A translog normalized restricted profit function is used to study the characteristics of the production function for electric energy. The results indicate that fuel choice in existing steam electric plants responds to changes in fuel prices. The production function is also tested for separability of fuels from capital and labor, homotheticity, returns to scale, and embodied technical change.

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

In nonrenewable resource industries, the existence of a markup of price over marginal market cost may reflect the existence of an implicit user cost for the resource rather than market power. We show that valid estimates of market power can be obtained by the joint estimation of a restricted cost function and an inverse supply relation. Estimation of the model with data for the largest firm in the international nickel industry indicates that output price substantially exceeded marginal market cost, with most of the difference due to the exercise of market power rather than the user cost of the resource.

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.