Thermodynamic constraints on optimal depletion of copper and aluminum in the United States: a dynamic model of substitution and technical change

Abstract

The paper proposes a methodology to integrate concepts from thermodynamics into economic models of optimal natural resource use and to empirically determine relationships between changes in thermodynamic states of materials and the use of high-quality energy sources. The integration is aimed at an assessment of technologies, substitution and technical change based on economic concepts that do justice to fundamental physical constraints. A model of natural resource use and production has been developed that combines econometric time series analysis with dynamic modeling techniques. The model explicitly includes thermodynamic constraints on (i) the process of separating minerals from crude ore, (ii) smelting processes, (iii) substitution among inputs, and (iv) endogenous technical change in mining, smelting and refining. Based on empirical information, the model has been simulated to assess outer limits of feasible resource savings in copper and bauxite mining, smelting and refining in the United States. Conclusions are drawn for the evaluation of products and effluents from mining, smelting and refining operations with regard to changes in the physical resource base and environmental quality.