The Commons and the Optimal Number of Firms

Abstract

The problem of the is a frequently cited example of market failure in which exploiters' pursuit of profits does not lead to the attainment of a social or Pareto optimum. In particular, a free-access equilibrium induces an unrestricted number of exploiters or firms to equate the variable input's average product, instead of its marginal product, to the input's real rental rate; hence, the rents of the variable input are driven to zero [Haveman, 1973].1 When the number of firms in a commons is unrestricted, the scarce factor (e.g., the fishery, the hunting ground) is not imputed a rent. A social optimum can be achieved if a single firm exploits a commons and sells its output in a perfectly competitive market [Weitzman, 1974]. The purpose of this note is to derive an expression for the optimal number of firms exploiting a commons when the resulting output is sold in an imperfectly competitive market.2 Since demand inelasticity due to monopoly power leads to overconservation, while an increase in the number of exploiting firms typically leads to underconservation, a finite number of firms for a commons can be found corresponding to a social or Pareto optimum. In particular, the optimum number of firms depends directly on the elasticity of the input productivity and inversely on the price elasticity of market demand.