An increase in the money supply growth rate is certain to increase seigniorage

# An increase in the money supply growth rate is

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Question 9‘An increase in the money-supply growth rate is certain to increase seigniorage revenues.’Thestatement isFALSE. 9
initiallyPand now rise toP0. The real value of the government’s seigniorage revenue isSeigniorage =M0-MP0.Suppose the money supply is growing at a rateg, which means that (M0-M)/M=g,and thusM0-M=gM. The inflation rateπis defined asπ= (P0-P)/P, soP0= (1+π)P.Hence, seigniorage is given bySeigniorage =gM(1 +π)P.Any amount of money supplied by the government must be willingly held by private agentsin the economy at some equilibrium price levelP(otherwise households would simply go outand spend the money, pushing up prices further). The demand function for money is (in realterms):MP=L(Y, i),whereYis real income, andiis the nominal interest rate. Demand for real money balancesis increasing in incomeYand decreasing in the interest ratei. The nominal interest rate isgiven by the Fisher equationi=r+πe,whereris the real interest rate andπeis expected inflation.For simplicity, assume that real income and the real interest rate are constant (Y=¯Y,r= ¯r).Assume also that any changes in inflation are expected, soπe=π.Suppose thatagents expect the inflation rate will not increase or decrease in the future, and thus the nominalinterest rateiand demand forrealmoney balancesM/Pare constant over time. If the ratioM/Pis constant, thenMandPmust be growing at the same rate, so the rate of inflation isequal to the rate of money supply growth:π=g. Therefore:Seigniorage =g1 +gMP=11 + (1/g)L(¯Y ,¯r+g).The expression for seigniorage is the product of two terms: 1/(1 + (1/g)), which is clearlyincreasing in the money-supply growth rateg; andL(¯Y ,¯r+g), which is decreasing ingbecause higher money-supply growth creates expectations of higher inflation, which raisesinterest rates, and reduces real money demandL(Y, i).This analysis implies that an increase ingis not certain to raise seigniorage revenues.Intuitively, faster money-supply growth means that more money is being created each period,so seigniorage revenues should be higher. But faster money growth reduces real money demandthrough the nominal interest rate, making agents less willing to hold money. This means that 10
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