On the Friedman Rule with Heterogeneous Agents

We consider a general equilibrium model where monetary policy has redistributive effects. Agents have stochastic preferences and face random buying and selling opportunities. We show that the Friedman rule is just the second best policy. However, the Friedman rule is Pareto optimal. It requires to set the gross growth rate of the money supply equal to the discount factor of the most patient agents. Second, we look at the real effects of a money supply shock. In contrast to standard infinitely-lived-representative-agent models, under the Friedman rule a positive shock increases aggregate production and consumption. Interestingly, the shock has no real consequences if monetary policy deviates from the Friedman rule