Resources for the Future
Krautkraemer and Toman
These conditions are known as the “Hotelling Rule” [see below] in honor of Hotelling's contribution to the literature. The first efficiency condition requires that at any point in time, the marginal gain from additional extractions equals the full opportunity cost of extraction, including the present value of future losses from a diminished future resource stock as well as conventionally defined incremental production costs.
The second efficiency condition requires that the rate of return to holding the asset be equal to the rate of discount. This condition can be thought of in terms of asset market equilibrium, since presumably the discount rate is the rate of return that could be earned by investing in other assets. The markets for assets will not be in equilibrium if the rate of return to holding one asset is greater than the rate of return to holding some other asset. If that were the case, investment in the higher (lower) return asset would increase (decrease). Thus, asset market equilibrium requires that the rate of return to holding a nonrenewable resource asset be the same as the rate of return to other assets in the economy as represented by the discount rate.
The user cost, or shadow price of the remaining stock, depends upon future extraction costs and the future price path. These depend in turn on developments in resource production technology, the size of the remaining stock, and future availability of substitutes. The future price of the resource can depend upon the general level of economic activity, so expectations about population and economic growth are important determinants of the scarcity rent or user cost. Technological progress can affect extraction cost, the availability of substitutes, and the remaining resource stock. For example, the development of directional drilling techniques has lowered the cost of extraction and increased the amount of recoverable oil from some deposits. Increased computing capability has enhanced the ability to use information from exploration activities and lowered the cost of discovering and developing new oil reserves (Bohi 1999).
The model we have described above can be extended in several directions. If we switch from considering a single competitive producer to a price-setting monopolist, we can infer that the monopolist will reallocate output from earlier to later in the life of the resource base, since this generates higher prices early on and near-term returns are worth more than discounted future returns. But since the stock of resource is fixed and is necessarily exhausted under either market structure, resources that are not produced earlier will be produced later. If, to take another scenario, the stock of the resource is fixed but uncertain, then again extraction early on would be