We formulate a central bank's problem of selecting an optimal long-run inflation rate as the choice of a distorting tax by a planner who wishes to maximize discounted stationary utility for a heterogeneous population of infinitely lived households in an economy with constant aggregate income and public information. Households are segmented into agents who store value in currency alone and agents who have access to both currency and loans. We show that the optimum inflation rate is positive, because inflation reduces the value of the outside option for credit agents and raises their debt limits.
