Abstract
Using a bioeconomic model with two separate forms of uncertainty (a diffusion process and a jump process) a perturbation method is used to determine optimal reserve size for a harvested population with density-dependent growth. The results show that the benefits of reserves are understated in deterministic models and that, even with optimal harvesting, risk neutrality, a persistent population and without initial overexploitation, reserves have a positive economic value. Concavity of the value function with respect to optimal reserve size under uncertainty implies that, for many harvested populations, a positive economic return will arise from initially establishing small reserves, even when harvesting is optimal. The results also lead to general ‘rules of thumb’ when establishing reserves. Namely, that optimal reserve size rises with (1) the greater the rate of transfer from the reserve, (2) the greater the magnitude or the likelihood of negative shocks, (3) the more the actual harvest exceeds the optimal harvest, (4) the lower the intrinsic growth rate, (5) an increase in price or demand provided the population is between zero and its maximum yield, (6) an increase in marginal harvesting costs provided the population is between its maximum yield and carrying capacity and (7) the lower the discount rate.