Voluntary Approaches and the Organisation of Environmental R&D

Transcription

1 Fondazione Eni Enrico Mattei Voluntary Approaches and the Organisation of Environmental R&D Joanna Poyago-Theotoky NOTA DI LAVORO Corso Magenta, 63, Milano, tel. +39/02/ fax +39/02/ C.F

2 Journal of Economic Behavior & Organization Vol. 62 (2007) The organization of R&D and environmental policy J.A. Poyago-Theotoky Department of Economics, Loughborough University, Loughborough, LE11 3TU, UK Received 3 July 2003; accepted 29 September 2004 Available online 20 December 2005 Abstract We consider a setting where firms undertake emission-reducing R&D and the regulator, who sets the emission tax, is unable to commit credibly. Firms are subject to research spillovers in emission reduction. We examine two regimes with respect to the organization of R&D: independent R&D and an environmental R&D cartel (ERC). Environmental R&D is higher in the ERC compared to independent R&D for small damages and also for large damages when R&D is efficient. In contrast, when damages are large and R&D is inefficient the opposite is true. The same ranking applies to the comparison of social welfare Elsevier B.V. All rights reserved. JEL classification: 032; L13; Q28 Keywords: Environmental R&D cartels; Environmental research joint venture; Cooperative R&D; Emission tax 1. Introduction The issue of R&D cooperation versus R&D competition has received considerable attention in recent years. Several papers in the industrial organization literature discuss the relative merits of different forms of organization of R&D from a number of different perspectives; D Aspremont and Jacquemin (1988), De Bondt and Wu (1997), Kamien et al. (1992), Pérez-Castrillo and Sandonís (1996), Suzumura (1992), and Vilasuso and Frascatore (2000), among others. As is well known from the R&D literature, there are fundamental market failures in the innovation process stemming from the public good nature of knowledge and information. A number of policy instruments have been used to address these market failures, most notably the granting of intellectual property rights (patents), licensing, R&D subsidies and the encouragement Tel.: ; fax: address: j.poyago-theotoky@lboro.ac.uk /$ see front matter 2005 Elsevier B.V. All rights reserved. doi: /j.jebo

3 64 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) of cooperative R&D. Before proceeding, it is important to discuss and understand these market failures in some detail. Suppose that there are no leakages of information; that is, spillovers are absent, perhaps as a result of a very effective patent system so that when firms choose their R&D strategically (in the sense that they choose R&D first, followed by output) they have a tendency to over-invest in R&D as they attempt to gain an advantage over their rivals. This is a strategic over-investment effect. In contrast, when there are leakages of information (i.e. there are positive spillovers), then the larger the spillover the smaller the incentive for R&D, so firms under-invest in R&D. This is the familiar appro-priability problem that gives rise to a strategic under-investment effect (or spillover effect). Both the strategic over-investment effect and the strategic under-investment effect are manifestations of an R&D market failure; for a variety of reasons firms will choose the wrong level of R&D relative to the social optimum. There is, in addition, a further problem that arises from the fact that innovators are not rewarded for sharing information. The patent system, by addressing some of the fundamental market failures, introduces additional distortions as it rewards firms for discoveries but not for sharing these with other firms. There is thus an information-sharing market failure that arises because firms operate under a sub-optimal level of information-sharing relative to the first best (which given the public good nature of information would require full information-sharing). In the present paper, we consider the case where R&D efforts are not directed towards costreduction or product quality enhancement as is the case of the literature referred to above, but instead R&D is directed towards emission reduction of harmful pollutants. In other words, we are interested in environmental R&D or abatement activities where firms undertake R&D in order to develop new processes to reduce toxic emissions. In this context, the introduction of pollution, an environmental externality, gives rise to a third market failure as firms tend to over-produce. As is well known this type of market failure can be addressed by an emission tax. We consider a setting allowing for oligopolistic interaction and concentrate on the case of a government or regulator who possesses limited commitment power; the key assumption here is that the R&D decision is made before the regulator chooses the level of the emission tax. This assumption is particularly valid when R&D is at stake given that R&D is typically a long-term activity. 1 The questions we address relate to the organizational structure of environmental R&D, cooperative versus independent, and how it relates to the relative performance in terms of environmental R&D, profits and social welfare. This is an issue that, to the best of our knowledge, has received limited attention in the literature, with the exception of Petrakis and Poyago-Theotoky (2002), Sandonís and Mariel (2004) and Scott (1996). 2 Petrakis and Poyago-Theotoky take the view that environmental policy is inactive, in the sense that the emission tax is fixed and beyond the control of the regulator, and compare the relative merits of two popular technology policies, R&D subsidization and the promotion of R&D cooperation when R&D is of the cost-reducing type and production generates pollution. In contrast, in the present paper environmental policy is active (emission tax), and technology policy is concerned with the relative performance of 1 The absence of commitment by the regulator is imposed by the long-term nature of R&D decisions as opposed to the shorter-term nature of emission tax setting. 2 Chiou and Hu (2001) examine the performance of a number of different cooperative scenarios when the emission tax is exogenous. However, in their R&D competition and cartelization cases firms emission reduction is not affected by spillovers whereas in the RJV competition and cartelization cases spillovers are present. Consequently, their results are affected by this dichotomous assumption on spillovers.

4 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) R&D cooperation versus R&D competition. Sandonís and Mariel extend Petrakis and Poyago- Theotoky in examining various regimes of cooperation in R&D, from simple R&D coordination to full collusion, with and without R&D subsidization. Scott provides an empirical analysis of environmental research joint ventures in the U.S. that were formed after the enactment of the 1984 National Cooperative Research Act (NCRA). Interestingly, at least one third of the NCRA joint ventures that Scott covers in his study address environmental concerns. In addition, it is reported that R&D cooperation takes place in response to both actual and anticipated regulation (as captured by the 1990 Clean Air Act Amendments (CAAA)). Given this evidence, it is surprising that so little attention has been devoted to a detailed examination of cooperative agreements that deal with environmental concerns. It is our aim in this paper to try to (partially) fill this gap. Basically we examine two regimes with respect to the organization of environmental R&D: (i) independent R&D and (ii) an environmental R&D cartel (ERC). This terminology is adapted from Kamien et al. (1992) who have provided a classification of different R&D organizational forms (in the absence of pollution effects) for the case of cost-reducing R&D; their is the closest paper to ours in terms of the theoretical framework used. We note here that we are not examining the case where firms collude fully as in most countries explicit collusive behavior in the product market is illegal. 3 In the present paper, R&D affects the emissions of a firm in the sense that by undertaking R&D a firm can reduce its polluting emissions (abatement); further, we posit that there are spillovers in the R&D process so that a firm can benefit from the R&D effort of its rival at no cost to itself. We study this in the context of a multi-stage game. In the first regime the structure of the multi-stage game is as follows: (1) firms choose their emission-reducing R&D non-cooperatively; (2) the regulator (or government) sets the emission tax; and (3) firms compete in the market by choosing quantities. In the second regime both the second and third stages remain the same; however, in the first stage firms form an industrywide R&D Cartel (ERC) that cooperatively undertakes environmental R&D. In both regimes, emissions are reduced by a firm s own R&D effort; in addition to some spillover from other firms R&D. In the ERC the spillover is not increased as a result of the cartelization. Moreover, in the context of R&D cooperation, we briefly consider the case of an environmental research joint venture (ERJV) where the spillover is set at its maximal value so that information is fully shared. The model used to address the questions posed above is based on a specification introduced by D Aspremont and Jacquemin (1988) and Kamien et al. (1992), suitably extended to accommodate environmental effects and emission-reducing R&D. 4 We concentrate on an industry in which each of two firms sells a homogeneous product. Contrary to the conventional presumption, an ERC can be detrimental to both emission reduction and social welfare 5 even when spillovers are large. In particular, we show that environmental R&D is higher in the case of an ERC compared to independent R&D for small damages as well as for large damages when R&D is efficient. In contrast, when damages are large and R&D is inefficient, the opposite is true. The same ranking applies to the comparison of social welfare. Further, we establish the superiority of an ERJV for 3 See Damania (1996) for an analysis of an infinitely repeated game where, in the absence of spillovers, an emission tax may both facilitate collusion and also lead to a reduction in abatement activities. 4 In line with the cited literature we cast the analysis in a full-information context. It should be noted though that there are real problems of contracting on R&D efforts as well as asymmetries of information between a regulator and firms. Incorporating such elements in the analysis lies outside the scope of the present paper but is left as a topic for further research. 5 Damania (1996) reaches a similar conclusion in the context of a supergame with no spillovers.

5 66 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) any degree of environmental damage. Introducing pollution effects results in a strikingly different welfare ranking of R&D organizational regimes. The rest of the paper is organized as follows. In Section 2, we describe the elements of the model. In Section 2.1, we derive the subgame-perfect equilibrium when firms undertake R&D in a non-cooperative manner; in Section 2.2, we do the same for the case of the environmental R&D cartel. In Section 2.3, we carry out a detailed comparison of the two R&D regimes and present the main results of the paper, and offer some concluding remarks in Section 3. Proofs of propositions appear in Appendix A The model We consider a model where two firms produce a homogeneous good under a linear demand specification p = a Q, Q = q i + q j, i j, i, j = 1, 2, where a is a measure of market size. Production generates pollution, which is taxed at the rate t on emissions while firm i can reduce its tax burden by undertaking environmental R&D, z i, to reduce its emissions. The cost function for firm i is given by c(q i,z i ) = cq i + (γz 2 i /2) where c is the unit cost of production (a > c); there are constant returns to scale, and γ captures the efficiency of the R&D technology. Notice that environmental R&D is characterized by decreasing returns as we assume γ > 0. Following Petrakis and Xepapadeas (1999) and Ulph (1996), after an appropriate choice of measurement units such that each unit of output generates one unit of pollution, we express firm i s (net) emissions as e i (q i, z i )=q i z i βz j,0 β 1 (i.e. there are spillovers in environmental R&D in that a firm benefits not only from its own R&D effort but also from its rival s effort by an amount β). 7 Thus, by investing an amount (γz 2 i /2) in environmental R&D, firm i can reduce its (gross) emissions q i by z i + βz j this latter term represents the effective R&D (or abatement) for firm i. Given pollution, the extent of damage is captured via a quadratic damage function, D = (1/2)dE 2, where E = e i + e j is total emissions and d is proportional to marginal damage (it captures the severity of damage). To guarantee an interior solution for R&D and a positive emission tax, we will assume d > (1/2) in what follows. In the sequel we compare two alternative R&D organization regimes: independent R&D and environmental R&D cartel (ERC) Non-cooperative R&D In the last (third) stage, firm i chooses output to maximize profit; max[(α q i q j )q i cq i γz2 i q i 2 t(q i z i βz j )]. The relevant first-order condition yields q i =(A t q j )/2, where A a c. Imposing symmetry, q i = q j = q, we obtain equilibrium output per firm, q =(A t/3), and equilibrium profit π i = q 2 + t(z i + βz j ) 1/2γz 2 i. Note that a firm s output decreases in the emission tax. 6 Appendix A is available on the JEBO website. 7 The particular choice for the specification of the pollution generation process is made for the sake of simplifying the analysis. We conjecture that even with a non-linear function between output and abatement the results would be similar, notwithstanding the fact that a firm would face a stronger strategic effect in engaging in emission reduction activities in order to induce a lower emission tax.

6 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) In the second stage, the regulator sets the emission tax, t, to maximize social welfare, expressed as the sum of producer and consumer surplus minus environmental damages, [ 2q max (a c x)dx 1 t 0 2 d 2q (1 + β) ] 2 ( ) z i 1 2 γ z 2 i, i i or equivalently ( max 2Aq 1 t 2 (2q)2 1 2 d 2q (1 + β) i z i ) γ ( i ) 2 z i. The first-order condition is [ ( 2 A 2q d 2q (1 + β) i z i )] dq dt = 0, which, 8 after some manipulation yields t = (2d 1)A 3d(1 + β) i z i. (1) 2(1 + d) From (1) notice that (dt/dz i )= (3d(1 + β))/2(1 + d) < 0; strategic effect in that it induces a firm to increase its R&D effort and thus face a lower emissions tax. Using (1) in the expression for output and profit we obtain q = A + d(1 + β)(z i + z j ) (2) 2(1 + d) and π i = [A + d(1 + β)(z i + z j )] 2 4(1 + d) 2 + (2d 1)A 3d(1 + β)(z i + z j ) (z i + βz j ) 1 2(1 + d) 2 γz2 i. (3) In the first stage the two firms choose their environmental R&D anticipating the choice of tax by the regulator and the subsequent product market competition. Each firm maximizes second-stage profits as given by (3), so the relevant first-order condition is 9 π i = 2d(1 + β)a + d(1 + β)(z i + z j )] z i 4(1 + d) 2 + (2d 1)A 3d(1 β)[2z i + (1 + β)z j ] γz i. 2(1 + d) In the symmetric equilibrium, z i = z j = z nc, the solution of the above first-order condition yields the equilibrium level of environmental R&D [(1 + d)(2d 1) + d(1 + β)]a z nc = 2γ(1 + d) 2 + d(1 + β)[3(3 + β) + d(7 + β)]. (4) Notice that z nc > 0 given our assumption that d > 1/ The second-order condition is ( (4/9)(1 + d)<0. 9 The second-order condition requires d(1 + β)[ 6+5(β 5)]/2(1 + d) 2 ( ( < 0)), which is satisfied for >0. 10 Notice that z nc > 0 is equivalent to 2d 2 + d(2d + ) 1 > 0. This gives two solutions for d, one negative (d 2 ) and one positive (d 1 ). This latter requires d 1 > 1 4 [ 12 + β(4 + β) (2 + β)] which is decreasing in β. Hence it is sufficient to

7 68 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) Using (4) into (1) and (2), we obtain the equilibrium emission tax and quantity per firm, respectively d(2d 3)(1 + β) 2 + 2γ(2d 2 + d 1) t nc = A, (5) 2 2d(1 + β)[3(3 + β) + d(7 + β)] + 4γ(1 + d) 2(1 + d)γ + d(1 + β)(7 + 4d + 3β) q nc = A. (6) 2 2d(1 + β)[3(3 + β) + d(7 + β)] + 4γ(1 + d) Using (6) and (4) in the expression for emissions, it is easy to check that e nc = q nc (1 + β)z nc >0. Further, and π nc = q 2 nc + t nc(1 + β)z nc 1 2 γz2 nc (7) SW nc = 2Aq nc 2q 2 nc 2d(q nc (1 + β)z nc ) 2 γz 2. (8) This concludes the analysis of the non-cooperative R&D regime Cooperative R&D environmental R&D Cartel We now consider the case of an environmental R&D cartel. As mentioned in the Introduction, stages 2 and 3 remain the same. However, in the first stage the two firms choose their environmental R&D cooperatively in that they coordinate their R&D activities (i.e. choose z i, i = 1, 2, to maximize the sum of their overall profit). Notice that this is an environmental R&D cartel (ERC) as it operates with the same spillover as the independent firms (i.e. firms coordinate their R&D but do not share information fully). In the case where firms would share information completely we would have an environmental research joint venture (ERJV), that is, β =1. 11 Thus, in stage 1 firms maximize Π erc = i π i where π i refers to the second-stage profit as given by (3). The first-order conditions require that ( π erc / z i )=0=( π erc / z j ); deriving these and then setting z i = z j = z erc, yields the symmetric equilibrium values, 12 z erc = [(1 + d)(2d 1) + 2d](1 + β)a 2(1 + d) 2 γ + 4d(3 + 2d)(1 + β) 2. (9) evaluate the above for β = 0 yielding d 1 > 1/2( 3 1) = It is then evident that our assumption that d > (1/2) is sufficient to ensure that z nc >0. 11 Kamien et al. (1992) refer to an RJV (research joint venture cartel in their terminology) as a situation where firms coordinate their R&D activities to maximize the sum of their overall profit while at the same time sharing R&D efforts and to avoid duplication of R&D activities. Further, the spillover is increased to its maximal level. Their definition of an R&D cartel is basically the same as in the present paper (save for the environmental effects). 12 The second-order conditions are satisfied.

8 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) Notice that here too z erc > 0 given that d > (1/2). 13 Using (9) into the relevant expressions for the emission tax and the quantity produced, we obtain t erc = [d(2d 3)(1 + β)2 + γ(2d 2 + d 1)]A 2(1 + d) 2 γ + 4d(3 + 2d)(1 + β) 2 (10) and q erc = [d(5 + 2d)(1 + β)2 + γ(1 + d)]a 2(1 + d) 2 γ + 4d(3 + 2d)(1 + β) 2. (11) Furthermore, it is straightforward to check, using (11) and (9), that e erc = q erc (1 + β)z erc >0, while profits per firm and total welfare are expressed as and π erc = q 2 erc + t erc(1 + β)z erc 1 2 γz2 erc. (12) SW erc = 2Aq erc 2q 2 erc 2d(q erc (1 + β)z erc ) 2 γz 2 erc. (13) Having described the cooperative R&D regime, we now proceed to a comparison of the two different forms of R&D organization A comparison: independent R&D versus ERC One question we address is whether cooperative R&D (in the form of an ERC) results in higher R&D effort (abatement) relative to non-cooperative R&D and how the optimal emission tax compares in these two regimes. First, we compare the R&D efforts, z erc and z nc. From (9) and (4) we obtain z erc z nc = A(1 + d)2 ϕ ΓΔ (14) where (ϕ d(3 2d)(1 + β) 2 (l β)+2γ(2d 2 β +2dβ β + d), Γ 2γ(1 + d) 2 + d(1 + β)[3(3 + β)+d(7 + β)] > 0 and 2γ(1 + d) 2 +4d(3+2d)(1 + β) 2 > 0. Further, from (10) and (5) we have 3Ad(1 + d)(1 + β)ϕ t erc t nc =. (15) 2ΓΔ We then present the following proposition and its corollary. Proposition 1. Given γ >0andd>(1/2) (i) for d <(3/2), the equilibrium R&D effort in the ERC is always greater than in the noncooperative R&D regime, z erc > z nc, while the optimal emission tax in the case of an ERC is lower than the optimal emission tax in non-cooperative R&D, t erc < t nc ; (ii) for d >(3/2) and γ> γ where γ is a critical R&D efficiency parameter, the equilibrium R&D effort in the ERC is always greater than in the non-cooperative R&D regime, z erc > z nc, while 13 Notice that z erc > 0 is equivalent to d 2 (2+2 )+d(3+3 ) (1 + ) > 0. This gives two solutions for d, one negative (d 2 ) and one positive (d 1 ). This latter requires d 1 > 1/4( 17 3) = It is then evident that our assumption that d > (1/2) is sufficient to ensure that z erc >0. 14 Note that setting β = 1 in these expressions gives the equilibrium values for the case of an ERJV.

9 70 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) the optimal emission tax in the case of an ERC is lower than the optimal emission tax in non-cooperative R&D t erc < t nc. For γ> γ, there is a critical value for the damage parameter d such that for d< d, the equilibrium R&D in the ERC is larger than the non-cooperative equilibrium R&D, z erc > z nc while for d> d, the opposite holds, z erc < z nc. Further, for d< d, t erc < t nc while for d> d, t erc > t nc. The critical value d is increasing in the spillover parameter while the critical value γ is decreasing in the spillover. Corollary 1. When β = 1(i.e. there is an environmental research joint venture (ERJV) with full information-sharing), it will generate more environmental R&D (and hence will face a lower emission tax) for any value of the damage parameter, d. The main message conveyed by Proposition 1 is that unless environmental damage is high enough (d > d) and R&D is relatively efficient (γ < γ), the ERC is superior to the independent firms in terms of emission reduction (z erc > z nc ). In the case of relatively small environmental damages ((1/2) <d< (3/2)), environmental R&D is higher with the ERC irrespective of the extent of R&D efficiency (part i). When damage is small we would expect the emission tax to be small. The implication of this observation is that the returns to R&D are high so that firms will invest a lot in R&D. Moreover, firms within an ERC have an additional incentive to invest in R&D as they maximize joint profits; this explains why they do more R&D than independent firms. However, when environmental damages are larger (d > (3/2)), the comparison between the two different forms of R&D organization depends on the efficiency of R&D and the severity of damage (part ii). Taking into account firms R&D incentives, there is a trade-off in operation here; when R&D is not as profitable (γ > γ) the additional incentive that independent firms have to invest in R&D when damages are substantial (d > d) is attenuated, and the ERC will invest more because of the joint-profit maximization effect. However, when R&D is very efficient (γ < γ), the former incentive dominates, and we obtain the counterintuitive result that environmental R&D is lower in the ERC. Further, as the spillover increases, the critical value for the R&D efficiency parameter decreases so that the ERC outperforms the independent R&D set-up in a wider class of cases; in effect the second effect identified above dominates. Fig. 1 illustrates Proposition 1 for the case of environmental R&D by plotting expression (14). The next question we pose concerns the relative profitability of firms under the two regimes. Using (7) and (12), after some manipulation, we obtain π erc π nc = A2 (1 + d) 2 κ 2 4ΔΓ 2 > 0 (16) where κ d(3 2d)(1 β)(1 + β) 2 +2γ[d + β(2d 2 +2d 1)]. It is obvious that it is profitable for a firm to participate in an environmental R&D cartel whatever the environmental damage (and emission tax); in this case a firm has a clear incentive to participate in an ERC. 15 This is expected 15 In the case of a n firm oligopoly this incentive would be present in a situation of an industry-wide ERC. However, allowing k firms in an ERC (k < n) (or generally in various types of R&D cooperation) would necessitate a careful examination of the profitability/incentives to join for the outside firms. These issues lie outside the scope of the present paper.

10 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) Fig. 1. Environmental R&D (emission reduction).

11 72 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) given that within an ERC each firm is maximizing joint profits by choice of its environmental R&D. Finally, we compare social welfare under the two forms of R&D organization. The following proposition summarizes the results. Proposition 2. Given γ >0andd>(1/2) (i) when d <(3/2) social welfare in the ERC is always greater than in the non-cooperative equilibrium, SW erc >SW nc ; (ii) when d > (3/2) and γ > γ, where γ is the critical R&D efficiency parameter, social welfare in the ERC is greater than in the non-cooperative scenario, SW erc >SW nc. When γ< γ, there is a d such that for all d< d, social welfare is greater in an environmental R&D cartel relative to environmental R&D competition SW erc >SW nc and for all d> d, the opposite is true, SW erc <SW nc. The critical value d is increasing with the spillover. According to Proposition 2, an environmental R&D cartel (ERC) can be detrimental to social welfare despite being desirable from the firms point of view; this holds for relative large environmental damages (d > d) and relatively efficient R&D process (γ < γ); in all other cases an ERC is welfare enhancing. Further, as the degree of spillover becomes larger, the critical value for the environmental damage ( d) increases so that the ERC becomes increasingly better. Note that when β = 1 the ERC (which in this case coincides with an ERJV) outperforms the independent R&D case for any degree of environmental damage; this is because it internalizes both the combined-profits externality and the appropriability problem. 16 The intuition here is a direct implication of the results on the relative ranking of environmental R&D provided in Proposition 1. Recall that the literature on cost-reducing R&D obtains the well-known result that, in the absence of environmental effects, R&D cartels are generally socially beneficial in comparison to independent R&D when spillovers are relatively large while research joint ventures with information-sharing are outperforming the other forms of R&D organization for any value of the spillover; for example, see D Aspremont and Jacquemin (1988), De Bondt and Wu (1997) and Kamien et al. (1992). Introducing pollution effects results in a strikingly different welfare ranking of R&D organizational regimes. Even when spillovers are small there are instances where an ERC results in higher social welfare relative to non-cooperative R&D; this is so for small values of environmental damage. More strikingly (and in clear contrast with the results obtained in previous papers), even for large spillovers an environmental R&D cartel is socially worse than independent R&D as long as environmental damage is large and R&D is highly efficient. The results contained in Proposition 2 point to some tentative policy implications. We have shown that firms find it profitable to participate in an ERC. However, ERCs are socially preferable only when damages are small or when they are relatively large but R&D is inefficient. This implies that there is a divergence between private interests and societal ones, and hence there is room for public policy. The nature of policy can take various forms, two of which we highlight here. 16 Note that in our model, it is assumed that within an ERJV full information-sharing takes place; in a context of costreducing R&D, Poyago-Theotoky (1999) has shown that the choice of β = 1 is the unique equilibrium outcome of a game where spillovers are endogenous under the influence of firms.

12 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) First, given the social superiority of ERJVs relative to independent R&D, public policy could take the form of actively encouraging firms to share information fully in order to transform any ERC into a welfare-improving ERJV. 17 Second, if ERJVs are not possible, perhaps being costly to sustain or form as argued by Vilasuso and Frascatore (2000), then public policy should promote competition in R&D and discourage R&D collaboration in the form of ERCs for the case of large environmental damages and inefficient R&D. 3. Concluding remarks In this paper we have addressed the question of the importance of the organization of environmental R&D in relation to emission reduction and associated social welfare. We have examined this in the context of a setting where the regulator/government is unable to commit to the environmental policy instrument (in this case an emission tax) credibly. We have shown that environmental R&D is higher in the case of an environmental R&D cartel (ERC) compared to independent R&D, except in the case of relatively large damages and efficient R&D when the opposite is true. The same ranking applies to the comparison of social welfare. It would seem then, in summary, that ERCs perform better than a non-cooperative R&D regime when environmental damage is low but also when it is large and R&D is inefficient. However, we should be aware that this tentative conclusion has been reached for the case where the environmental policy tool is a tax on a firm s emissions. By using a different policy instrument, for example an asmbient tax (imposed on total emissions), the regulator might be able to induce firms to internalize their actions on other firms. This observation leads us to suggest studying the impact of a change in the tax design to examine how the possible welfare differences between independent R&D and an ERC depend on the instrument used by the regulator. Further, and in relation to the result about the superiority of an ERJV (under which firms share information fully) for any degree of damage, the role of policy might be to facilitate information exchange between firms in order to transform any ERC into a welfare-improving ERJV. In addition, we should note that these results have been obtained in the context of a duopolistic market. Extending the analysis to an n-firm oligopoly would exacerbate the free-rider problem so that cooperation in the form of an environmental R&D cartel would probably result in higher environmental R&D and welfare in a wider class of cases; however, with more than two firms we would have to consider cooperation encompassing less than the total number of firms in the market and examine the effects on insiders (cooperating firms) and outsiders (non-cooperating firms) and how the interplay of these sets of firms affects social welfare and so on. Moreover, issues of multiple, competing ERCs would need to be addressed. 18 We leave these interesting topics for future research. Acknowledgements I thank Katrin Millock, the coeditor, Matti Pohjola and two anonymous referees for helpful comments and suggestions that have improved the paper. The usual disclaimer applies. 17 There is the potential here for implementation problems, especially in a context where asymmetries of information are pervasive. 18 On this see Kamien and Zang (1993) for the case of cost-reducing R&D in the absence of pollution effects.

13 74 J.A. Poyago-Theotoky / J. of Economic Behavior & Org. 62 (2007) Appendix A A.1. Proof of proposition 1 From (14) and (15), z erc z nc and t erc t nc, respectively, if and only if ϕ 0, where ϕ d(3 2d)(1 + β) 2 (1 β)+2γ(2d 2 β +2dβ β + d). (i) The second term in the above expression for ϕ is positive for all admissible values of d and β The first term is positive if and only if d < (3/2) (recall that d > (1/2) by assumption) and thus, ϕ >0. (ii) Let d > (3/2). Note that ϕ(d; β) is convex if γ>((1 β)(1 + β) 2 /(2β)) γ Then ϕ d=3/2,γ= γ = (1 β)(1 + β) 2 (3 + 13β)/(2β) 0 so that z erc > z nc. Next consider the case where γ< γ. Define d {d ϕ = 0} as the critical environmental parameter. For β =0, ϕ = d(3 2d +2γ) 0, there exists d, d = γ + (3/2 > 0), such that if d> d, then z erc < z nc and if d< d then z erc > z nc.forβ =1, ϕ =2 [d(3+2d) 1] > 0 so that z erc > z nc. Then, by continuity, for β (0, 1) there exists a critical value 19 d such that for d> d, z erc < z nc while for d< d, z erc > z nc. Further, it can be shown that d is increasing in β. The argument for the emission tax is identical except for a reversal in the inequalities; see (15). A.2. Proof of Corollary 1 From (14), z erc > z nc if and only if ϕ >0.Forβ =1,ϕ =2γ[d(3 + 2d) 1] > 0. The argument for the emission tax is analogous and hence omitted Proof of Proposition 2 From (8) with (13) we obtain after some manipulation SW erc SW nc = A2 (1 + d) 2 Ωϕ 4K 2 Λ 2 (A1) where Ω >0, Ω 2d 2 (1 + β) 4 ω 1 + d (1 + β) 2 ω (1 + d) 2 ω 3 > 0, and ω 1 [3(7 + β)+d ( β + d(26+6β))], ω 2 [29+7β + d (36+28β + d(29+55β +2d(7+13β)))]γ, and ω 3 [2 + β + d (2dβ 1)]γ 2. Further, K 6d +4d 2 +12dβ +8d 2 β +6dβ 2 +4d 2 β 2 + γ +2dγ + d 2 γ, 9d +7d 2 +12dβ +8d 2 β +3dβ 2 + d 2 β 2 +2γ +4dγ +2d 2 γ and ϕ has been defined previously. It is then obvious that sign[sw erc SW nc ] = sign(ϕ). We can then use the formal similarity with the proof of Proposition 1 to obtain the result. References Chiou, J.-R., Hu, J.-L., Environmental research joint ventures under emission taxes. Environmental and Resource Economics 21, Damania, D., Pollution taxes and pollution abatement in an oligopoly supergame. Journal of Environmental Economics and Management 30, The critical value d is given by d = [3β(β 2 + β 1) 3 2γ 4βγ + 16βγ((β 1)(1 + β) 2 + 2βγ) + (3 3β(β 2 + β 1) + 2γ + 4βγ) 2 ]/ 4[β(2γ + β 2 + β 1) 1].

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