Efficient propagation of shocks and the optimal return on money

We study optimal allocations in an environment in which money is essential due to lack of commitment and anonymity of individuals. Because the economy features aggregate preference shocks, we apply a notion of implementability that allows for allocations with non-trivial business-cycle dynamics for the propagation of shocks. We show that history dependence is predicted by the theory of second best and becomes necessary for optimality when the degree of patience is neither too low nor too high. Our analysis concludes with a discussion of whether there is a role for the propagation of shocks in alternative economic environments.