Optimal harvesting of a fishery subject [to] random catastrophic collapse

Date

2009-08-20T00:29:10Z

Authors

Reed, William

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Abstract

The socially optimal harvesting policy for a fishery subject to random catastrophic collapse is determined. It is shown how the problem can be converted to one of deterministic optimal control, and a solution obtained using the Pontryagin Maximum Principle. The optimal stock biomass satisfies a golden-rule equation containing extra terms reflecting the density-dependent and density-independent effects of the risk of collapse. These effects have opposite influences on the optimal biomass level. The optimal policy when there is the possibility of a recovery after a collapse is discussed. Economic interpretations of the results are given, and some numerical results presented.

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Keywords

optimal harvesting, catastrophic collapse, hazard, golden rule equation, bioeconomics, maximum principle, stochastic dynamic programming

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