Optimal management of renewable resources : a general feedback approach

Abstract

Analytical solutions for optimal exploitation of renewable capital stocks are derived as feedback rules for a quite general optimization problem. By feedback rules is meant that optimal exploitation is given as an explicit function of the capital stock. The value of analytical expressions for the optimal control will be appreciated by all who have tried to determine the separatrix solutions numerically and experienced problems. The method described here can be applied to fisheries management, animal stock conservation and conservation of the environment in general. The operationality of the method outlined here is illustrated by two simple examples, one related to fisheries management and one related to pollution control.