DETERMINISTIC models demonstrate that when the economic discount rate of future harvests exceeds a critical value related to population growth rate, the strategy that maximizes the present value of cumulative harvest is immediate extinction (liquidation) of the population(1-3). Here we analyse stochastic models to derive optimal strategies that maximize the expected present value of cumulative harvest before extinction of a fluctuating population. Stochastic models reveal that discount rates below the critical value can substantially reduce the mean time to extinction and the expected real harvest before extinction. With an unstable equilibrium at small population size (Allee effect(4-6) or depensation(2)), the critical discount rate is lower in the stochastic model than in the corresponding deterministic model. These results argue against economic discounting in the development of optimal strategies for sustainable use of biological resources.