Optimality of Ramsey–Euler policy in the stochastic growth model

Abstract

For the canonical one sector stochastic optimal growth model, we outline a new set of conditions for a policy function that satisfies the Ramsey–Euler equation to be optimal. An interior Ramsey–Euler policy function is optimal if, and only if, it is continuous or alternatively, if, and only if, both consumption and investment are non-decreasing in output. In particular, we show that under these conditions, the stochastic paths generated by the policy must satisfy the transversality condition; the implication is that in applying our result, one does not need to verify the transversality condition when checking for optimality of a policy function.