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Optimal exploitation of renewable resource stocks: necessary conditions

✍ Scribed by J. Baumeister; A. Leitão

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
302 KB
Volume
25
Category
Article
ISSN
0143-2087

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✦ Synopsis

Abstract

We study a model for the exploitation of renewable stocks developed in Clark et al. (Econometrica 1979; 47:25–47). In this particular control problem, the control law contains a measurable and an impulsive control component. We formulate Pontryagin's maximum principle for this kind of control problems, proving first‐order necessary conditions of optimality. Manipulating the correspondent Lagrange multipliers we are able to define two special switch functions, that allow us to describe the optimal trajectories and control policies nearly completely for all possible initial conditions in the phase plane. Copyright © 2004 John Wiley & Sons, Ltd.

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