We study several popular monetary models which generate a non-degenerate stationary distribution of money holdings. Across these environments, our principal finding is as follows: a monetary policy that sets long run nominal interest rates to zero (the Friedman rule) does not typically maximize ex-post social welfare if it can generate redistributive effects. An increase in the rate of growth of the money supply has the standard partial-equilibrium effect of making money a less desirable asset thereby decreasing the utility of all moneyholders. A second, general-equilibrium effect, is a transfer from one type of agent to the other. For each environment, when the rate of growth of the money supply is not too high, an increase in the latter away from the Friedman rule may produce a transfer effect that dominates the partial equilibrium effect thereby rendering the Friedman rule ex-post suboptimal.