This papaer assesses some of the costs and benefits of aloowing banks to pay interest on demand deposits. With the help of a simple short-run model of the financial sector, it is shown that, barring a possible but unlikely perverse reaction, the deposit rate will tend to move in the same direction as other rates. This will moderate changes in the money supply accompanying a given change in interest rates; conversely, a given change in the excess demand for money will cause larger fluctuations in the level of interest rates. This can either be good or bad; if the excess demand for money corresponds to an excess demand for real output, the wider fluctuations in the interest rate will be more effective in eliminating it.