Capital-Resource Substitution and the Discount Effect in Depletable Resources

Abstract

It is a central proposition of the economics of natural resources that an increase in the discount rate will cause an increase in the rate of extraction for depletable minerals. This traditional discount derives from treating the resource stock as a kind of capital, which will be left in unprocessed form only when the opportunity cost of so doing is low (the Hotelling Rule [10]). This relationship is a cornerstone of the contention by some resource economists that a competitive resource industry extracts too fast, for it is held that risk raises the discount rate used by resource firms above the optimal rate for society. The high real discount rates of recent years, in this view, were also seen as a major contributor to the depressed mineral markets of the early 1980s. Mineral extraction and processing is highly capital-intensive, however, and the opportunity cost of capital will be increased by a higher discount rate. When this disinvestment effect is included Gordon [5], in fact, showed that the overall discount is ambiguous. Neher [13] and Farzin [2], employing specialized assumptions concerning the extractive technology, subsequently showed the sign of the to depend on the relative present values of capital and resource costs in overall mineral extraction and processing.' The purpose of this paper is to extend Neher and Farzin's result by analyzing the discount in terms of general resource industry characteristics such as the elasticity of demand and of substitution, as well as the shares of capital and unprocessed resources in overall cost. We then attempt to apply our results in the third section of the paper using parameters estimated by others for a number of resource industries. Given these parameters it appears that the usual effects of discount changes do apply with respect to the value and price of the unprocessed resource, an increase in the discount rate increasing the demand and lowering the value of the raw mineral, but this is not the case with respect to the processed resource. Because of relatively high capital intensity, over half of the mineral industries surveyed appear to behave as non-resource industries in that they can be expected to reduce overall processed mineral output in response to a discount rate increase. 1. Neher, following Gordon, employed a model in which mineral output is identical with the raw resource input, and in which capital cost is a fixed proportion of the total cost of extracting the resource. This implies the average cost of extraction is simply the sum of average capital and resource costs, unlike in the model to follow, and could realistically apply only to the very first stage of mineral processing.