A Simple Model of Replenishable Natural Resource Exploitation

Abstract

The purpose of this paper is to consider maximum sustained yield programs of replenishable natural resource exploitation and to question the validity of these programs in satisfying social goals. In the treatment of such programs, two fundamental problems arise. The first is that the existence of a social discount factor (or interest rate) may cause the maximum sustained yield program to be nonoptimal.1 The second problem, considered recently in the literature, relates to the many externalities which may be present in harvesting resources.2 The most significant of these externalities is the 'stock' externality in production. That is, there is a potential misallocation of inputs in the production of natural resource product due to the fact that one input, the natural resource itself, contributes to production but may not receive payment (for example, its marginal product) because no one owns the resource. Recently, research in this area has been directed at finding optimal taxing schemes which will have the effect of assigning to an unappropriated natural resource its imputed rent.3 In this paper, a simple model will be developed which will illustrate the nature of the first of these problems in a case where the second problem is not present. To accomplish this, production will be assumed 'costless' in the sense that no inputs are used. (Production, which will be the same as consumption, has a 'cost' in the sense that it diminishes the stock of resource available for consumption in all subsequent periods.) The use of a natural resource in this model is parallel in theory to the use of capital, and the term 'investment' will be used here to indicate simply 'foregone consumption.' The intertemporal aspect of the problem suggests a dynamic model, and the model is formulated as an optimal control question. The approach parallels Kenneth Arrow in his treatment of the Reversible Ramsey Problem.