Money and Crime in a Cash-In-Advance Model

A cash-in-advance model, in which holding money is risky, is constructed to study the coexistence of multiple means of payment and monetary policy implications. In steady-state equilibrium, the marginal rate of substitution of cash goods for credit goods depends on the crime rate as well as the nominal interest rate. Credit may be in use, although the return on money is not positive. With theft, a money injection reduces the crime rate and makes cash more preferable for a greater variety of goods. Inflation improves welfare. However, without theft, inflation makes credit more preferable and decreases welfare. In general, the Friedman rule is not optimal.