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 utility for a heterogeneous population of infinitely-lived households in an economy with constant aggregate income. Households are divided 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 rates consistent with a resource constraint along 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 rate of inflation is positive, and the optimum nominal interest rate is higher than the inflation rate, if the social welfare function weighs credit agents no more than their population fraction.