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A dynamic model of renewable resource harvesting with Bertrand competition

Beard, Rodney (2008): A dynamic model of renewable resource harvesting with Bertrand competition.

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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.

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