Abstract
The established view on oligopolistic competition with environmental externalities has it that, since firms neglect the external effect, their incentive to invest in R&D for pollution abatement is nil unless they are subject to some form of environmental taxation. We take a dynamic approach to this issue, using a simple differential game to show that the conclusion reached by the static literature is not robust, as the introduction of dynamics shows that firms do invest in R&D for environmental-friendly technologies throughout the game, as long as R&D is accompanied by an output restriction exhibiting a distinctively collusive flavour. We also examine the social planning case and the effects of Pigouvian taxation, to show that there exists a feasible tax rate inducing profit-seeking firms to choose a combination of output and R&D such that the resulting social welfare level is the same as in the first best.
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Notes
- 1.
On the optimality of free trade with environmental externalities, see Copeland and Taylor (1994, 2004) and Antweiler et al. (2001). As to the role of environmental issues in growth theory, see Grossman and Krueger (1995), Bovenberg and de Mooij (1997), Bartz and Kelly (2008), Itaya (2008) and Dragone et al. (2010), inter alia.
- 2.
- 3.
See, e.g., Klemperer (2007).
- 4.
- 5.
- 6.
In a similar setting, Benchekroun and Chaudury (2011) show that imposing a Markovian tax on emissions may bring about a stable cartel, while this does not happen with a uniform tax.
- 7.
Here we assume firm-specific externalities and R&D activities, as it appears to be reasonable in examining investments in environmental-friendly technologies. Hence, we rule out the possibility of spillovers in R&D.
- 8.
Note that, since (2) contains a product between a control and a state, the model is not a linear-quadratic one, and therefore there exists no obvious candidate for the optimal value function that one should adopt to solve the feedback game.
- 9.
Using a repeated game with infinite Nash reversion, Damania (1996) finds that firms may not be willing to buy pollution-abating technologies if the associated exogenous cost is too high.
- 10.
Moreover, this eliminates any issue concerning the possibility of unilateral deviations, as it is the outcome of a fully noncooperative behaviour.
- 11.
We attribute to the planner the same time discounting that we have used to measure firms’s time preferences in the previous section. One might, however, suppose that the planner’s discount rate be significantly lower than firms (possibly even nil), in order to give an appropriate weight to the welfare of future generations. For a thorough appraisal of this issue, see the Stern Review (Stern 2007) as well as Dasgupta (2007), Nordhaus (2007) and Weitzman (2007).
- 12.
That is, the equivalent of Remark 5 holds here. The proof of this fact follows the same lines as for the Cournot equilibrium of the open-loop game among firms. The details have been omitted for brevity.
- 13.
Note that the corresponding steady state profits are independent of θ:
$$\pi_{4,5}^{\theta }=\frac{\delta \sigma ( \sigma \pm \sqrt{\varOmega }) -2\eta ( N+1 ) r\varUpsilon }{2\delta ( N+1 )^{2}} $$where Ω=σ 2−8ηρ(N+1)r and ϒ=2ρ 2(N+1)N+δ[η(N+1)+2ρN 2]. There exist admissible parameter regions where the above profits are strictly positive.
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Acknowledgements
We thank Hassan Benchekroun, Guido Cozzi, Aart de Zeeuw, Christoph Grimpe, Morton Kamien, Paul Klemperer, Arkady Kryazhimskiy, George Leitmann, Emmanuel Petrakis, Vladimir Veliov, Franz Wirl and the audience at IIOC’09 (Boston), the 14th Symposium of ISDG (Banff, 2010) and the workshop on Economic Growth and the Environment (TU Wien, Dec. 8, 2011) for useful comments and discussion. The usual disclaimer applies.
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Appendix: List of Symbols
Appendix: List of Symbols
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N: number of oligopolistic firms;
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q i (t): i-th firm’s output at time t;
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Q −i (t): aggregate output of all firms except the i-th one at time t;
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Q(t): aggregate output of all firms at time t;
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k i (t): R&D effort level of the i-th firm at time t;
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p(t)=a−Q(t): inverse market demand function at time t, where a>0 is the related reservation price;
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C i =cq i (t): production cost function for the i-th firm at time t, where c>0 is the related marginal cost;
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b i (t): marginal contribution of the i-th firm to the stock of pollution at time t;
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S(t): aggregate stock of pollution at time t;
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Γ i (t)=rk i (t)2: R&D cost function for the i-th firm at time t, weighted by the constant r>0;
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π i (t)=(p(t)−c)q i (t)−Γ i (t): profit function for the i-th firm at time t;
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η>0: regeneration rate for the marginal contribution of firms over time;
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δ>0: decay rate for the stock of pollution over time;
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ρ>0: intertemporal discount rate of the market;
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σ=a−c>0: market dimension parameter;
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λ i (t), μ ii , μ ij : shadow prices attached by firms to all the dynamic constraints of the model;
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CS: consumer surplus;
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SW: social welfare.
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Dragone, D., Lambertini, L., Palestini, A. (2013). The Incentive to Invest in Environmental-Friendly Technologies: Dynamics Makes a Difference. In: Crespo Cuaresma, J., Palokangas, T., Tarasyev, A. (eds) Green Growth and Sustainable Development. Dynamic Modeling and Econometrics in Economics and Finance, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34354-4_8
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