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

a) The assumption that the inflation rate (?P/P= ?) equals the growth rate of money supply (?M/M) is realistic when velocity and output do not change very much.

b) Real seignorage revenue is defined as: ?M/P= (?M/P)(M/M). When we rearranging terms on the right-hand side, it gives ?M/P= (?M/M)(M/P). Now, using the assumption ?M/M= ?P/P lets us write the definition of real seigniorage revenue as ?M/P= (?P/P)(M/P). This equation states that real seigniorage revenue is the product of real money supply & the inflation rate

c) The higher inflation rate will increases the term (?P/P) in the definition of real seigniorage revenue and leads to increased revenue. The second term (M/P) will start decreasing as the inflation rate increases. According to the equation it is possible that real seigniorage is very small or falls as inflation rises when inflation (?P/P) coincides with a drop in the real money supply (M/P)

d) When M/P falls, then a relatively small increase in ?M/P must be due to an increase in the term ?P/P, the inflation rate. This increase must be large to counteract the fall in M/P. Generating a small amount of seigniorage to finance a small in-crease in the government budget deficit is consistent with high inflation when real money supply falls