In this paper, we explore the connection between optimal monetary policy and heterogeneity among agents. We study a standard monetary economy with two types of agents in which the stationary distribution of money holdings is non-degenerate. 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 social welfare either. Indeed, one or, more surprisingly, both types may benefit if the central bank deviates from the Friedman rule. Our results suggest a positive explanation for why central banks around the world do not implement the Friedman rule.