Question

Assume that a central bank’s nominal seigniorage revenue equals the change in the money supply, denoted ?M. Real seigniorage revenue is ?M/P. Assume the inflation rate equals the growth rate of the money supply, which is ?M/M

a. What is the rationale for these assumptions? Are they realistic?

b.Write real seigniorage revenue in terms of the inflation rate and the real money supply, M/P.

c. When inflation rises, what happens to the real money supply and to seigniorage revenue? (Hint: In equilibrium, money supply must equal money demand.)

d. Sometimes a small increase in the government budget deficit produces a large increase in inflation. Explain this fact using the answer to part (c).

Answer #1

Part a

Actually, the nominal seigniorage revenue of central bank is equal to change in the monetary base. Now change in M is equal to money multiplier multiplied by the change in the monetary base. When the money multiplier is equal to 1 then the seigniorage revenue equals to change in the monetary base. The assumption is realistic when the money added is held in terms of currency or reserves. If the output does not change very much the assumption of inflation rate equals the growth rate of the money supply is realistic.

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D. as expected inflation increases, households hold less wealth
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