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.

Most studies of nonrenewable resource production and pricing assume there is a fixed reserve base to be exploited over time, but in fact, with economic incentives reserves can be increased. Here we treat the reserve base as the basis for production and exploratory activity as the means of increasing or maintaining reserves. "Potential reserves" are unlimited, but as depletion ensues, given amounts of exploratory activity result in ever smaller discoveries. Given these constraints, resource producers must simultaneously determine their optimal rates of exploratory activity and production. We solve this problem for competitive and monopolistic markets and show that if the initial reserve endowment is small, the price profile will be U-shaped; at first production will increase as reserves are developed, and later production will decline as both exploratory activity and the discovery rate fall.