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Conservation and the Theory of Exhaustible Resources*

Published online by Cambridge University Press:  07 November 2014

Richard L. Gordon
Richard L. Gordon*
Affiliation:
Pennsylvania State University
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Conservationists have long argued that the free market neglects the needs of future generations. Economists who have examined this argument have stressed the dubious realism of any rigorous formulation of the conservationist position, but relatively little attention has been paid to the implications of policies designed to increase the weight given to future demands. Scott has conjectured that such policies might speed exhaustion of mineral resources. If he is correct, the usual conservationist argument that neglect of the future is equivalent to a too rapid use of resources would no longer hold. This article seeks to provide a rigorous proof of Scott's hypothesis.

The economic literature has shown that all rigorous definitions of neglect of the future involve the use of higher than “desirable” interest rates. To explore the consequences of such interest rates, one requires a theory of how resource producers act. Such guidance is provided by the Gray-Hotelling pure theory of exhaustion. A simple test of the basic question is provided by showing how an industry that behaves according to theory would alter its actions if interest rates were lowered.

Section III of this paper provides such a test. The first two sections provide the necessary preliminaries—examination of the justifications given for the contention that interest rates are too high, and a brief explanation of the pure theory of exhaustion. The final section discusses further implications of the basic theorem set out in Section III.

La conservation et la theorie des ressources epuisables

La Conservation et la Theorie des Ressources Epuisables

La littérature sur la conservation comporte depuis longtemps des discussions à propos de l'effet du taux d'intérêt du marché sur la répartition temporelle de l'exploitation des ressources naturelles. On peut prétendre que le taux du marché est trop élevé par suite des divergences qui existent entre le risque privé et le risque social. Ou encore, on peut invoquer l'argument de Ramsey à l'effet que l'utilité future ne devrait pas être escomptée pour défendre un taux d'intérêt social plus bas. Les auteurs qui ont centré l'attention sur l'effet d'escompter les revenus futurs ont souligné que des taux d'intérêt plus élevés avaient tendance à réduire l'attrait du futur et par conséquent à hâter l'exploitation. Scott a supposé que des taux d'intérêt plus élevés, en réduisant l'investissement, avaient tendance à retarder l'exploitation. Ces propositions n'ont jamais été vérifiées à l'aide du modèle économique qui s'y rapporte, à savoir la théorie de Gray-Hotelling sur les ressources épuisables.

Dans cet article, grâce à une modification au modèle le plus simple de Hotelling, on montre que l'effet net des changements du taux d'intérêt sur la répartition temporelle de la production des ressources épuisables est indéterminé. Des taux d'intérêt plus élevés peuvent prolonger ou réduire l'existence d'une ressource. L'observation est aussi faite que l'horizon fini (bliss) dans le modèle de Ramsey est incompatible avec l'existence de ressources épuisables. L'exploitation des mines constitue un investissement profitable qui doit être terminé avant la fin du monde; à un taux d'intérêt égal à zéro pour toujours, il est profitable de toujours attendre avant de miner.

Type
Research Article
Information
Canadian Journal of Economics and Political Science/Revue canadienne de economiques et science politique , Volume 32 , Issue 3 , August 1966 , pp. 319 - 326
Copyright
Copyright © Canadian Political Science Association 1966

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Footnotes

*

This paper was inspired by discussions with Anthony Scott and Orris Herfindahl about their manuscripts on the pure economics of mining. Dr. Herfindahl and my colleague, Thomas Iwand, provided valuable comments, particularly on the use of the Ramsey model.

References

1 Scott, Anthony, Natural Resources: The Economics of Conservation (Toronto, 1955) 78–80.Google Scholar

2 Gray, L. C., “Rent Under the Assumption of Exhaustibility,” Quarterly Journal of Economics, 05 1914, 466–89CrossRefGoogle Scholar; Hotelling, H., “The Economics of Exhaustible Resources,” Journal of Political Economy, 04 1931, 137–75.CrossRefGoogle Scholar Gray used numerical examples and dealt with the individual firm; Hotelling, the calculus of variations and the industry. The present author has recently completed a manuscript presenting a reinterpretation of this work.

3 See Scott, , Natural Resources, 88–98 Google Scholar, and Herfindahl, O. C., “Goals and Standards of Performance for the Conservation of Minerals,” Quarterly of the Colorado School of Mines, 10 1962, 153–71.Google Scholar

4 A review of Ramsey's model and the requisite mathematics appears in Allen, R. G. D., Mathematical Analysis for Economists (London, 1938), 537–40.Google Scholar

5 Conard, J. W., An Introduction to the Theory of Interest (Berkeley, 1959), 83–9.Google Scholar

6 Herfindahl, , “Goals and Standards,” 162–6Google Scholar, and Scott, , Natural Resources, 88–98.Google Scholar

7 Note that the theory implies that the conventional profit maximization rule MR = MC is no longer valid. It pays to sacrifice some profits in earlier periods so one can enjoy more valuable profits later. The presentation here abstracts from complications introduced when costs depend upon both the current rate of production (qt ) and cumulative production. The rigorous proof of all this is derived by introducing Hotelling's definition of exhaustion as a constraint on the present value function and maximizing present value subject to the constraint.

8 This condition assumes that production actually occurs currently; the model discussed below employs assumptions that guarantee this. In general, however, growth at r per cent starts when production starts and some deposits may not be exploited until a later date.

9 Prices that do not satisfy (4) will cause concentration of output at a single point of time. For example, if prices do not rise at all, the present value of marginal profits is greatest at time zero and all output would occur at zero. However, this would normally create a disequilibrium. The output planned for time zero would probably exceed that demanded at the assumed price; supply in other periods would obviously be below demand at the price. Only prices satisfying (4) would avoid such concentration and make equilibrium possible.

10 The life approaches infinity as the interest rate approaches its upper limit so that quite different maximum life figures emerge depending upon the cutoff rate used. For example, in this case, the life at 22.5 per cent is some 19,000 years.

11 Natural Resources, 88–98.