Prices of durable nonrenewable natural resources under stochastic investment opportunities

We take a capital asset pricing approach to the determination of the price of a nonrenewable natural resource in the case where the resource is durable, in the sense that once extracted it becomes a productive asset held above ground. The portfolio choice is then made up of the following assets: a stock of nonrenewable resource held in the ground that yields no dividend, a stock of resources held above ground that yields a dividend in the form of a flow of productive services, and a stock of composite good that can be held either in the form of productive capital or of a bond whose return is given. There is a stochastic element to the rate of change of productivity in both the production of the composite good and in the extraction of the resource. It is shown that the resulting prediction for the price path of the resource differs considerably from the one that follows from the elementary Hotelling model and that no unambiguous prediction can be drawn analytically about the pattern of behavior of that price path.