On the Optimal Order of Natural Resource Use When the Capacity of the Inexhaustible Substitute is Limited

Consider a general equilibrium framework where the marginal cost of extraction from several deposits of an exhaustible resource is constant in terms of an inexhaustible perfect substitute and differs between deposits. The instantaneous rate of production from the inexhaustible resource is subject to a capacity constraint. We show, under standard assumptions, that not only may it be optimal to begin using a high cost resource before a lower cost one is depleted, as shown in Kemp and Long (1980a), but it may be optimal to begin using it strictly before the lower cost one is even put into use. Thus the intuitive principle, derived from partial equilibrium analysis, that when the rate of discount is positive natural resources should always be exploited in strictly increasing order of costs, not only does not hold in a general equilibrium context, but may be totally reversed.