Who is afraid of the Friedman rule?

We explore the connection between optimal monetary policy and heterogeneity among agents. We utilize a standard monetary economy with two types of agents that differ in the marginal utility they derive from real money balances — a framework that produces a nondegenerate stationary distribution of money holdings. Without type-specific fiscal policy, we show that the zero-nominal-interest-rate policy (the Friedman rule) does not maximize type-specific welfare; further, it may not maximize aggregate ex ante social welfare. Indeed one or, more surprisingly, both types of agents may benefit if the central bank deviates from the Friedman rule.