Optimal Economic Growth And Uncertainty: The Discounted Case

The cornerstone of one-sector optimal economic growth models is the existence and stability of a steady-state solution for optimal consumption policies. The optimal consumption policy is the stable branch of the saddle point solution of the system of differential equations governing the dynamics of the economy. Examples of this type of behavior can be found in Cass [2] and Koopmans [4]. However, the stable branch solution is a knife-edge policy in the sense that any perturbation, no matter how small, results in instability and eventual annihilation. (This phenomenon is true when the Euler conditions are adhered to after the perturbation). Small pertubations might occur due to observation errors or the lack of knowledge of the exact production functions. It seems reasonable to expect that all sorts of human errors influence decision variables. Hence unless perfect knowledge of all variables, present and future, were known with complete certainty, and unless all decisions were made with exactness, economies of the one-sector deterministic type would lead at best to suboptimal consumption and investment policies. One would expect analogous instability results if production due to aggregation error, say, were not known with certainty. Moreover, it should be expected that planners know the future with something less than certainty. Since it seems impossible, in the face of uncertainty of the future,