Extraction Costs in the Theory of Exhaustible Resources

Abstract

This paper has two objectives.First, it reformulates the theory of optimal use of an exhaustible resource with more attention to the costs of extraction than has been customary in the literature.The output and shadow-price implications of optimal extraction are studied under these broader assumptions.Second, the paper provides some numerical solutions of a simple two-grade case, to give some feeling for the quantitative importance of changes in the supply of exhaustible resources.Our most striking result is, in fact, the suggestion that relatively large changes in resource availability generate very small changes in the sustainable level of final consumption. Q=C+K+eR.(5)The operation of the economy is now described by ( 1), (4), and (5).3At any instant the economy is characterized by its (constant) l We assume a > b for reasons explained in Solow (1974). 2 No difficulty of principle would be involved in allowing the distribution of resources by quality to be discrete or mixed.Later on, we do sample computations with a two-point distribution.3 From the form of ( 3) and ( 5), one can see that the model will bear an alternative