Too many or too few? On the optimal number of firms in the commons

Abstract

In this paper, we consider common-pool non-renewable resource industries and study the socially optimal industry size. Our analysis is conducted in terms of an infinite-horizon differential game (with either open-loop or feedback strategies). We derive two main results. First, we show that there exists a unique state-independent efficiency-inducing industry size, ranging between 1 and infinity, if and only if the elasticity of the price-cost margin (capturing static market power) and the elasticity of the difference between social and private resource rents (capturing the tragedy of the commons) are the same. Second, allowing for entry/exit, we show that the regulator can set a license fee to be paid by firms to get access to the resource such that the endogenous number of firms in the equilibrium with regulated entry is socially optimal.