Efficiency and optimality in stochastic models with production

We consider a discrete-time, infinite-horizon, one-good stochastic growth model and we solve the central planner's optimization problem by developing a stochastic version of Pontryagin's maximum principle for Markov 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 efficiency conditions which are expressed in terms of stochastic multipliers, for which we provide an economic interpretation. We also apply the mathematical tool we develop to a central planner's problem in an overlapping-generations model.