Conclusions concerning trends in natural resource scarcity may depend critically on the choice of scarcity index. Unfortunately, the prevalence of vertical integration in natural resource industries has hindered the use of some otherwise desirable scarcity measures. In this paper duality theory is used to derive an econometric procedure for estimating one such measure, the shadow price of the resource in situ. Empirical results for the Canadian metal mining industry indicate that resource scarcity as measured by this shadow price has decreased substantially over time.

Robert Halvorsen, Tim R. Smith, Substitution Possibilities for Unpriced Natural Resources: Restricted Cost Functions for the Canadian Metal Mining Industry, The Review of Economics and Statistics, Vol. 68, No. 3 (Aug., 1986), pp. 398-405

Conclusions concerning trends in natural resource scarcity may depend critically on the choice of scarcity index. Unfortunately, the prevalence of vertical integration in natural resource industries has hindered the use of some otherwise desirable scarcity measures. In this paper duality theory is used to derive an econometric procedure for estimating one such measure, the shadow price of the resource in situ. Empirical results for the Canadian metal mining industry indicate that resource scarcity as measured by this shadow price has decreased substantially over time.