A Markov Decision Process model is developed for analyz­ ing the socially optimal allocation of a replenishable or non replen­ ishable resource over time. The resource is managed by choosing the rate of extraction in each period to maximize the discounted stream of expected social returns. Elements of uncertainty enter the analysis in three ways:                                                                                (1) Uncertainties may exist about the current size of the resource, either because of difficulties in observing the stock, as in the case of a fishery, or because of the possibilities of finding new reserves th:rough exploration, as in the case of minerals and oil.  (2) The market value of the resource and the cost of extracting it may be random, due to varyingeconomic conditions. (3) Unpredictable changes in the environ­ ment may perturb the natural rate of growth or deterioration of the resource, as well as the effective rate of depletion by man.

The model is used to answer these questions: How do opti­mal programs for allocating resources in a deterministic environ­ ment compare with optimal programs under stochastic conditions? Do different attitudes toward social risk bearing as regards varia­ tions in resource rents, have an effect on optimal decision rules? What is the effect of increased uncertainty about resource prices, extraction costs,  and resource  growth and depletion rates on optimal programs?

The questions posed above are considered in the context of an empirical study. of the Eastern Pacific yellowfin tuna fishery. The main conclusions of the study are that: (1) Optimal programs for resource management are more moderate, with smaller varia­ tions in the rate  of fishing over time, when society is risk averse rather than risk neutral. This difference betweeen risk neutral and risk averse programs is accentuated with increasing uncertainty about market prices,  fishing costs, and the future availability of the resource, (2) "Cyclical" fishing, in which the stock is depleted rapidly over a short time period and then allowed to grow back, is optimal if scale economies exist in the fishing industry. This con­trasts with the optimal ''steady state" fishing programs that are emphasized in the control theory literature on resource management.