Environmental Modeling & Assessment

, Volume 23, Issue 6, pp 671–689 | Cite as

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

  • Guiomar Martín-Herrán
  • Santiago J. RubioEmail author


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.


Monopoly Abatement Emission tax Emission standard Stock pollutant Differential games 



The authors would like to thank the participants at the IV Encuentro Conjunto Real Sociedad Matemática Española-Sociedad Matemática Mexicana (Valladolid), 23rd 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), 19th Annual BIOECON Conference (Tilburg), 17th International Symposium on Dynamic Games and Applications, and one anonymous referee for their helpful comments. Usual caveats apply.

Funding Information

Guiomar Martín-Herrán thanks the financial support from the Spanish Ministry of Economics and Competitiveness under projects ECO2014-52343-P and ECO2017-82227-P, and Junta de Castilla y León under project VA024P17. Santiago J. Rubio thanks the financial support from the Spanish Ministry of Economics and Competitiveness under project ECO2016-77589-R and Valencian Generality under project POMETEO II/2014/054.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Economics and IMUVaUniversity of ValladolidValladolidSpain
  2. 2.Department of Economic Analysis and ERI-CESUniversity of ValenciaValenciaSpain

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