We study monetary models with nondegenerate stationary distributions of money holdings. We find that the Friedman rule does not typically maximize ex post social welfare. An increase in the rate of growth of the money supply has two effects: the standard distortionary, or rate‐of‐return, effect makes money a less desirable asset for all moneyholders. A second, redistributive effect, creates a transfer from one type of agent to the other. An increase in the rate of growth of money away from the Friedman rule can produce a rate‐of‐return effect that dominates the standard effect.