Academic journal article Quarterly Journal of Business and Economics

A Test of the Theory of Exhaustible Resources

Academic journal article Quarterly Journal of Business and Economics

A Test of the Theory of Exhaustible Resources

Article excerpt

I. INTRODUCTION

More than half a century ago Hotelling |1931~ provided a rigorous theoretical model of the dynamic behavior of private markets for exhaustible resources. After a long period of relative neglect, the theory of exhaustible resources has received greatly increased attention since the early 1970s, and there now exists a large and well-developed literature based on the theoretical framework introduced by Hotelling. However, the ability of the theory of exhaustible resources to describe and predict the actual behavior of resource markets remains an open question.

The principal obstacle to empirical tests of the theory of exhaustible resources has been data availability. The implications of the theory for economic behavior are expressed in terms of the time path of the shadow price of the unextracted resource (also referred to as the resource's in situ price, scarcity rent, or net price). However, because of vertical integration in natural resource industries, market transactions generally occur only after a resource has been extracted and processed. In addition, the effect of cumulative extraction on the marginal cost of extraction, which is one of the major theoretical factors determining the time path of prices, is not directly observable.

In this paper we use duality theory to derive an econometric model that provides a statistical test of the theory of exhaustible resources. Following Halvorsen and Smith |1984~, a restricted cost function is used to obtain estimates of the shadow prices of unextracted resources from cost and production data for vertically integrated natural resource industries. The restricted cost function used here also provides estimates of the effects of cumulative extraction on the marginal cost of extraction.

The implications of the theory of exhaustible resources are expressed as parametric restrictions on the restricted cost function model and are tested using a Hausman |1978~ specification test. The procedure is illustrated with data for the Canadian metal mining industry. For this industry the parametric restrictions implied by the theory of exhaustible resources are strongly rejected.

The following section reviews the implications of the theory of exhaustible resources for the behavior of vertically integrated natural resource firms. The results of previous attempts to test the empirical relevance of the basic theoretical framework are reviewed in Section III. The econometric model is described in Section IV, and the empirical results are discussed in Section V. Section VI contains concluding comments.

II. THE THEORY OF EXHAUSTIBLE RESOURCES

This section reviews the implications of the theory of exhaustible resources for the dynamic behavior of private markets for exhaustible resources. Except for explicitly recognizing that firms may process as well as extract the resource, the model is a standard competitive market model of exhaustible resource extraction under conditions of certainty (see, e.g., Levhari and Liviatan |1977~ and Weinstein and Zeckhauser |1975~). The principal feature of the model that distinguishes it from Hotelling's original competitive model is that extraction costs are assumed to be a function of cumulative extraction as well as of the current rate of output.

The resource-owning firm is assumed to be vertically integrated in that it engages in both the extraction and processing of an exhaustible resource. In each period the firm chooses the quantity of final output of the extracted and processed resource, Q, the quantity of the resource to be extracted, N, and the vectors of reproducible inputs, |Mathematical Expression Omitted~, to be used in the extraction and processing activities, respectively.

Assuming that the quantities of inputs used in extraction are separable from those used in processing, the firm's production function can be written as

(1) |Mathematical Expression Omitted~

where Z is cumulative extraction, time T indexes the state of technology, and N(*) is the extraction subproduction function. …

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