The Effect of the Discount Rate on the Optimal Exploitation of Renewable Resources

Abstract

In a recent paper, Farzin (1984) has shown that the impact of the discount rate on the optimal rate of depletion of an exhaustible resource is ambiguous. This is so because not only is the discount rate an expression of time preference, it also reflects the opportunity cost of capital. As the extraction of an exhaustible resource typically requires investment in buildings, equipment, etc. , a higher discount rate will raise the cost of extraction. In terms of the Hotelling rule, dP/dt = r(P c ) where P is the price of the extracted product, c is the unit cost of extraction, and r is the discount rate, a higher r will be associated with a higher c, and so the implication for the rate of price increase is ambiguous. Furthermore, a higher discount rate is likely to affect the backstop price of the resource. What, then, about renewable resources? Ever since Clark's famous paper on the discount rate and the extinction of animal species (Clark, 1973), it has been recognized that a higher dis-