Beard, Rodney (2008): A dynamic model of renewable resource harvesting with Bertrand competition.
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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 ) 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 . Consequently the results presented here are not only new, but possibly of greater empirical relevance than existing results on quantity competition.
|Item Type:||MPRA Paper|
|Original Title:||A dynamic model of renewable resource harvesting with Bertrand competition|
|Keywords:||linear-state differential game, Bertrand competition, renewable resources, fisheries|
|Subjects:||L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Q - Agricultural and Natural Resource Economics; Environmental and Ecological Economics > Q2 - Renewable Resources and Conservation > Q22 - Fishery; Aquaculture
D - Microeconomics > D4 - Market Structure and Pricing > D43 - Oligopoly and Other Forms of Market Imperfection
Q - Agricultural and Natural Resource Economics; Environmental and Ecological Economics > Q2 - Renewable Resources and Conservation > Q20 - General
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||Rodney Beard|
|Date Deposited:||30. May 2008 23:19|
|Last Modified:||12. Feb 2013 06:22|
 Adelaja, A., Menzo, J., McCay, B. Market power, Industrial organization and Tradable Quotas Review of Industrial Oganization, 13, pp. 589-601, 1998.  Arnold, M. Costly search, capacity constraints and Bertrand equilibrium price dispersion, International Economic Review 41(1), pp. 117-131, 2000.  Cellini, R and Lambertini, L. A dynamic model of dierentiated oligopoly with capital accumulation, Journal of Economic Theory, Vol. 83, pp. 145- 155.  Cellini, R., Lambertini, L. and Mantovani, A. Persuasive advertising under Bertrand competition: A dierential game, Operations Research Letters, Volume 36, Issue 3, 2008.  Dockner, E., Jorgensen, S., Long, N-V., Sorger, G. Dierential Games in Economics and Management Science, Cambridge University Press, 2000.  Feichtinger, G. and Dockner, E. Optimal pricing in a duopoly: a noncooperative dierential games solution Journal of Optimization Theory and Applications, vol. 45, No.2, pp. 199-218, 1985.  Gaudet, G. and Moreaux, M. Price versus Quantity Rules in Dynamic Competition: The Case of Nonrenewable Natural Resources, International Economic Review, Vol. 31, No. 3, pp. 639-650, 1990.  H�ardle, W. and Kirman, A. Nonclassical demand: a model free examination of price-quantity relations in the Marseille sh market, Journal of Econometrics, Vol. 67, pp. 227-257.  Jensen, F. and Vestergaard, N. Prices versus quantities in sheries models Land Economics, vol. 79, No. 3, pp. 415-425, 2003.  Kirman, A. and Vriend, N. Evolving market structure: An ACE model of price dispersion and loyalty, Journal of Economic Dynamics and Control, vol. 25, pp. 459-502, 2001.  Neher, P. Natural resource economics: Conservation and exploitation, Cambridge University Press, 1990.  Sandal, L. and Steinshamn, S. Dynamic Cournot-competitive harvesting of a common pool resource, Journal of Economic Dynamics and Control, 28, pp.1781-1799, 2004.  Spence, M. Product dierentiation and welfare The American Economic Review Papers and proceedings, Vol. 66, no.2, pp. 407-414, 1976.  Martin-Herran, G., Rincon-Zapatero, J. Ecient Markov perfect Nash Equilibria: theory and application to dynamic shery games, Journal of Economic Dynamics and Control 29, pp. 1073-1096, 2005.  Vilchez, M-L. and Velasco, F. and Herrero, I. An optimal control problem with hopf bifuracations: An application to the striped venus shery in the Gulf of Cadiz Fisheries Research, 67, pp. 295-306, 2004.  Weninger, Q. Equilibrium prices in a vertically co-ordinated shery, Journal of Environmental Economics and Management, Vol. 37, 290-305, 1999.