Answer to Question #265833 in Macroeconomics for Happy

Question

Real money demand is

It) = 02Y – 5001

Where Y is real income and i is the nominal interest rate.

The economy has a fixed real output Y= 1,000.

Assume further that the central bank maintains a constant money growth rate to have a constant inflation rate and a fixed real interest rate of r= 0.04

1. Draw the graph with real seigniorage revenue on the vertical axis and inflation on the horizontal axis. Show the values of seigniorage for inflation rates of 0; 0.04; 0.18 and 0.3 in the graph.

2. Solve for the inflation rate that maximizes seigniorage revenue. What is the maximum

amount of seigniorage revenue? 3. Repeat part 1 and 2 for Y 1,000 but r= 0.08

Answer 1

Solution:

1.). The graph showing the values of the real seigniorage revenue and inflation is as below:

2.). The inflation rate that maximizes seigniorage revenue = 0.04

IT = 0.2Y – 500i = 0.2(1000) – 500(0.04) = 200 – 200 = 0

 

The maximum amount of seigniorage revenue = 200

 

IT = 0.2Y – 500i = 0.2(1000) – 500(0.08) = 200 – 400 = -200

The inflation rate that maximizes seigniorage revenue = 0.04

At this rate, inflation tax is equal to zero.