A stochastic model for the economic management of a renewable animal resource

An optimal economic harvesting policy, which maximizes the present value of an animal population, capable of renewing itself, is discussed. It is assumed that, unhindered, the successive population levels, Xn, form a Markov chain, with transitions Xn+1=ƒ(Xn) + ϵnƒ(Xn) , where f is the recruitment function, and {ϵn} is an iid sequence of random shocks. When a positive set-up cost is present an optimal policy is of the (S,s) type. The optimal population level is compared with that of an equivalent deterministic model. Bioeconomic conditions, which imply the optimality of conservation, or extinction are investigated.