Optimal Starting and Stopping Rules for Resource Depletion when Price is Exogenous and Stochastic

Abstract

Optimal developement of exhaustible natural resources is analyzed under the assumption that oil prices follows a geometrical browninan motion: Under specific assumption on cost structure closed form soltions for the reservation price (the price above which start of depletion is optimal), the halt price (the price below which shut down is optimal), and the start halt price (where no production is optimal below, and full capacity utilization is optimal above) are derived. From the theorems we derive rules of thumb for the impact of uncertainty and the impact of different types of costs. In the final section we demonstrate in a numerical model that our rules of thumb applies even to more general cases than those studied in the analytical part of the paper.