Second best pricing policies for an exhaustible resource

In the theory of exhaustible resources, the classical result, originally derived by Harold Hotelling (J. Polit. Econ., 39: 137-75 (1931)) is that the scarcity rent of the resource must increase at the rate of interest. The scarcity rent is the market price of the resource less extraction costs. At the depletion time, the market price must be equal either to the zero demand price or the cost of a perfect substitute, assuming no adjustment costs in switching to the substitute. The substitute may be either a natural resource with a higher extraction cost or a backstop technology. The Hotelling result is a price equilibrium condition in a competitive asset market (Solow, Amer. Econ. Rev. Proc., 64: 1-14 (1974)). It is also an efficiency condition for allocating the resource over time in a first best world. However, Solow raises the possibility that constraints creating a wedge between interest rates may be important considerations in the resource allocation problem. In a second-best world it is not at all clear how fast the scarcity rent of the resource should increase from a social viewpoint. However, for one simple case the analysis of this problem is straightforward. Suppose consumption is determined by a Keynesianmore » consumption function with marginal propensity to consume (1 - s); s is marginal propensity to save. With consumption determined in this behavioral manner, savings may be inadequate to reduce the market interest rate to the point where it is equal to the social rate of time preference. It is argued here that for this case the scarcity rent of the resource should increase at a rate equal to a weighted combination of these two interest rates.« less