On the optimal harvesting of age-structured populations: Some simple models☆

Abstract In this paper we develop optimal harvesting policies for age-structured populations using a model for which the basic equations reduce to a pair of ordinary diffential equations for the total population and the per-capita birth-rate. Our assumptions insure the existence of a critical size Pc(t) which maximizes the instantaneous growth-rate at time t. We study the infinite-horizon problem, using the overtaking criterion of optimality, and show that: for a large population with ample per-capita birth-rate the optimal policy is to instantly reduce the stock to the critical value Pc(0), and then to harvest along the path Pc(t); for a sufficiently small population it is optimal to refrain from harvesting until the population reaches Pc(t), and then to harvest along Pc(t) for all subsequent time; for a large population with a small per-capita birth-rate, it is generally best to initially remove a given amount of stock, then to refrain from harvesting until the population reaches Pc(t), and finally to harvest alongPc(t).

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