Perverse environmental effects of ambient charges in a Bertrand duopoly

Abstract

This paper investigates the effect of an increase in ambient charges on total pollution in a Bertrand-type duopolistic market. We analyse two distinct models. In the first model, the regulator announces the ambient charge and then both firms set their prices simultaneously. In the second model, after the regulator announces the ambient charge, both firms simultaneously choose their pollution abatement technologies in the first stage and prices in the second stage. An interesting conclusion of this paper is that in both models the strategic interaction between the firms can lead to a “perverse” ambient charge effect on total pollution. That is, an increase in the ambient charge may lead to greater pollution.

Keywords:

• ambient charge
• Bertrand duopoly
• environmental regulation
• pollution

Notes

1. Introducing uncertainty due to natural phenomena such as wind and rainfall does not bring about any substantial changes in the results. We rule out uncertainty and assume that total pollution generated by the firms is equal to the ambient concentration of the pollution. “Total pollution” and “ambient concentration” are used synonymously in this paper.

2. Ambient charges are not common but there are some real world examples of such charges. A recent study by the National Audit Office of Estonia tried to assess if ambient air pollution permits encouraged investment in pollution abatement technology. See http://www.riigikontroll.ee/Suhtedavalikkusega/Pressiteated/tabid/168/557GetPage/3/557Year/–1/ ItemId/9/amid/557/language/en-US/Default.aspx.

3. We assume that output and the polluting input are related by a fixed coefficient technology and there is no substitutability between polluting and non-polluting inputs. This makes the distinction between output-based pollution and input-based pollution trivial.

4. The formulation of the ambient charge in this paper follows directly from Segerson (1988) without the fixed penalty imposed whenever the ambient standard is exceeded.

5. These results may arise in perfect competition only if the stability conditions are not satisfied.

6. The equilibrium outputs at these prices are positive and the second order conditions for profit maximisation are satisfied.

7. The equilibrium quantities at these prices are positive. Also, the second order conditions for profit maximisation are satisfied at these equilibrium values.