On the Optimal Number of Firms in the Commons: Cournot vs Bertrand

Abstract

We revisit the debate on the optimal number of firms in the commons in a differential oligopoly game in which firms are either quantity- or price-setting agents. Production exploits a natural resource and involves a negative externality. We calculate the number of firms maximizing industry profits, finding that it is larger in the Cournot case.

While industry structure is always inefficient under Bertrand behavior, it may or may not be so under Cournot behavior, depending on parameter values. The comparison of private industry optima reveals that the Cournot steady state welfare level exceeds the corresponding Bertrand magnitude if the weight of the stock of pollution is large enough.

Keywords: natural resources, oligopoly, pollution, tragedy of commons

JEL Classification: C73, L13, Q20, Q51