Optimal Inflation Rates: A Generalization: Note

Abstract

In his classic article, Welfare Cost of Inflationary Finance, (1956), Bailey indicted the use of the printing presses to raise resources on the grounds that the average ratio of the welfare cost to the revenue becomes excessive at moderate rates of inflation. He generalized these results to a competitive banking system paying interest on its deposits, but subject to a sterile legal reserve requirement. Any single bank would be forced by competition to pay interest on its deposits equal to the yield on its assets times (l-f), wheret is the legal reserve ratio. The opportunity cost of holding deposits is then the return on assets minus the yield on deposits which, in turn, is equal to the yield on assets timest. Bailey assumed the real rate was zero (not a crucial assumption) and that at high enough rates of inflation no one would use currency, so that all money would be held as interest bearing deposits. 1 The opportunity cost of holding deposits would then be the actual (and anticipated) rate of inflation, Tr, times the reserve ratio, while the seignorage accruing to the authorities would be TrfM/ P, the return on assets, 7rM/ P, multiplied by the ratio of high-powered money to the money supply. Bailey showed that to get the same tax revenue as in a pure currency system (t= 1), the authorities must inflate at a much higher rate, namely, the rate of inflation (whent= 1) times the reciprocal of the reserve ratio [r(l /t)]. A reduction in the reserve ratio raises the inflation rate needed to command the same resources (a proposition rediscovered by Calvo and Fernandez [1983]). A1-