The Optimal Consumption of Depletable Natural Resources: An Elaboration, Correction, and Extension

M. L. Cropper; Milton C. Weinstein and Richard J. Zeckhauser , The Quarterly Journal of Economics, Vol. 92, No. 2. (May, 1978), pp. 337-344. 92(2) , 337-334 , May 1978.

Competitive behavior in an extractive industry with increasing
marginal costs of production will generate a socially efficient pattern
of production over time. The Weinstein-Zeckhauser analysis of this
result assumed that marginal extraction costs at a mine depend only
on the amount extracted from the mine to date. This note clarifies the
original Weinstein-Zeckhauser proof and goes on to consider more
explicitly what happens when extraction costs depend not only on the
amount extracted at each site, but also on the firm doing the extraction.
When costs of extraction at a site depend only on the cumulative
amount extracted there to date, all that is required for efficiency is
that there be competitive markets for the extracted commodity.
Section 2 of this note shows that the optimality result need not apply
if technological capabilities differ among firms (or nations), so that
the cost of extraction depends as well on the firm extracting the resource.
However, if there exist competitive markets for trading extraction
technologies or extraction rights, an efficient outcome is
guaranteed. This situation of differential extraction costs is obviously
of considerable policy relevance, particularly as the ownership of
natural resource deposits shifts increasingly toward the developing
world and away from the more technologically advanced nations. In
recognition of this situation, both categories of nations have made
recent proposals to facilitate the trade and transfer of extractive

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