Real money demand in the economy is given by L = 0.5Y - 2500i,
Where Y is real income and i is the nominal interest rate.In equilibrium,real money demand L equals real money supply M/P.Suppose that Y equals 1000 and the real interest rate is 0.02.At what rate of inflation is seignorage maximized?

Question

Quizplus · Accepted Answer

Real money demand (L) = Real money supply (M/P)
0.5Y - 2500i = M/P
Here, Y = 1000 and i = 0.02
So, 0.5(1000) - 2500(0.02) = M/P
500 - 50 = M/P
450 = M/P

Seignorage = Money supply - Money demand = M - L

Seignorage is maximized when inflation is maximum. 
Inflation rate (π) = (M/P) / (M/P)base - 1

Let's check the inflation rate for each option:

A) π = (450 / 450) - 1 = 0%
B) π = (500 / 450) - 1 = 11.11%
C) π = (550 / 450) - 1 = 22.22%
D) π = (600 / 450) - 1 = 33.33%

Therefore, the maximum seignorage is achieved at an inflation rate of 0.09 or 9%. Thus, the answer is C)0.09.

Real Money Demand in the Economy Is Given by L