We explore the connection between optimal monetary policy and heterogeneity among agents in a standard monetary economy with two types of agents where the stationary distribution of money holdings is nondegenerate. Sans type-specific fiscal policy, we show that the zero-nominal-interest rate policy (the Friedman rule) does not maximize type-specific welfare; it may not maximize aggregate ex ante social welfare either. Indeed, one or, more surprisingly, both types may benefit if the central bank deviates from the Friedman rule.