An economic model is developed for petroleum reservoir management; this model includes interaction among current production rates, the role of investment, and the possible dependence of recoverable stocks on the time-path of production. The model depicts production relations in a manner consistent with current methods used by petroleum engineers to predict reservoir performance. Section I provides a physical description of a petroleum reservoir. The management model is presented in Section II. Section III interprets economically the resulting decision rules for production and investment, while Section IV expands discussion of the implications of such rules for policy and compares results from previous works. The concluding section suggests extending this management model to determine optimal expenditures for exploration. (30 references) (BYB)