The optimal inflation target in an economy with limited enforcement

We formulate the 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 cash agents, who store value in currency alone, and credit agents who have access to both currency and loans. The planner?s problem is equivalent to choosing inflation and nominal interest rates consistent with a resource constraint, and with an incentive constraint that ensures credit agents prefer the superior consumption- smoothing power of loans to that of currency. 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.