Trade policy reform, endogenous lobby group formation, and environmental policy

Journal of Economic Behavior & Organization Vol. 52 (2003) 47–69

Trade policy reform, endogenous lobby group formation, and environmental policy Richard Damania a , Per G. Fredriksson b,∗ b

a School of Economics, University of Adelaide, Adelaide, South Australia 5005, Australia Department of Economics, Southern Methodist University, P.O. Box 750496, Dallas, TX 75275-0496, USA

Received 30 May 2001; accepted 18 February 2002

Abstract This paper explores the effects of trade liberalization on environmental policy outcomes when collective action is endogenous. The polluting industry’s ability to undertake lobbying is shown to depend on the degree of competition in the product market, establishing a new link between trade and environmental policies. If trade liberalization causes industry collective action to become harder to sustain, the stringency of the environmental policy is likely to rise. These results highlight the role of trade liberalization on product market competition and its consequent impact on the incentive to lobby for less stringent environmental policies. © 2002 Elsevier Science B.V. All rights reserved. JEL classification: D78; Q28; F13 Keywords: Collective action; Lobbying; Political economy; Integration; Protectionism; Pollution tax

1. Introduction Following recent failed attempts to launch the “Millennium Round” of trade talks, a polarized discussion on the effects of open trade on environmental policy and quality has re-emerged. Proponents of free trade argue, for example, that it creates an economic surplus that can be used for environmental protection (see Nordström and Vaughan, 1999). Environmentalists fear, among other things, that further economic liberalization will create increased political pressures to reduce the stringency of environmental regulations in order to protect production and employment and this could lead to a “race to the bottom.” Given the deeply held views on both sides, further progress in multilateral trade negotiations may depend crucially on the ability to shed light on this issue. ∗ Corresponding author. Tel.: +1-214-768-3520; fax: +1-214-768-1821. E-mail address: [email protected] (P.G. Fredriksson).

0167-2681/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 2 6 8 1 ( 0 2 ) 0 0 1 9 4 - 4

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In this paper we study the effects of trade liberalization on environmental policy, explicitly taking into account the political pressures feared by many environmentalists. We focus upon a hitherto unexplored link between trade liberalization and environmental policies. In particular, we analyze the relationship between trade liberalization and a polluting industry’s ability to form a lobby group and sustain lobbying for favorable environmental policies. We find that changes in the ability of polluters to sustain lobbying as a result of trade policy reform have implications for environmental policy. The small but growing literature on the relationship between openness to trade and environmental protection has ignored this link (see, e.g. Copeland and Taylor, 1995; Antweiler et al., 2001).1 Predictions built on the assumption of exogenously organized producer lobby groups may be inaccurate, however. The political process should preferably be modeled in more detail, in our view.2 We believe our theory will be helpful in future empirical work in this area. Our model of political choice builds on Grossman and Helpman (1994), who use the common agency model by Bernheim and Whinston (1986). Grossman and Helpman model lobby groups that offer promises of political contributions in return for favorable trade policies. In their paper lobby groups represent the owners of sector-specific capital in sectors with perfect competition. Lobby group formation is exogenous, and considerations of imperfect market structures and collusion are absent from their model. Moreover, they abstract from the fixed costs associated with lobbying. In practice, lobby groups incur set-up costs such as maintaining offices and support staff, and hiring lawyers and lobbyists. These costs 1 See Schulze and Ursprung (2001) for a survey of this literature. Hillman and Ursprung (1994) study the relationship between environmental preferences and trade policy in a model of political competition. They show that the resulting trade policy depends on the nature of the negative externality from pollution (consumption or production) and whether the environmentalists’ preferences are defined over the global or only the domestic environment. Leidy and Hoekman (1994) explore the effects of environmental policy instruments associated with different degrees of inefficiency on trade policy determination. They find that polluting industries prefer inefficient environmental policy instruments because these increase the level of trade barriers. Rauscher (1994) provides a model of an open economy where the polluting export sector is found to have ambiguous lobbying incentives. Copeland and Taylor study the strategic interaction between rich and poor countries in the move from autarky to free trade, allowing for income-induced environmental policy responses. Fredriksson (1999) finds that in a perfectly competitive sector, trade liberalization reduces (increases) both industry and environmental lobby groups’ incentive to influence environmental policy if the country has a comparative disadvantage (advantage) in the polluting sector. Thus, the final policy effect depends on the relative shifts in political pressures. Bommer and Schulze (1999) show that environmental policy is tightened (relaxed) by trade liberalization if the exporting (import competing) sector is relatively pollution-intensive. See Heyes and Dijkstra (2001) for a survey of political economy models of environmental policy. 2 Olson’s (1965) seminal transaction cost theory of collective action argues that concentrated interests more easily form lobby groups. Empirically, the relationship between concentration and policy outcomes appears weaker than argued by Olson; see the survey by Potters and Sloof (1996). Note that Salamon and Siegfried (1977) report that larger industries are less successful in their political efforts. Moreover, they find a positive relationship between an industry’s ability to avoid taxes and firm size, but a negative relationship between political success and concentration. Pittman (1988) finds that the level of federal regulations significantly determines the level of campaign contributions, but only in concentrated industries. Zardkoohi (1985) finds no effect of concentration on political contributions, but a positive relationship between the interaction of concentration and the potential rents. This suggests that Olson’s description may be incomplete, since it fails to take account of the strategic incentives of firms in concentrated industries, in particular the ones with relatively high levels of collusion. Friedman (1971) shows that collective action can be sustained in infinitely repeated games, depending on the discount factor. Our theory does not build on this argument, although discounting is part of the model.

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are necessary to influence policymakers, but are largely unrelated to the environmental policy obtained and may be regarded as fixed costs associated with lobbying. Damania and Fredriksson (2000) show the importance of collusion for firms’ ability to organize lobbying on pollution tax policy issues in a closed economy. However, Damania and Fredriksson ignore the fixed costs associated with lobbying. We extend Grossman and Helpman and Damania and Fredriksson by introducing fixed lobbying costs into an open economy model with imperfect competition in the domestic market. It is shown that when firms incur fixed lobbying costs, lobbying is sustainable only if there is some degree of tacit collusion. This is because some of the benefits to lobbying are public, while the costs are private. Thus, each firm has an incentive to free ride on its rival’s contributions. Only if the losses from deviation (the loss of future collusive profits) are greater than the benefits (a one-time gain from deviations in lobbying and collusion) will firms sustain cooperation. We demonstrate that since trade reform affects the level of tacit collusion (competition), it will also effect environmental policy lobbying and thus environmental policy outcomes. We analyze a three-stage game. In the first stage, each duopoly firm decides whether to pay for the fixed costs associated with lobbying and offer the government a joint contribution schedule. If both firms decide that this is in their interest, an industry lobby group is organized. The lobby offers the government a contingent contribution schedule that mirrors the attractiveness of the pollution tax policy selected.3 In the second stage, the government selects the tax that maximizes its own payoff and collects the corresponding contribution.4 In the third stage, the two firms determine the optimal output levels, given the tax rate that materializes in the present period (due to the lobbying carried out in the previous period). The game is repeated over an infinite horizon, so that tacit collusion in both the lobbying and output stages may occur under certain circumstances. Firms use a trigger strategy to sustain cooperation. First, we find that the elasticity between the prices of the domestic and foreign goods is important for determining whether trade liberalization decreases the incentive for oligopoly firms to collude tacitly. Trade liberalization reduces tacit collusion if there is a sufficiently strong shift in demand towards the foreign good so that the more intense competition compels the domestic producers to lower their price. Second, we show that if the elasticity between the domestic and foreign substitute prices is sufficiently high, trade liberalization reduces the firms’ incentive to contribute to pollution tax lobbying. The intuition is that when demand for the domestic good is responsive to the tariff, the degree of collusion decreases as a result of trade reform, and profits fall. The opportunity cost of free riding on the competitors’ lobbying effort therefore diminishes. In this case, both collusion and the firms’ incentive to undertake lobbying consequently decrease with trade liberalization. Third, it follows that trade liberalization raises the pollution tax if the elasticity between the domestic and foreign substitute prices is sufficiently high. The pollution tax rises if 3 A contribution schedule offered by one firm alone is not considered equivalent to lobby group formation in this paper. 4 This tax rate is not implemented until the subsequent period (i.e. the lobby faces a lag of one period from the time of its lobbying effort to the time of benefit). This reflects the delay caused (in practice) by administrative procedures, legislative processes, and other lags from the time it takes to gather information and lobby to when the final decisions are made and implemented by policy makers.

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trade liberalization reduces collusion sufficiently because this causes a decline in lobbying intensity. To our knowledge, these three results are new contributions to the literature. A policy conclusion that emerges is that trade liberalization is more likely to increase the stringency of environmental policy when foreign and domestic goods are close substitutes. This is more likely to occur when economic integration occurs between countries of similar economic structure and development, such that the quality difference between the rival goods is small (see Bloningen and Wilson, 1999). Thus, contrary to the fears expressed by some critics of free trade (see, e.g. Daly and Cobb, 1989), intense foreign competition may make lobbying more difficult and therefore result in more stringent environmental regulations. On the other hand, in the case when the goods are not close substitutes, the theory points to the need to undertake other competition enhancing reforms simultaneously with trade reform (to increase the intensity of product market competition). This could mitigate the negative effects of lobbying on environmental policy. The paper is organized as follows. Section 2 describes the model and analyzes the effect of a tariff on collusion. Section 3 discusses the political equilibrium, and Section 4 explores the incentive to form a lobby group. Section 5 analyzes the effect of trade liberalization on environmental policy, taking into consideration the collective action problems associated with lobbying. Section 6 concludes. Appendix A contains the proofs of two lemmas, and Appendix B shows that our results hold also if an environmental lobby group is organized.

2. The output market A small open economy has two sectors. A perfectly competitive numeraire sector produces good z, with a domestic and world market price normalized to unity. An import competing duopoly faces a perfectly competitive world market, where the foreign and domestically produced goods are imperfect substitutes. The duopoly may be sustainable even with free trade due to the role of product, industry, political, and “home bias” factors (see Bloningen and Wilson, 1999). Let Q denote the output of the domestic duopoly good, with price p, and let Q∗ denote the foreign substitutes with world market price p∗ . The domestic duopoly firms are protected by an exogenous tariff τ, implying that the foreign substitute is sold on the domestic market at a price P = (1 + τ)p∗ . All agents in this country take the tariff rate as given as this small country has only a negligible impact on multilateral trade negotiations.5 The domestic good is produced under constant returns to scale using labor and a sectorspecific input. Each unit of domestic production involves local pollution emissions at a rate θ. Total local emissions are consequently given by E = θQ. All consumers are adversely affected by pollution damage, and the aggregate damage function is defined as D(E), with ∂D/∂E > 0, and ∂2 D/∂E2 > 0. Consumers are assumed to disregard the effects of their 5 We thus abstract from the determination of the tariff rate in this paper. As pointed out by Ederington (2000), the success of GATT negotiations in lowering tariff barriers worldwide has resulted in a shift in attention towards the use of domestic policies as secondary trade barriers. Ederington (2000) and Conconi and Perroni (2001) discuss the formation of multi-dimensional international agreements. At the very minimum, it appears fair to conclude that WTO membership severely restricts trade policy choice, in particular in small countries. Moreover, few pollutants are determined by international agreements.

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own consumption on pollution emissions.6 The utility of the representative consumer is given by7 U = z + u(Q, Q∗ ) − D(E),

(1)

where u(Q, Q∗ ) is a twice differential concave subutility function. As shown by Singh and Vives (1984), this formulation of the utility function yields demand for the domestic and foreign goods, respectively, as Q = Q(p, P) and Q∗ = Q∗ (P, p), where we assume ∂Q/∂p < 0, ∂Q/∂P > 0, ∂Q∗ /∂P < 0, and ∂Q∗ /∂p > 0. The inverse demand functions are given by p = p(Q, P) and P = P(Q∗ , p), where we assume ∂p/∂P > 0. Consumers are assumed to have an exogenous labor income. The government is assumed to tax emissions at a rate t ∈ T ⊂ R+ , and the pollution tax is determined without interference from foreign influences. In addition, firms have access to a pollution abatement technology, and per unit emissions are a function of the level of abatement A per unit of output, such that θ = θ(A), ∂θ/∂A < 0, ∂2 θ/∂A2 ≥ 0.8 The government may be persuaded by the firm lobby group to set a more favorable pollution tax in return for a political contribution, as discussed below. The owners of the firms, assumed to be a negligible part of the population, are unaffected by pollution. Thus, their aggregate utility function equals the firm’s profit function. The firms have constant marginal production costs. Taking the pollution tax and contribution schedules as given, the profits of domestic firm i, i = 1, 2, are defined as πi = [p(Q, P) − tθ(A) − v − c(A)]qi − Si (t)i ,

(2)

where qi denotes output of firm i, with Q = qi + qj ; v is the constant production costs, c(A) the abatement costs with ∂c/∂A > 0, ∂2 c/∂A2 ≥ 0, Si (t) = si (t) + Fi , where si (t) is firm i’s contribution paid to the government contingent on the tax rate t, and Fi represents firm i’s contribution to the fixed costs of lobbying.9 The fixed costs are associated with organizing lobbying activities such as setting up an office with support staff, travelling to meetings with government officials, or hiring lobbyists who carry out the lobbying activities for the firms. An active lobby requires Si (t) > Fi , ∀i, i = 1, 2 (i.e. the fixed costs are covered, and both firms offer the government prospective funds). Define the sum of consumer surplus from consumption of the non-numeraire goods, tax and tariff revenues, and pollution damage as10


Q

W CONS (t) ≡ 0




Q∗

p(χ, P) dχ − p(Q, P)Q +

P(χ∗ , p) dχ∗

0

−(P(Q∗ , p) − τp∗ )Q∗ + tθQ − D(E).

(3.1)

6 This assumption implies that each consumer is small in the sense that the consumption activities of each has a negligible impact on total pollution levels. 7 For a similar specification of a model with a numeraire sector and a duopoly/oligopoly facing foreign competition, see Brander and Spencer (1992). 8 The properties of the abatement technology specified here closely follows that which is widely used in the literature (e.g. Conrad, 1993). 9 Lobby group formation is discussed in more detail below. 10 In this formulation there is no consumer surplus from consumption of the numeraire good (see Grossman and Helpman, 1994).

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The net effects of the pollution tax on consumer surplus, pollution tax and tariff revenues, and aggregate pollution damage are given by −

∂p ∂Q Q, ∂Q ∂t

θQ + tQ

∂Q∗ ∂p ∂Q ∂Q ∂θ ∂A + tθ + τp∗ , ∂A ∂t ∂t ∂p ∂Q ∂t

and θ

∂D ∂θ ∂A ∂D ∂Q +Q , ∂E ∂t ∂E ∂A ∂t

respectively. The direct effect on consumer surplus from consumption of the domestic good is negative, as the tax raises the price. The direct effect of the tax on consumer surplus from consumption of the foreign good is zero since its price is exogenous. The effect on aggregate revenues is ambiguous, but damage unambiguously declines. Aggregate social welfare gross-of-contributions is given by the sum of expression (3.1) and gross-of-contributions profits, ˜ W(t) ≡ W CONS (t) + π,

(3.2)

where π˜ = π˜ i + π˜ j , and π˜ i = πi + Si (t). In a one-shot game, output levels are defined by the Cournot–Nash equilibrium which is denoted as qin ∈ arg max πi . From the profit function in (2), the first-order condition is given by ∂p ∂πi = qi + p − v − tθ(A) − c(A) = 0. ∂qi ∂qi

(4.1)

Let qin = qjn = qn be the solution to Eq. (4.1). Similarly, equilibrium abatement levels are given by the solution to the first-order condition ∂θ(A) ∂c(A) ∂πi = −t − = 0. ∂A ∂A ∂A

(4.2)

Let A(t) be the solution to (4.2). Observe that the per unit equilibrium abatement level depends on the tax rate but is independent of the output level. Thus, equilibrium emissions are given by Ei = θ(A(t))qi .11 It is assumed that the firms interact over an indefinite period of time. It is well established that under certain conditions, this provides an incentive to collude tacitly.12 Such collusion, however, gives rise to the familiar problem that each firm has an incentive to defect, given that its rival sets some collusive output level. More specifically, let qjc denote some collusive output level set by firm j. Then the defection output level of its rival i, qid , is determined by qid = arg max πid ≡ (p(qid , qjc ) − v − tθ(A) − c(A))qid − Si (t), 11 12

For notational simplicity we do not explicitly state the arguments of A in what follows. In the case of >2 firms, collusive behavior would become less stable.

(5)

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53

where qid is firm i’s defection output level. The first superscript will hereafter apply to the output stage (and the second to the lobbying stage, as discussed below). The first-order condition of Eq. (5) equals ∂πid ∂qid

= p qid + p − v − tθ(A) − c(A) = 0.

(6)

Defection can be prevented if firms adopt a credible and severe threat of punishment. In what follows it is assumed that firms employ the familiar “grim trigger strategy” to deter defection.13 This strategy serves to deter defections if the following incentive compatibility constraint is satisfied: πid (qid , qjc , τ, t, Fi ) − πic (qic , qjc , τ, t, Fi ) ≤

πic (qic , qjc , τ, t, Fi ) − πin (qin , qjn , τ, t) r

,

(7)

where r is the discount rate, πin (qin , qjn , τ, t) are profits of firms i = 1, 2 at the Cournot–Nash equilibrium output level (qin , qjn ), and πic (qic , qjc , τ, t, Fi ) are collusive profits of firms i = 1, 2. We assume that capital markets are perfect and that the firms have free access to international capital markets. Thus, the discount rate is fixed in this small economy. When Eq. (7) is satisfied, firm i has no incentive to deviate from the collusive output level, qic , given τ and t. In determining its own tacitly collusive output level each firm must consider the impact of its production decision on its rival’s incentive compatibility constraint. More specifically, this requires that firm i’s collusive output levels are determined by the solution to the constrained maximization problem max πc (qic , qjc , τ, t, F) ≡ πic (qic , qjc , τ, t, Fi ) + πjc (qic , qjc , τ, t, Fj ), c qi

(8.1)

such that Ωj ≡ πjd (qjd , qic , τ, t, Fj ) − πjc (qjc , qic , τ, t, Fj ) −

πjc (qjc , qic , τ, t, Fj ) − πjn (qjn , qin , τ, t) r

≤ 0.

(8.2)

Thus, each firm chooses collusive output levels to maximize joint profits subject to the constraint that its rival does not deviate from the collusive path. If constraint (8.2) does not bind, the monopoly output level can be sustained. This is defined by the solution to qM = qiM = qjM ∈ arg max[πic (qic , qjc , τ, t, Fi ) + πjc (qic , qjc , τ, t, Fj )].

(9)

When constraint (8.2) binds there is constrained collusion with output in the interval qic ∈ (qM , qn ). Suppose the constraint (8.2) binds at some output level qic . 13 Specifically, both firms abide by the tacit agreement and produce at some collusive output level as long as there is no defection. However, if a firm defects, its rival immediately reverts to the Cournot–Nash equilibrium output level denoted qin so that the collusive agreement is dissolved.

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Lemma 1. An increase in firm j’s output lowers its rival’s incentive to defect: (dΩi /dqjc ) < 0. Lemma 1 reveals that when firm j’s collusive output level increases, both the rival’s incentive to defect and its collusive profits decrease. However, the profits obtained by the rival from defection decline more rapidly than its profits from collusion. There is therefore less incentive to defect. This implies that a firm may influence its rival’s incentive to collude tacitly by changing its own output level. It follows that when a firm determines its collusive output level, it must take into account the impact of its production decisions on its rival’s incentive to defect.14 As is well known, the properties of the resulting equilibrium depend critically upon the prevailing discount rate. Accordingly, rearranging constraint (8.2) we define a threshold discount rate: πic (qic , qjc , τ, t, Fi ) − πin (qin , qjn , τ, t) rq ≡ d c d , (8.2 ) πi (qi , qj , τ, t, Fi ) − πic (qic , qjc , τ, t, Fi ) where t is the pollution tax determined by lobbying. Let r be the prevailing discount rate. There are three distinct possible cases, but we focus on r = rq since we wish to investigate the impact of marginal changes in collusion on equilibrium protection levels and lobbying.15 In this case, constraint (8.2) holds with equality, implying that we have constrained collusion. Output levels are determined by the solution to the incentive compatibility constraint, a “balanced temptation equilibrium” (Friedman) in which the industry is neither as collusive as in the joint profit maximizing outcome, nor as competitive as in the Cournot–Nash equilibrium. For future reference, we begin by deriving the effect of a change in the tariff on profits. Differentiation of Eq. (2) yields   dπi ∂p ∂πi ∂qi = p∗ + qi . (10) dτ ∂qi ∂P ∂P The first term on the right-hand side of Eq. (10) summarizes the collusive effects of the tariff, and the second term defines the impact of the tariff on domestic demand. When output is at the joint profit maximizing level, qM , then by the Envelope Theorem, ∂πi (qiM )/∂qiM = 0. Since ∂p/∂P > 0, by assumption it follows that in this case dπi (qiM ) ∂p = p∗ qiM > 0. dτ ∂P

(11)

Note, however, that when constraint (8.2) binds, ∂πi (qi )/∂qi = 0. However, since qi ∈ (qiM , qid ), it follows that ∂πi (qi )/∂qi = p (Q)qi + p − t(A)θ − c(A) − v ≥ 0. Thus, Eq. (10) is unambiguously positive. Not unexpectedly, this implies that higher tariffs always result in increased collusive profits. However, whether an increase in the tariff induces greater 14

This explains the structure of the optimization problem in Eqs. (8.1) and (8.2). The other two cases have (i) r < rq and (ii) r > rq , ∀qi ∈ [qiM , qin ). In case (i) the incentive compatibility constraint (8.2) holds with slack, and collusive output levels are determined by unconstrained joint profit maximization. In this case each firm produces half the monopoly output level. In case (ii) the incentive compatibility constraint is violated and collusion is not sustainable. Hence, output levels are at the Cournot–Nash equilibrium. 15

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collusion depends critically upon the manner in which the tariff affects the payoffs from collusion relative to those from defection. Let pc = p(Qc ) where Qc = qic + qjc , pd = p(Qd ) where Qd = qid + qjc , and pn = p(Qn ) where Qn = qin + qjn . Moreover, define ηk ≡ (∂pk /∂P)(P/pk ), k = c, n, d as the cross-elasticity of inverse demand for the domestic good with respect to the foreign good under collusion, non-cooperation, and defection, respectively. Proposition 1 explores the effect of the tariff on the incentive to collude as defined by the incentive compatibility constraint (8.2). Proposition 1. Ceteris paribus, in a tacitly collusive equilibrium, trade liberalization reduces the domestic firms’ incentive to collude if the price elasticity of the domestic good with respect to the price of the foreign substitute is relatively greater under collusion than under non-cooperation and defection, such that   1 pn pd c η 1+ > ηn c + ηd c . r rp p Proof. Differentiating constraint (8.2) yields     d 1 ∂πin 1 dπic ∂Ωi ∗ ∂πi =p + − 1+ , ∂τ ∂P r ∂P r dP

(12)

where ∂P/∂τ = p∗ .16 From Eq. (11) we know that at a given collusive output level, ∂πik ∂pk = p∗ qik , ∂τ ∂P

(11 )

for k = c, d, n.

Substituting Eq. (11 ) into Eq. (12) yields     d qin ∂pn 1 c ∂pc ∂Ωi ∗ d ∂p = p qi + − 1+ qi . ∂τ ∂P r ∂P r ∂P

(13)

Note that by construction qin > qid > qic , thus pn (qin , P) < pd (qid , P) < pc (qic , P). Hence, a necessary condition for (13) to be negative is   ∂pd 1 ∂pn 1 ∂pc + < 1+ , (14) ∂P r ∂P r ∂P which can be rearranged into17   pn pd 1 c η 1+ > ηn c + ηd c . r rp p

䊐

(15)

16 The impact of τ on the equilibrium is determined as follows. First we determine the impact of an increase in τ on the incentive compatibility constraint (8.2) at a given collusive output level. Then by Lemma 1 the impact on collusive output levels can be determined. We thus follow the commonly established procedure in such supergame models (see, e.g. Shapiro, 1990). 17 It can be shown that condition (15) always holds if the inverse demand function is sufficiently convex in the price of the foreign good: ∂2 p/∂P 2 > −ηp[(1 − η)/P 2 ]. Such conditions are frequently encountered in models with strategic interactions (e.g. Brander and Spencer, 1992).

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A high elasticity between the domestic price and the foreign good price implies a high degree of substitutability between the domestic and foreign good. Thus, Proposition 1 reveals that trade liberalization reduces collusion if there is a sufficiently strong shift in demand towards the foreign good when domestic prices are relatively high (i.e. there is collusion). In this case, more intense competition compels the domestic producers to lower their price. On the other hand, a higher tariff will lead to greater collusion only if it induces a substantial increase in demand for the domestic good so that domestic price can be increased sufficiently.

3. Political equilibrium This section explores the effects of lobbying by firms on the political equilibrium pollution tax. The consumers are assumed unable to organize a lobby due to severe free riding problems and insufficient stake in the policy outcome (see Olson, 1965). However, in Appendix B we extend the analysis to incorporate an opposing lobby group. We now explicitly take the timing of lobbying into account. It is assumed that if the industry lobby is formed in period n, this yields benefits in the form of a lower tax only in the following period.18 Each firm offers the government a political contribution schedule sin (tn+1 ) in stage 1, where the second subscript denotes time in addition to the firm-specific notation introduced previously. The schedule offered in period n depends on the tax that the government implements in period n + 1.19 The aggregate political expenditures of the lobby group are defined as Sn (tn+1 , Fn ) = [sin (tn+1 ) + Fin ] + [sjn (tn+1 ) + Fjn ].

(16)

The part of lobby group expenditures transferred to the government is contingent on the tax chosen by the government.20 Note also that the tax policy is not implemented until the beginning of the next period. Given knowledge of the contribution schedule, the government selects its optimal tax policy and collects the associated contribution from the lobby. When selecting the tax policy, the government is assumed to maximize a weighed sum of the aggregate political contributions (received in period n) and aggregate social welfare gross-of-contributions (from period n + 1). In period n, the government’s objective function is thus given by  µ  Sn (tn+1 ) + µaW(tn+1 ) , Gn (tn+1 ) = (17) 1−µ where a is the weight given to aggregate social welfare relative to political contributions, and µ = 1/(1 + r) is the discount factor.21 For simplicity we assume (as is customary in 18

Subscript n refers to timing throughout the paper. The timing of the lobbying game is closely tied to the sequence of events in the output stage of the game, where a firm defects in period n and in that period collusion continues by the rival. With the timing as in our game, a firm defects on its lobbying contributions and in the defection period it continues to enjoy the lower tax t∗ . 20 The game is also applicable to a game between polluting firms and an independent regulatory authority, in which case the political contribution should be viewed as an outright bribe. 21 Contributions can be used for activities such as political advertising, whereas a greater average level of social welfare increases the probability of the government winning re-election in a (implicitly modeled) future election (see Grossman and Helpman, 1994). 19

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most supergame models) that the game is stationary, such that tn = tn+k , k = 1, 2, . . . , ∞. Without stationarity, the lobby group’s contribution schedules may vary between periods. As discussed by Bernheim and Whinston (1986) and Dixit et al. (1997), the following ∗ , t∗ } two necessary conditions yield a subgame perfect Nash equilibrium {Sin n+1 i=1,2 when 22 both firms offer the government political contribution schedules: µ ∗ tn+1 maximizes Gn (tn+1 ) = (CI) [S ∗ (tn+1 ) + µaWn+1 (tn+1 )] on T ; 1−µ n ∗ maximizes tn+1

c c πin+1 (Qn+1 , τ, tn+1 , Fin ) + πjn+1 (Qn+1 , τ, tn+1 , Fjn )

1+r

+Gn (tn+1 ) on T.

(CII)

Maximizing (CI) and (CII) and substituting appropriately reveals that in equilibrium the contribution schedule of the industry lobby group (when both firms participate in the lobbying process) satisfies c c ∗ ,F ) + π ∗ , F )] ˜ jn+1 [π˜ in+1 (Qn+1 , τ, tn+1 (Qn+1 , τ, tn+1 in in ∗ ∂tn+1

=

∗ ) ∂Sn∗ (tn+1 ∗ ∂tn+1

,

(18)

where π˜ ic ≡ (p(Q) − θt)qi are profits gross-of-contributions. Eq. (18) suggests that in equilibrium the change in the lobby group’s contribution equals the effect of the tax on the utility (profits) of the lobby group (i.e. the schedule is locally truthful). By substituting Eq. (18) into the first-order condition of (CI), the political equilibrium tax in a given period, tn∗ , is found to be the solution to ∂W(tn∗ ) ∂π(Q, τ, tn∗ , F) + α = 0, ∂tn∗ ∂tn∗

(19)

∗ in period n + 1, and we therefore drop where α ≡ µa. A similar condition holds for tn+1 the time subscripts from this point. Note that the equilibrium tax is necessarily lower than the welfare maximizing tax, defined as

t w ∈ arg maxW(t).

(20)

This is because the industry lobby’s effort to reduce the tax is unopposed in this model. Bernheim and Whinston (1986) and Grossman and Helpman (1994) extend the concept of local truthfulness to a contribution schedule that is globally truthful (i.e. a contribution schedule that accurately represents the preferences of the interest group at all policy points). The equilibrium contribution to the government (with one lobby group) is given by the difference between social welfare when the government sets the welfare maximizing tax tw , and the political equilibrium t∗ . Specifically, the necessary contribution to the government from the industry lobby group (or the one lobbying firm) is defined by ˜ = α[W(t w ) − W(t ∗ )]. S(t)

(21.1)

22 Condition (CI) states that the pollution tax must maximize the government’s discounted payoffs. In contrast, by (CII) the tax must also maximize the joint discounted payoffs of the firms and the government. If this condition is not satisfied, then the lobbyists will have an incentive to alter their contribution and capture more of the surplus.

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Observe that α[W(t w ) − W(t ∗ )] defines the utility loss to the government when the tax deviates from the welfare maximizing level. Thus, the contributions perfectly compensate the government for the welfare loss associated with the participation of the industry lobby group in the political process. The welfare loss is weighted by α in order to adjust for its importance in the government’s objective function. Moreover, it is clear that the lobby has no incentive to pay the government any more than is necessary to induce it to alter its policies. Hence, (21.1) must hold with equality. As noted above, in the present model we extend the analysis by Grossman and Helpman (1994) by assuming that there are fixed costs associated with lobbying. Thus, lobbying is feasible only if total industry contributions are sufficient to cover the fixed costs of lobbying, F, and compensate the government for the welfare loss of lobbying as defined in (21.1), such that S(t ∗ ) = α[W(t w ) − W(t ∗ )] + F.

(21.2)

Under symmetry, each firm i must contribute Si (t ∗ ) = S(t ∗ )/2 for lobbying to occur; in a symmetric equilibrium the firms are assumed to both offer identical funds for the purpose of covering the fixed costs and identical contribution schedules to the government (Si∗ (t ∗ ) = Sj∗ (t ∗ )).23 Having defined the optimal levels of industry contributions and lobbying expenditures, we now determine whether the firms have sufficient incentive to form a lobby.

4. The decision to form a lobby group Since firms are assumed to interact over an indefinite period, each firm’s decision to offer a contribution schedule and pay its share of the fixed cost at each point in time, specifically to participate in the activities of the lobby group, is influenced by its long-term profitability.24 We analyze the conditions under which it is rational for firms to participate in the lobbying process rather than to free ride. It is assumed that tacit collusion is sustainable in the output stage of the game so that output levels are given by the solution to the problem stated in (8.1) and (8.2). 4.1. The infinitely repeated lobbying game It is well known that greater levels of cooperation can be sustained in an infinitely repeated game framework. Accordingly, we explore whether the fixed costs of lobbying can be covered when firms interact over an infinite horizon. If contributions are to be increased beyond the finite period Nash equilibrium levels, then firms must adopt some credible strategy to sustain these higher contributions. As in the previous section, we consider the 23 Although the presence of fixed costs yields a declining lobbying cost per unit of resulting profit increase, when S(t) > F , the lobbying incentives do not increase due to the fixed costs. The aggregate contributions offered by the government are still globally truthful and determined by (21.1) (as in Grossman and Helpman, 1994). 24 As noted by a referee the effective discount rate used by agents may depend on the duration of the game. In what follows for brevity we do not explore this issue.

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possibility of deterring free riding on the fixed costs of lobbying by employing the familiar grim trigger strategy. Thus, it is assumed that each firm abides by a tacitly collusive strategy that requires it to contribute half the amount implied by Eq. (21.2) to the lobby group as long as its rival does not defect (i.e. free rides). If the rival deviates from this strategy, the firm immediately reverts to the one-shot Nash equilibrium. It can be shown that this implies that there is no lobbying, as the fixed costs of lobbying are not covered. In this case, the government sets tw to maximize social welfare. This strategy will serve to deter free riding if the following incentive compatibility constraint is satisfied: πicd (τ, t ∗ ) − πicc (τ, t ∗ , Fi ) ≤

πicc (τ, t ∗ , Fi ) − πicn (τ, t w ) , r

(22)

where πicd (τ, t ∗ ) ≡ (p(Qc (t ∗ ), τ, t ∗ ) − t ∗ θ(A) − c(A) − v)qic (t ∗ ) are the profits of firm i when it colludes in the output stage but free rides on its contributions, given that its rival contributes the full amount Sj∗ (t ∗ ), and πicc (τ, t ∗ , Fi ) = (p(Qc (t ∗ ), τ, t ∗ ) − t ∗ θ(A) − c(A) − v)qic (t ∗ )−si (t ∗ )−Fi are profits when both firms abide by the collusive agreement in both the output and lobbying stages by contributing symmetric amounts Si∗ and Sj∗ , respectively.25 Finally, πicn (t w ) = [p(Qc , τ, t w )−t w θ(A)−c(A)−v]qic (t w ) are profits when firm i colludes in the output stage, but there is no lobbying so that the tax equals the welfare maximizing level, tw . The left-hand side of constraint (22) defines the one period gains to firm j when it free rides on the lobbying costs in the present period, while the right-hand side defines the profits foregone because in the next period lobbying ends and the tax is set at tw . When constraint (22) is satisfied, contributing to the fixed costs of the lobby group is the individually rational strategy for each firm.26 We rearrange (22) to define a critical discount rate: rL ≡

πicc (τ, t ∗ , Fi ) − πicn (τ, t w ) πicd (τ, t ∗ ) − πicc (τ, t ∗ , Fi )

.

(22 )

Observe that from Eq. (22 ), the equilibrium contributions of Si∗ , i = 1, 2, i = j, can be sustained by this strategy if the prevailing discount rate r ≤ rL . Having defined the conditions necessary to make lobbying feasible in an infinitely repeated game, we now turn to the equilibrium properties and explore how trade policy influences the incentive to form a lobby group on environmental policy. We therefore begin by assuming that lobbying is feasible, which by Eq. (22 ) requires r ≤ rL . The properties of the resulting equilibria depend not only on the level of the prevailing discount rate but also on the relative positions of the critical levels rq and rL as defined in Eqs. (8.2 ) and (22 ), respectively. In what follows, we are interested in analyzing how the tariff, via changes in 25 Since the game is assumed stationary, time subscripts on π cc , π cd , and π cn can be ignored. The incentive compatibility constraint in (22) and the timing of events assumed are analogous to the usual case of output collusion between firms, where defection output is the same in each period; if a defection occurs in period n, the rivals hold output at the collusive level in the period in which a defection occurs. Thus, the defecting firm enjoys a one period gain from defection. Similarly, in this case, a firm which defects on its lobbying contributions at time n enjoys a one period gain of a lower tax in period n. 26 The incentive compatibility constraint (22) is based on the implicit assumption that tacit collusion in the output stage is feasible, even in the absence of lobbying. Altering this assumption would merely strengthen the results outlined below without altering the qualitative conclusions.

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the degree of collusion in the output market, affects the incentive to contribute to the lobby group. Hence, we focus only on those equilibria in which lobbying is feasible and there is constrained tacit collusion.27 This is equivalent to assuming that r = rq ≤ rL . Moreover, since we require symmetric contributions, if S < S ∗ there is no lobbying, the tax equals tw , and dt/dS = 0. 5. Trade liberalization and lobby group formation In this section, we explore the properties of the lobbying equilibria when there is constrained tacit collusion in the output market. From Proposition 1, we know that trade liberalization reduces the firms’ incentive to collude in the output market provided that the relative elasticity between the prices of the domestic and foreign goods is sufficiently high when there is tacit collusion. We determine whether the incentive to offer a contribution schedule with the purpose of gaining a favorable pollution tax is affected by variations in the tariff level. In order to do so, define   πcn (τ, t w ) 1 Ψi ≡ πicd (τ, t ∗ ) − πicc (τ, t ∗ , Fi ) 1 + + i (23) r r as the incentive compatibility constraint in the lobbying stage of the game. Proposition 2 states our result on the relationship between trade liberalization and lobby group formation. Proposition 2. In the political equilibrium, trade liberalization reduces the firms’ incentive to contribute to lobbying for a lower pollution tax (i.e. dΨi /dτ < 0) if the elasticity between the price of the domestic good and the price of the foreign substitute, ηpc P ≡ (∂pc /∂P)(P/pc ), is relatively great such that the following condition holds: ηpc P > ∆,

(24)

where [−((εpc qc + 1)pc − tθ(A) − c(A) − v)ε(qc /t)τ + (tθ(A) +εcA εAt c(A))εqc τ − (ε(pc /qc )τ + εpc qc εqc τ )pc εqc t ] , ∆= εq c t p ∗ τ and the elasticities in ∆ are defined as εhb ≡

∂h b , ∂b h

h, b = pc , qc , c, A, t, τ,

q c pc , . t qc

27 There are other equilibria in the model with lobbying where output is at the joint profit maximizing outcome (i.e. r ≤ rL and r < rq ). In this case, lobbying and tacit collusion in the output stage are sustainable. Since r < rq , the incentive compatibility constraint in Eq. (8.2) holds with slack, and output is at the joint profit maximizing level. For brevity this case is ignored since marginal variations in contributions have no effect on the degree of collusion in the output market when constraint (8.2) holds with slack (i.e. the joint profit maximizing outcome is sustainable). Finally, we could also have r ≤ rL and r > rq . From Eq. (22 ), lobbying is incentive compatible since r ≤ rL . However, since r > rq , tacit collusion in the output stage of the game cannot be sustained. Thus, output levels are set at the Cournot–Nash equilibrium. In this case, lobbying takes place even in the absence of tacit collusion in the output market.

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Proof. First, note that πicc (τ, t ∗ ) = πicd (t ∗ ) − Fi − si . Since we wish to evaluate how the incentive to contribute to lobbying changes with a lower tariff, we hold the contribution level constant when we evaluate how (23) changes with the tariff. We then determine how changes in the incentive compatibility constraint affect contributions.28 Let τ¯ > τ and define 1 Ψi (τ) = Fi + si − (πcc (τ, t ∗ ) − πcn (τ, t w )), r and 1 Ψi (¯τ ) = Fi + si − (πcc (¯τ , t ∗ ) − πcn (¯τ , t w )). r By assumption, t w > t ∗ . Note also that a decrease in τ increases the incentive to free ride if Ψi (¯τ ) < Ψi (τ). This implies πcc (τ, t ∗ ) − πcc (¯τ , t ∗ ) < πcn (τ, t w ) − πcn (¯τ , t w ) which in turn implies that πcn (¯τ , t w ) − πcc (¯τ , t ∗ ) < πcn (τ, t w ) − πcc (τ, t ∗ ). From Lemma A1 (see Appendix A) it follows that this inequality holds if ∂2 πc (τ, t) < 0. ∂t∂τ

(25)

To determine when condition (25) holds, differentiate (2) with respect to t, holding Si constant, which yields  c  c ∂πc ∂q ∂c(A) ∂A c ∂p c c q + p − tθ(A) − c(A) − v = − θ(A)qc − q. ∂t ∂qc ∂t ∂A ∂t Upon further differentiation, the cross-partial equals ∂2 π c = ∂t∂τ

 ∂2 pc c ∂pc ∂qc ∂pc ∗ ∂qc q + c + p ∂q∂τ ∂q ∂τ ∂P ∂t  c  2 c   ∂p c ∂ q ∂c(A) ∂A ∂qc c + q + p − tθ(A) − v − c(A) − θ+ , ∂qc ∂t∂τ ∂A ∂t ∂τ 

which after rearrangements implies that condition (24) must hold for (25) to hold. When condition (24) holds, a lower tariff reduces each firm’s incentive to contribute to the lobby group. 䊐 If the demand for the domestic good is highly responsive to the tariff (i.e. the price of the foreign good), then collusion in the output stage is less sustainable as a result of trade liberalization (see Proposition 1). Since the degree of collusion falls, profits are lower. The opportunity cost of free riding in the lobbying stage of the game therefore decreases, since firms now have less to lose by free riding on the rival firm’s lobbying effort (and not obtaining a more favorable pollution tax). Collusion, and the firms’ incentive to undertake lobbying for a lower pollution tax, consequently decrease with trade liberalization when 28

See Shapiro for other examples of this procedure.

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ηpc P is sufficiently high.29 It is instructive to describe expression ∆. The numerator of (24) indicates that the direct effect of a lower tariff, represented by ηpc P , should be large relative to the impact of the tariff on the sum of three elements: (i) the (negative of the) effect of the pollution tax on collusive profits (the first term in the numerator), (ii) the pollution tax burden and abatement costs (the second term in the numerator), and (iii) the (negative of the) indirect effect of the tariff on the collusive price via the change in quantity. The denominator suggests that partial effects (i) and (ii) are adjusted by the tax elasticity of supply. Corollary 1. In the political equilibrium, trade liberalization increases the pollution tax if the elasticity between the price of the domestic good and the foreign substitute, ηpc P ≡ (∂pc /∂P)(P/pc ), is relatively great, such that the following condition holds ηpc P > Θ,

(26)

where



 

 βε(Qc /t)τ − εQc τ εθA εAt θ ∂D +E ∂2 D + θ(1+r) 2 ∂E α ∂ D ∂E2  Θ =  Eθ ε c −ψτ − 2 Q τ c c ε ∂Q Q t ×

1+τ , pc τ

and the elasticities in Θ are defined as εhb ≡

∂h b , ∂b h

h, b = pc , Qc , t, τ,

Qc , t

and where ψ ≡ p∗ m[εQ∗ pc εpc Qc + τ(εpc Qc ε(Q∗ /pc )τ + εQ∗ pc ε(pc /Qc )τ )], β ≡ pc − c(A) − v − θ −

∂D + τεQ∗ pc εpc Qc m ∂E

εAt (εcA c(A) + εθA εDE D), t

and

m≡

Q∗ . Qc

Proof. From the government’s maximization problem given by condition (C1), at t∗ , ∂S(t ∗ ) α ∂W(t ∗ ) ∂G(t ∗ ) = + = 0. ∂t ∂t 1 + r ∂t

(27)

Totally differentiating and rearranging expression (27) yields dt ∗ ∂2 G/∂t∂τ =− 2 . dτ ∂ G/∂t 2

(28)

29 Gawande and Bandyopadhyay (2000) report a negative relationship between the cross-price elasticity of demand and the level of US non-tariff protection. Thus, a greater cross-price elasticity gives lower lobbying success in the area of US trade policy.

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Assuming a unique maximum, such that ∂2 G/∂t 2 < 0, it follows that the sign of (28) equals the sign of its numerator. To determine the sign of this expression, note that by local truthfulness, ∂π/∂t = ∂S/∂t. From the profit function we obtain ∂π/∂t = −θQc (t ∗ ), and thus ∂2 S ∂Qc (t ∗ ) = −θ . ∂t∂τ ∂τ

(29)

From the expression for aggregate social welfare (3.2) we find ∂W/∂t = β(∂Qc /∂t). Thus,

c  2 c ∂2 W ∂p ∂Q ∂ 2 Qc 2 ∂ D ∂Q = −θ + ψ + β ∂t∂τ ∂τ ∂t ∂t∂τ ∂E2 ∂τ   ∂Qc ∂θ ∂A ∂D ∂2 D − + θQc 2 . ∂τ ∂A ∂t ∂E ∂E

(30)

Substituting (29) and (30) into ∂2 G ∂2 S α ∂2 W = + , ∂t∂τ ∂t∂τ 1 + r ∂t∂τ and rearranging, noting that ∂pc ∂pc ∂P ∂pc ∗ = = p , ∂τ ∂P ∂τ ∂P yields (26).

䊐

The intuition behind condition (26) (Corollary 1) is that the pollution tax increases if trade liberalization reduces collusion sufficiently, in turn causing a decline in the intensity of lobbying. Whether this occurs depends critically upon the degree of substitutability between the imported and the domestic good. When the two goods are close substitutes, trade liberalization results in lower lobbying, which in turn translates into higher pollution taxes.

6. Conclusion and final remarks This paper develops a theory of the multifaceted relationships between collusion, lobby group formation, trade liberalization and environmental policy. Three testable predictions emerge. If the elasticity between the prices of the domestic and foreign goods is sufficiently high, trade liberalization: (i) reduces collusion in the domestic output market, (ii) reduces the incentive to lobby for less stringent environmental (pollution tax) policy, and (iii) raises the stringency of environmental policy. The main environmental policy conclusion that emerges is that trade liberalization tends to increase the stringency of environmental policy primarily when foreign and domestic goods are close substitutes. This appears likely when economic integration occurs between

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countries producing goods of relatively similar quality (e.g. between industrialized countries). On the other hand, when a developed country liberalizes its trade with a developing country, lobbying on environmental policy issues becomes easier to sustain, and the policy stringency may fall unless other measures that reduce the level of product market collusion are undertaken simultaneously. An analysis of such complementary pro-competitive policies is left for future work. There are a number of other significant issues that have not been considered in this paper.30 First, note that if there is an independent regulatory body with a mandate to review prices, then the scope for output collusion may be severely curtailed. This issue has been ignored in the paper since collusion is assumed to be tacit and emerges as the non-cooperative equilibrium of a repeated game. Thus, Tirole (1998) suggests that such equilibria should be interpreted as representing a situation in which firms do not compete aggressively rather than as a formal collusive cartel (i.e. the outcome of a cooperative game). It is therefore possible that tacit collusion may be difficult for regulators to both to detect and to control. However, where regulators succeed in preventing collusive activities, our results suggest that in a political equilibrium, greater openness lowers lobbying by reducing rents and thus results in more stringent environmental regulations. A further simplification is the assumption that the tariff and tax are determined independently and that the tariff is taken as given by the small country under consideration. As noted earlier, this assumption seems to reflect the prevailing view that WTO membership invariably restricts the trade policy choices of small countries (see Footnote 5). This assumption could also be justified by assuming that the emission tax is actually a shadow tax representing other environmental regulations and is therefore not directly observable by trade negotiators. Alternatively, the tariff may be viewed as representing trade frictions (e.g. transactions costs, and other trade costs). Thus, a tariff reduction could be interpreted as representing a fall in a variety of trade-related costs. Finally, as in the Grossman–Helpman model, it has been assumed that all agents have full information about a, the relative weight given to welfare in the government’s utility function. It would clearly be more realistic to assume that there is uncertainty about the value of a. However, this would necessitate modeling a repeated signaling game of imperfect information, an important and seemingly complex task left for future research.

Acknowledgements The authors are grateful to Bouwe Dijkstra, Angeliki Kourelis, Karl-Johan Belfrage, Daniel Millimet, Dan Sasaki, Hal Varian, Peter Wagstaff, and two helpful referees for constructive comments and discussions. This paper was partially written while the second author visited the University of Lund (Lund, Sweden) and ZEW (Mannheim, Germany), and he thanks these institutions for their hospitality. A travel grant from SMU is also gratefully acknowledged. The usual disclaimers apply. 30

We are grateful to a referee for these points.

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Appendix A Lemma 1. An increase in firm j’s output lowers its rival’s incentive to defect, i.e. (dΩi /dqjc ) < 0. Proof of Lemma 1. Let (qic , qjc ) be the output levels at the constrained maximum where the incentive compatibility constraint (8.2) binds. By symmetry we have qic = qjc = qc , and Ωi = 0. Suppose that Lemma 1 is not true; then dΩi /dqc ≥ 0. Then by constraint (8.2), a fall in the collusive output level, qc , brings output closer to the unconstrained joint profit maximizing level and raises collusive profits. Since dΩi /dqc ≥ 0, this does not prompt any defection. This, however, contradicts the hypothesis that qjc is the solution to the constrained 䊐 maximum in (8.2). Thus, dΩi /dqc < 0. Lemma A1. Let f(x, y) be a differentiable function, with fx , fy > 0, ∀x, y > 0. Let x¯ > x, y¯ > y. If fxy < 0, then f(¯x, y¯ ) − f(¯x, y) < f(x, y¯ ) − f(x, y). Proof. Rearranging the inequality in the lemma yields f(¯x, y¯ ) − f(x, y¯ ) < f(¯x, y) − f(x, y). From this it follows that ∂f(x, y¯ )/∂x < ∂f(x, y)/∂x and ∂f(x, y¯ )/∂x − ∂f(x, y)/ ∂x < 0, which implies ∂2 f(x, y)/∂x∂y ≡ fxy < 0. 䊐

Appendix B In this appendix, we demonstrate that the central results of the paper hold when the industry lobby group is opposed by a rival environmental lobby group. Since the focus of the analysis is on the formation of industry lobby groups, for brevity we ignore free riding and other collective action problems that may hamper the formation of environmental lobby groups.31 Thus, for simplicity it is assumed that the economy consists of two types of citizens. The environmentalists (denoted by e) consume only the numeraire good z and suffer disutility from pollution. The consumers (denoted by k) consume both the numeraire good, the polluting good Q, and its imported substitute Q∗ . The utility function of environmentalists is U e = z − D(E(t)),

(B.1)

and that of consumers is U k = z − u(Q, Q∗ ).

(B.2)

For simplicity, both groups have exogenous incomes and receive a proportional share of tax and tariff revenues. The environmentalists form themselves into a lobby group that offers the government a contribution schedule C(t) to influence the government’s environmental 31 Olson (1965), for instance, argues that where the benefits of such actions are sufficiently high it is easier to overcome free-riding problems and form collective action groups. Thus, such lobbying activities may be expected to occur in cases where environmental damage is perceived to be sufficiently severe.

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policy. Thus, with an industry and an environmental lobby group, the government’s objective function is given by ˜ + αW(t), G(t) = C(t) + S(t)

(B.3)

where S(t) is defined in (21.1). The tax rate that maximizes the government’s welfare is defined by the first-order condition ∂G ∂C ∂S˜ ∂W = + +α = 0. ∂t ∂t ∂t ∂t

(B.4)

As noted earlier, in a subgame perfect equilibrium contribution schedules are locally truthful. ˜ Thus, using the local truthfulness property (i.e. ∂C/∂t = ∂U e /∂t and ∂S/∂t = ∂πc /∂t), condition (B.4) may be expressed as ∂D(E) ∂E ∂πc ∂W ∂G =− + +α = 0. ∂t ∂E ∂t ∂t ∂t

(B.5)

Let t0 be the solution to (B.5). For future reference, we define the tax that eventuates when firms do not lobby the government: t e ∈ arg max Ge ≡ C(t) + αW(t).

(B.6)

Similarly, from (CI) (in the text) we define the tax that eventuates when environmentalists do not lobby the government: ˜ + αW(t). t ∗ ∈ arg max G∗ ≡ S(t)

(B.7)

Comparison of the associated first-order conditions reveals that t e > t 0 > t ∗ . Grossman and Helpman demonstrate that with rival lobby groups, the equilibrium contribution of each group must satisfy: C(t 0 ) = [πc (t ∗ ) + αW(t ∗ )] − [πc (t 0 ) + αW(t 0 )];

(B.C1)

S(t 0 ) = [U(t e ) + αW(t e )] − [U(t 0 ) + αW(t 0 )] + F.

(B.C2)

As noted earlier, the firm lobby group will prevent free riding on its contributions defined in (B.C2) if the following incentive compatibility constraint is satisfied: Ψi = πicd (τ, t 0 ) − πicc (τ, t 0 , Fi ) −

πicc (τ, t 0 , Fi ) − πicn (τ, t e ) = 0. r

(B.8)

Observe that with a rival environmental lobby group in existence, if firms do not lobby the government, the tax rate that eventuates is te as defined in (B.6). We now show that Proposition 2 and Corollary 1 continue to hold in this context. Proposition B1. In the political equilibrium, trade liberalization increases the firms’ incentive to contribute to lobbying for a lower pollution tax (i.e. dΨi /dτ > 0) if the cross-price elasticity of domestic demand is relatively low. Proof. Let τ¯ > τ and define Ψi (τ) = Fi + si − 1/r(πcc (τ, t 0 ) − πcn (τ, t e )), and Ψi (¯τ ) = Fi + si − 1/r(πcc (¯τ , t 0 ) − πcn (¯τ , t e )). By construction, t e > t 0 . The remaining part of the

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67

proof follows the proof of Proposition 2. Proposition B1 holds when a condition identical 䊐 to (25) holds. Corollary B1. In the political equilibrium, trade liberalization increases the pollution tax if the elasticity between the price of the domestic good and the foreign substitute, ηpc P ≡ (∂pc /∂P)(P/pc ), is relatively great, such that the following condition holds: ηpc P > Γ, where

(B.9)





∂2 D c ε − ψτ Γ ≡  Eθ 2 Q τ ∂Qc

∂2 D βε(Qc /t)τ − εQc τ εθA εAt θ ∂D + E + ∂E ∂E2 − εQc t

(θ+Ω)(1+r) α

  1+τ, pc τ

and where the elasticities on the RHS are defined as εhb ≡

∂h b , ∂b h

h, b = pc , Qc , t, τ,

Qc ; t

and where ψ ≡ p∗ m[εQ∗ pc εpc Qc + τ(εpc Qc ε(Q∗ /pc )τ + εQ∗ pc ε(pc /Qc )τ )], β ≡ pc − c(A) − v − θ and

m≡

Q∗ , Qc

∂D εAt + τεQ∗ pc εpc Qc m − (εcA c(A) + εθA εDE D), ∂E t

  Qc 1 E ∂2 D ∂D εθA εAt εQc t ∂2 c εQc τ εEt =− + + ε(Qc /t)τ . Ω≡ ∂t∂τ t ∂E2 τ ∂E t τ

Proof. Totally differentiating and rearranging expression (B.4) yields dt 0 ∂2 G/∂t∂τ . =− 2 dτ ∂ G/∂t 2

(B.10)

Assuming a unique maximum, such that ∂2 G/∂t 2 < 0, it follows that the sign of (B.10) equals the sign of its numerator. To determine the sign of this expression, note that by local truthfulness, ∂π/∂t = ∂S/∂t. From the profit function we obtain ∂π/∂t = −θQc (t 0 ), and thus ∂2 S ∂Qc (t 0 ) = −θ . (B.11) ∂t∂τ ∂τ Similarly for the environmental lobby group, by local truthfulness ∂C/∂t = (∂D(E)/∂E) (∂E/∂t), and thus   ∂2 D(E) ∂Q ∂E ∂D(E) ∂θ ∂Q ∂A ∂2 Q ∂2 C = −θ − + θ . (B.12) ∂t∂τ ∂E ∂A ∂τ ∂t ∂t∂τ ∂E2 ∂τ ∂t

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Combining (B.11) and (B.12) with (30) (in the text) yields (B.9).

䊐

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