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A dynamic model of renewable resource harvesting with Bertrand competition

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  • Beard, Rodney

Abstract

In this paper a dierential game model of renewable resource ex- ploitation is considered in which rms compete in exploiting a com- mon resource in a Bertrand price-setting game. The model character- izes a situation in which rms extract a common renewable resource which after harvesting may be considered a dierentiated product. Firms then choose prices rather than harvest quantities. Quantities extracted are determined by consumer demand. Optimal price and harvest policies are determined in a linear state dierential game for whichr open-loop and feedback strategies are known to be equuiva- lent. Furthermore, the case of search costs and capacity constraints is analysed and the role they play in determining the dynamics of the resource stock is considered. The results are compared to those of Cournot competition which has been analysed extensively in the literature. Previous studies of dierential games applied to renewable resource harvesting have concentrated on quantity competition (see for example [12]) and the case of price competition has been largely ignored. the exceptions to this have been in the more empirical litera- ture where evidence for price competition versus quantity competition for renewable resources such as sheries is mounting [1]. Consequently the results presented here are not only new, but possibly of greater empirical relevance than existing results on quantity competition.

Suggested Citation

  • Beard, Rodney, 2008. "A dynamic model of renewable resource harvesting with Bertrand competition," MPRA Paper 8916, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:8916
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    File URL: https://mpra.ub.uni-muenchen.de/8916/1/MPRA_paper_8916.pdf
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    References listed on IDEAS

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    1. Weninger, Quinn, 1999. "Equilibrium Prices in a Vertically Coordinated Fishery," Journal of Environmental Economics and Management, Elsevier, vol. 37(3), pages 290-305, May.
    2. Kirman, Alan P. & Vriend, Nicolaas J., 2001. "Evolving market structure: An ACE model of price dispersion and loyalty," Journal of Economic Dynamics and Control, Elsevier, vol. 25(3-4), pages 459-502, March.
    3. Arnold, Michael A, 2000. "Costly Search, Capacity Constraints, and Bertrand Equilibrium Price Dispersion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 117-131, February.
    4. Gaudet, Gerard & Moreaux, Michel, 1990. "Price versus Quantity Rules in Dynamic Competition: The Case of Nonrenewable Natural Resources," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 639-650, August.
    5. Martin-Herran, G. & Rincon-Zapatero, J.P., 2005. "Efficient Markov perfect Nash equilibria: theory and application to dynamic fishery games," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1073-1096, June.
    6. Hardle, Wolfgang & Kirman, Alan, 1995. "Nonclassical demand : A model-free examination of price-quantity relations in the Marseille fish market," Journal of Econometrics, Elsevier, vol. 67(1), pages 227-257, May.
    7. Neher,Philip A., 1990. "Natural Resource Economics," Cambridge Books, Cambridge University Press, number 9780521311748, March.
    8. Spence, Michael, 1976. "Product Differentiation and Welfare," American Economic Review, American Economic Association, vol. 66(2), pages 407-414, May.
    9. Frank Jensen & Niels Vestergaard, 2003. "Prices versus Quantities in Fisheries Models," Land Economics, University of Wisconsin Press, vol. 79(3), pages 415-425.
    10. Cellini, Roberto & Lambertini, Luca, 1998. "A Dynamic Model of Differentiated Oligopoly with Capital Accumulation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 145-155, November.
    11. Sandal, Leif K. & Steinshamn, Stein I., 2004. "Dynamic Cournot-competitive harvesting of a common pool resource," Journal of Economic Dynamics and Control, Elsevier, vol. 28(9), pages 1781-1799, July.
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    Cited by:

    1. Florian Diekert, 2012. "Growth Overfishing: The Race to Fish Extends to the Dimension of Size," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 52(4), pages 549-572, August.

    More about this item

    Keywords

    linear-state differential game; Bertrand competition; renewable resources; fisheries;

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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