The Optimal Exploration and Production of Nonrenewable Resources

Abstract

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.