Uncertainty and the pricing of exhaustible resources

Abstract

Demand and reserve uncertainty are included in a simple model of an exhaustible resource market by allowing the demand function and the reserve level to fluctuate via continuous-time stochastic processes. Thus, producers always know current demand and reserves, but do not know what demand and reserves will be in the future. We show that demand uncertainty has no effect on the expected dynamics of market price, while reserve uncertainty shifts the expected rate of change of price only if extraction costs are nonlinear in reserves. However if the demand function is nonlinear, both demand and reserve uncertainty affect the dynamics of production, whatever the character of extraction costs. The model is also extended to include exploration, first as a means of reducing uncertainty, and second as a means of accumulating reserves, with uncertainty over the future response of discoveries to exploratory effort.