Heterogeneous discount rates: A generalization of Hotelling's rule

Abstract

In this paper we introduce the notion of the firm's discount rate as used in the context of modern financial theory into the theory of exhaustible resources. This leads us to considering heterogeneous firms with respect to discount rates due to dissimilar risks.

Our analysis follows the partial equilibrium approach and our techniques used are those of the deterministic optimal control. The problem addressed is as follows: Given a market of an exhaustible resource which has attained an equilibrium with the market price growing at a rate α, what is the optimal policy of a given competitive firm with a discount rate δ_i? We offer an answer to this problem, when extraction costs are fixed, and generalize Hotelling's rule by showing that firms with discount rates higher than the market price growth rate will all produce at maximum capacity.