Exhaustible Resources in a Dynamic Input–Output Model with ‘Classical’ Features

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Abstract
This paper discusses the problem of exhaustible resources in a dynamic input–output model with ‘classical’ features. Both the quantity side and the price and distribution side are discussed. The argument is developed using the simplifying assump- tions that there is no technical progress and that no new deposits of the exhaustible resources are discovered. To avoid the ' end-of-world’ scenario, it is assumed that there is a ‘backstop technology’: this implies that exhaustible resources are useful but not necessary in the production and reproduction of commodities. A necessary and sufficient condition for the existence of paths of prices, quantities produced, and stocks of resources converging to the ultralong-period position is determined, provided that the backstop technology exhibits some appropriate properties. In addition, an algorithm to determine these paths is suggested. A numerical example illustrates the findings.