A Theory of 'Oil'Igopoly: Cournot Equilibrium in Exhaustible Resource Markets with Fixed Supplies

Abstract

The emergence of an effective and powerful cartel in the international petroleum market has stimulated considerable effort among economists to develop models of pricing and supply behavior for this industry.2 This modeling task poses two basic difficulties. First, as in the standard oligopoly problem, one must characterize the behavior of several sellers in a market, aware of each other and of their effect on market price. Second, there is here the added difficulty of treating the explicitly intertemporal nature of suppliers' decision, wherein a limited stock must be optimally allocated over time. This paper studies the implications of the simplest non-trivial postulates about these two aspects of the problem. It is assumed that suppliers are non-cooperative Cournot-Nash players, each of whom is imagined to select an optimal supply strategy taking as given the strategies of the others. Moreover, it is hypothesized that the feasible strategies are limited to open loop paths, chosen at the initial date to maximize the present value of profits in light of the paths of supply which the others have chosen.3 These basic postulates, together with a few technical assumptions concerning the structure of resource demand, permit one to demonstrate the existence of at least one non-cooperative equilibrium. Concerning thisequilibrium we show that: (1) the average and marginal return on resource stocks is inversely related to the size of a player's initial endowment; (2) aggregate production decreases over time until all stocks are exhausted, while firms with smaller stocks exhaust their supplies no later than firms with larger stocks do; (3) the present value of price net of extraction cost declines over time; (4) industry production maximizes a weighted average of intertemporal consumer's surplus and producers' profits;