On the depletion of non-durable, non-renewable resources with a monopolistic supplier

The aim of this article is to provide elements to answer the question of how and when the situation the situation of depletion of a non-renewable, non-durable resource would be reached. To this end, a nonlinear programming model is used under the assumption that the resource is in the hands of a monopolist who knows the corresponding demand functions and is trying to maximize the present value of their net income. General properties of optimal extractive policies and corresponding prices are established, and the cases of negative exponential and linear demand functions are analyzed. The study shows that it is not possible to determine a pattern of optimal policy that is valid for all scenarios, since such a policy depends on the initial availability of the resource, the demand functions, the costs, the interest rate and the duration of the planning horizon adopted by the monopolist.