# Optimal Environmental Policy for a Polluting Monopoly with Abatement Costs: Taxes Versus Standards

## Abstract

In this paper, we characterize the optimal environmental policy for a polluting monopoly that devotes resources to abatement activities when damages are caused by a stock pollutant. With this aim, we calculate the stagewise feedback Stackelberg equilibrium of a (differential) policy game where the regulator is the leader and the monopolist is the follower. Our analysis shows that the first-best policy consists of applying a Pigouvian tax and a subsidy on production equal to the difference between the price and the marginal revenue. However, for a stock pollutant, the Pigouvian tax is not equal to the marginal damages but is given by the difference between the *social* and *private* valuation of the pollution stock. On the other hand, if a second-best emission tax is used, the tax is lower than the Pigouvian tax and the difference decreases with the price elasticity of the demand. Finally, we find that taxes and standards are equivalent in a second-best setting. In the second part of the paper, we solve a linear-quadratic differential game and we obtain that the first-best tax increases with the pollution stock whereas the subsidy decreases. Moreover, the tax is negative for low values of the pollution stock, i.e., for low values of the pollution stock, we obtain that the social valuation of the stock is lower than the private valuation. Furthermore, when a second-best policy is applied, the steady-state pollution stock is lower than the steady-state pollution stock associated with the efficient outcome.

## Keywords

Monopoly Abatement Emission tax Emission standard Stock pollutant Differential games## Notes

### Acknowledgments

The authors would like to thank the participants at the IV Encuentro Conjunto Real Sociedad Matemática Española-Sociedad Matemática Mexicana (Valladolid), 23^{ r d } Annual Conference of the European Association of Environmental and Resource Economists (Athens), Singapore Economic Review Conference 2017, Second AERNA Workshop on Game Theory and the Environment (Madrid), XXXII Jornadas de Economía Industrial (Pamplona), 19^{ t h } Annual BIOECON Conference (Tilburg), 17^{ t h } International Symposium on Dynamic Games and Applications, and one anonymous referee for their helpful comments. Usual caveats apply.

## References

- 1.Barnett, A.H. (1980). The Pigouvian tax rule under monopoly.
*American Economic Review*,*70*, 1037–1041.Google Scholar - 2.Benchekroun, H., & Van Long, N. (1998). Efficiency-inducing taxation for polluting oligopolists.
*Journal of Public Economics*,*70*, 325–342.CrossRefGoogle Scholar - 3.Benchekroun, H., & Van Long, N. (2002). On the multiplicity of efficiency-inducing tax rules.
*Economic Letters*,*76*, 331–336.CrossRefGoogle Scholar - 4.Bergstrom, T.C., Gross, J.G., Porter, R.C. (1981). Efficiency-inducing taxation for a monopolistically supplied depletable resource.
*Journal of Public Economics*,*15*, 23–32.CrossRefGoogle Scholar - 5.Buchanan, J.M. (1969). External diseconomies, corrective taxes, and market structure.
*American Economic Review*,*59*, 174–177.Google Scholar - 6.Feenstra, T., Kort, P.M., de Zeeuw, A. (2001). Environmental policy instruments in an international duopoly with feedback investment strategies.
*Journal of Economic Dynamics & Control*,*25*, 1665–1687.CrossRefGoogle Scholar - 7.Golombek, R., Greaker, M., Hoel, M. (2010). Carbon taxes and innovation without commitment.
*B.E. Journal of Economic Analysis and Policy*,*10*(1), 1935–1682.CrossRefGoogle Scholar - 8.Hoel, M., & Karp, L. (2001). Taxes versus quotas for a stock pollutant with multiplicative uncertainty.
*Journal of Public Economics*,*82*, 91–114.CrossRefGoogle Scholar - 9.Hoel, M., & Karp, L. (2002). Taxes versus quotas for a stock pollutant.
*Resource and Energy Economics*,*24*, 367–384.CrossRefGoogle Scholar - 10.Karp, L. (1992). Efficiency inducing tax for a common property oligopoly.
*Economic Journal*,*102*, 321–332.CrossRefGoogle Scholar - 11.Karp, L., & Livernois, J. (1992). On efficiency-inducing taxation for a non-renewable resource monopolist.
*Journal of Public Economics*,*49*, 219–239.CrossRefGoogle Scholar - 12.Karp, L., & Zhang, J. (2005). Regulation of stock externalities with correlated abatement costs.
*Environmental and Resource Economics*,*32*, 273–299.CrossRefGoogle Scholar - 13.Karp, L., & Zhang, J. (2006). Regulation with anticipated learning about environmental damages.
*Journal of Environmental Economics and Management*,*51*, 259–279.CrossRefGoogle Scholar - 14.Karp, L., & Zhang, J. (2012). Taxes versus quantities for a stock pollutant with endogenous abatement costs and asymmetric information.
*Economic Theory*,*49*, 371–409.CrossRefGoogle Scholar - 15.Kort, P.M. (1996). Pollution control and the dynamics of the firm: the effects of market-based instruments on optimal firm investments.
*Optimal Control Applications & Methods*,*17*, 267–279.CrossRefGoogle Scholar - 16.Kydland, F.E., & Prescott, E.C. (1977). Rules rather than discretion: the inconsistency of optimal plans.
*Journal of Political Economy*,*85*, 473–492.CrossRefGoogle Scholar - 17.Masoudi, N., & Zaccour, G. (2014). Emissions control policies under uncertainty and rational learning in a linear-state dynamic model.
*Automatica*,*50*, 719–726.CrossRefGoogle Scholar - 18.Martín-Herrán, G., & Rubio, S.J. (2016). The strategic use of abatement by a polluting monopoly.
*FEEM Nota di Lavoro, 58.2016*.Google Scholar - 19.Petrakis, E., & Xepapadeas, A. (2003). Location decisions of a polluting firm and the time consistency of environmental policy.
*Resource and Energy Economics*,*25*, 197–214.CrossRefGoogle Scholar - 20.Poyago-Theotoky, J., & Teerasuwannajak, K. (2002). The timing of environmental policy: a note on the role of product differentiation.
*Journal of Regulatory Economics*,*21*, 305–316.CrossRefGoogle Scholar - 21.Saltari, E., & Travaglini, G. (2011). The effects of environmental policies on the abatement investment decisions of a green firm.
*Resource and Energy Economics*,*33*, 666–685.CrossRefGoogle Scholar - 22.Stimming, M. (1999). Capital-accumulation games under environmental regulation and duopolistic competition.
*Journal of Economics*,*69*, 267–287.CrossRefGoogle Scholar - 23.Weitzman, M. (1974). Prices versus quantities.
*Review of Economic Studies*,*41*, 477–491.CrossRefGoogle Scholar - 24.Wirl, F. (2014). Taxes versus permits as incentive for the intertemporal supply of a clean technology by a monopoly.
*Resource and Energy Economics*,*36*, 248–269.CrossRefGoogle Scholar - 25.Xepapadeas, A.P. (1992). Environmental policy, adjustment costs, and behavior of the firm.
*Journal of Environmental Economics and Management*,*23*, 258–275.CrossRefGoogle Scholar - 26.Yanase, A. (2009). Global environment and dynamic games of environmental policy in an international duopoly.
*Journal of Economics*,*97*, 121–140.CrossRefGoogle Scholar