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. I 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.

Optimal Exploration and Production of a Nonrenewable Resource Earlier studies of exhaustible resource production and pricing usually assume that there is a fixed reserve base that can be exploited over time. In reality there is no "fixed " reserve base (in an economically meaningful sense), since as price rises, additional proved and potential reserves become economical. Here we view a resource like oil as being "nonrenewable " rather than "exhaustible." There is a proved reserve base which is the basis for production, and exploratory activity is the means of increasing or maintaining this proved reserve base. "Potential reserves " are unlimited, but as depletion ensues, given amounts of ex-ploratory activity result in ever-smaller discoveries. Thus resource producers must determine simultaneously their optimal rate of exploratory activity and their optimal rate of production. Optimal trajectories for exploratory activity and production are determined for both competitive and monopolistic producers, and are applied to a simple model of oil production in the Permian region of Texas.