Skip to main content
Log in

The economics of harvesting predator-prey systems

  • Published:
Journal of Economics Aims and scope Submit manuscript

Abstract

The economics of harvesting a renewable natural resource is well-developed in a framework where environmental conditions of the species looked at are kept constant. For the case of two interacting species as a prey-predator relationship the economics of harvesting one of the two species is analyzed. Questions of existence, uniqueness, and stability are looked at. Applying optimal control theory, a modified golden rule of harvesting is derived.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anderson, L. G. (1982): “Marine Fisheries.” InCurrent Issues in Natural Resources Policy, edited by P. R. Portney and R. B. Haas. Baltimore: John Hopkins.

    Google Scholar 

  • Beddington, J. R., and May, R. M. (1980): “Maximum Sustainable Yields in Systems Subject to Harvesting at More than One Trophic Level,”Mathematical Biosciences 51: 261–281.

    Google Scholar 

  • — (1982): The Harvesting of Interacting Species in a Natural Ecosystem.”Scientific American 247: 42–49.

    Google Scholar 

  • Berck, P., and Sydsaeter, K. (1991):Economists' Mathematical Manual. Berlin: Springer.

    Google Scholar 

  • Brauer, F., and Soudack, A. C. (1979): “Stability Regions and Transition Phenomena for Harvested Predator-Prey Systems.”Journal of Mathematical Biology 7: 319–337.

    Google Scholar 

  • Bulmer, M. G. (1976): “The Theory of Prey-Predator Oscillations.”Theoretical Population Biology 9: 137–150.

    Google Scholar 

  • Clark, C. W. (1976):Mathematical Bioeconomics: the Optimal Management of Renewable Resources. New York: Wiley.

    Google Scholar 

  • — (1982): “Models of Fishery Regulation.” InEssays in the Economics of Renewable Resources edited by L. J. Mirman and D. F. Spulber. Amsterdam: North-Holland.

    Google Scholar 

  • Clark, C. W., and Munro, G. R. (1975): “Economics of Fishing and Modern Capital Theory: a Simplified Approach.”Journal of Environmental Economics and Management 2: 92–106.

    Google Scholar 

  • Flaaten, O. (1988):The Economics of Multispecies Harvesting: Theory and Application to the Barents Sea Fisheries. Berlin: Springer.

    Google Scholar 

  • Gauze, G. F. (1964):The Struggle for Existence. New York: Hafner.

    Google Scholar 

  • Goh, B. S. (1976): “Global Stability in Two-Species Interactions.”Journal of Mathematical Biology 3: 313–318.

    Google Scholar 

  • Goh, B. S., Leitman, G., and Vincent, T. L. (1974): “Optimal Control of a Predator-Prey System.”Mathematical Biosciences 19: 263–286.

    Google Scholar 

  • Kamien, M. I., and Schwartz, N. L. (1981):Dynamic Optimization, The Calculus of Variations and Optimal Control in Economics and Management, 2nd edn. Amsterdam: North-Holland.

    Google Scholar 

  • Larkin, P. A. (1963): “Interspecific Competition and Exploitation.”Journal of the Fisheries Research Board of Canada 23: 647–678.

    Google Scholar 

  • — (1966): “Exploitation in a Type of Predator-Prey Relationship”.Journal of the Fisheries Research Board of Canada 23: 349–356.

    Google Scholar 

  • Leslie, P. H. (1948): “Some Further Notes on the Use of Matrices in Population Mathematics.”Biometrics 35: 213–245.

    Google Scholar 

  • Lotka, A. J. (1925):Elements of Physical Biology. Baltimore: Williams and Wilkins.

    Google Scholar 

  • May, R. M. (1980): “Modelle für zwei interagierende Populationen.” InTheoretische Ökologie, edited by R. M. May, Weinheim: VCH.

    Google Scholar 

  • Quirk, J. P., and Smith, V. L. (1970): “Dynamic Economic Models of Fishing.” InEconomics of Fisheries Management: a Symposium edited by A. D. Scott. Vancouver: University of British Columbia.

    Google Scholar 

  • Ragozin, D. (1982): “Self-regulating Two Species Systems Have no Limit Cycles.” Mimeo, University of Washington.

  • Samuelson, P. A. (1967): “A Universal Cycle?”Operations Research Verfahren 3: 170–183.

    Google Scholar 

  • Steele, H. H., and Henderson, E. W. (1984): “Modelling Long-term Fluctuations in Fish Stocks.”Science 224: 985–987.

    Google Scholar 

  • Ströbele, W. J., and Wacker, H. (1991): The Concept of Sustainable Yield in Multi-Species Fisheries.”Ecological Modelling 53: 61–74.

    Google Scholar 

  • Volterra, V. (1928): “Variations and Fluctuations of the Number of Individuals in Animal Species Living Together.”Journal du Conseil 3: 1–51.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ströbele, W.J., Wacker, H. The economics of harvesting predator-prey systems. Zeitschr. f. Nationalökonomie 61, 65–81 (1995). https://doi.org/10.1007/BF01231484

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01231484

Keywords

Navigation