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The conservation and exploitation of vulnerable resources

1992; Springer Science+Business Media; Volume: 54; Issue: 2-3 Linguagem: Inglês

10.1007/bf02464829

1522-9602

William J. Reed, Hector Echavarría Heras,

Economic theories and models

The maximum principle of deterministic optimal control, which has proved to be a very useful tool in theoretical bioeconomics, is extended in this article to cover the optimal exploitation of a biological resource vulnerable to catastrophic collapse, the probability of which may depend in general on the state of the resource, the current control and time. A general formulation of the maximum principle for such stochastic problems is presented and a number of applications are outlined. These include: optimal harvesting of a fishery vulnerable to catastrophic collapse; optimal thinning of a forest vulnerable to fire; optimal expenditure and investment in forest fire protection and optimal consumption-pollution tradeoffs in an ecosystem vulnerable to pollution-related collapse. In addition an application of the method to a highly stylized behavioral ecology model is given.