ON THE OPTIMAL DEPLETION OF A NONRENEWABLE NATURAL-RESOURCE UNDER CONDITIONS OF INCREASING MARGINAL EXTRACTION COSTS

The model analyzed in this paper is that of the optimal exploitation o f a nonrenewable natural resource under the ownership of a monopolist who faces increasing marginal costs of extraction. Optimal depletion l evels are derived under the criterion of maximizing discounted future profits. It is shown that the optimal steady state solution may not ex haust the resource totally. The usual sufficiency conditions for optim al control (concavity of the maximized Hamiltonian in the state variab le) cannot be satisfied with this model. Hence a relatively new suffic iency condition is utilized.