EFFICIENCY AND OPTIMALITY IN STOCHASTIC-MODELS WITH PRODUCTION

We consider a discrete-time, infinite-horizon, one-good stochastic gro wth model and we solve the central planner's optimization problem by d eveloping a stochastic version of Pontryagin's maximum principle for M arkov controls. An approximation method is used in order to extend to an infinite horizon the stochastic maximum principle derived by Arkin and Evstigneev (1987) for the finite-horizon case. We obtain efficienc y conditions which are expressed in terms of stochastic multipliers, f or which we provide an economic interpretation. We also apply the math ematical tool we develop to a central planner's problem in an overlapp ing-generations model.