We examine the characteristics of optimal monetary policies in a gener
al equilibrium model with incomplete markets. Markets are incomplete b
ecause of uninsured preference uncertainty, and because productive cap
ital is traded infrequently. Rational individuals are willing to hold
a liquid asset-''money''-at a premium. Monetary policy interacts with
existing financial institutions to determine this premium, as well as
the level of precautionary holdings. We show that inflation is expansi
onary, and that the optimal inflation rate is positive if there is no
operative banking system (the Tobin effect). Otherwise, efficiency req
uires that money be undominated in its rate of return (the Friedman Ru
le).