Abstract
This paper describes a simple linearized model for the optimal control of a natural resource stock. Applications of the model to fisheries and forestry, as well as to mineral exploration and recovery, are discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. J. Arrow, Optimal capital policy with irreversible investment, in J. N. Wolfe, ed.Value, Capital and Growth, Papers in Honour of Sir John Hicks, Edinburgh Univ. Press (Edinburgh), 1–20, 1968.
R. J. H. Beverton, and S. J. Holt,On the Dynamics of Exploited Fish Populations, Ministry Agr. Fish Food (London), Fish. Invest. Ser. 2 (19) (1957).
C. W. Clark, The economics of overexploitation, Science 181, 630–634, (1973).
C. W. Clark, and G. R. Munro, Economics of fishing and modern capital theory: a simplified approach,J. Environmental Economics & Management 2, 92–106 (1975).
H. S. Gordon, Economic theory of a common-property resource: the fishery, Journal of Political Economy62, 124–142, (1954).
R. L. Gordon, A reinterpretation of the pure theory of exhaustion, Journal of Political Economy75, 274–286, (1967).
H. Hermes, and J. P. La Salle,Functional Analysis and Time Optimal Control, Academic Press (New York), 1969.
H. Hotelling, The economics of exhaustible resources,Journal of Political Economy 39, 137–175, (1931).
M. D. Intriligator,Mathematical Optimization and Economic Theory, Prentice-Hall (Englewood Cliffs, N.J.), 1971.
P. Kilkki, and U. Vaisanen, Determination of the optimal policy for forest stands by means of dynamic programming,Acta Forestalia Fennica 102, 100–112, (1969).
L. S. Pontrjagin, V. S. Boltjanskii, R. V. Gamkrelidze, and E. F. Mishchenko,The Mathematical Theory of Optimal Processes, Pergamon (Oxford), 1964.
M. B. Schaefer, Some considerations of population dynamics and economics in relation to the management of marine fisheries,J. Fish. Res. Bd. Canada 14, 669–681, (1957).
R. M. Solow, The economics of resources or the resources of economics,American Economic Review 64, 1–14, (1974).
R. Uhler, The rate of petroleum exploration and extraction, University of B.C. Dept. of Economics, Resources Paper No. 14, (1977).
Author information
Authors and Affiliations
Additional information
Communicated by J. L. Lions
Research supported partially by the National Research Council of Canada, Grant A-3990.
Rights and permissions
About this article
Cite this article
Clark, C.W., De Pree, J.D. A simple linear model for the optimal exploitation of renewable resources. Appl Math Optim 5, 181–196 (1979). https://doi.org/10.1007/BF01442553
Issue Date:
DOI: https://doi.org/10.1007/BF01442553