of production in the foreign country, so that governments play a subgame simultaneously choosing the levels of protection, while firms play à la Cournot, being at the same time, followers whether adopting or not the cleaner technology through the protection granted in the second stage.