Optimality of Ramsey-Euler policy in the stochastic growth model

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.