Chapter 15, Problem 8NP

a)

To determine

To plot:Graphical representation of inflation rates.

Answer to Problem 8NP

  

Explanation of Solution

Given Information:

Given the following information:

L = 0.2Y-500i

L = M/P

Y = 1000

r = 0.04

i = r + inflation(p)

Where,

i is the nominal interest rate

r is the real interest rate

M is the nominal money supply

L is the real money demand

Substitute the value of nominal interest rate into the equation of real money demand to get:

  $L=0.2Y-500(r+\pi )$

  $L=0.2(1000)-500(0.04+\pi )$

  $L=200-20-500\pi$

  $L=180-500\pi$

Since at equilibrium L = M/P, therefore,

  $\frac{M}{P}=180-500\pi$ …..(1)

Formula to calculate seignorage revenue is:

  $R=\pi \frac{M}{P}$

Substituting equation (1) in the above equation to get

  $R=\pi \frac{M}{P}$

  $R=\pi (180-500\pi )$

  $R=180\pi -500{\pi }^2$

Plotting the above equation for values of p = 0, 0.02, 0.04...0.3 in the form of a graph gives the following:

Table-1

Inflation	Revenue
0	0
0.02	3.4
0.04	6.4
0.06	9
0.08	11.2
0.1	13
0.12	14.4
0.14	15.4
0.16	16
0.18	16.2
0.2	16
0.22	15.4
0.24	14.4
0.26	13
0.28	11.2
0.3	9

  

Economics Concept Introduction

Introduction:

Inflation is the persistent increase in price level over a short period of time.

b)

To determine

Inflation rate that maximizes seignorage.

Answer to Problem 8NP

Inflation rate that maximizes seignorage is 0.18.

Explanation of Solution

Given Information:

L = 0.2Y-500i

L = M/P

Y = 1000

r = 0.04

i = r + inflation(p)

Where,

i is the nominal interest rate

r is the real interest rate

M is the nominal money supply

L is the real money demand

Inflation	Revenue
0	0
0.02	3.4
0.04	6.4
0.06	9
0.08	11.2
0.1	13
0.12	14.4
0.14	15.4
0.16	16
0.18	16.2
0.2	16
0.22	15.4
0.24	14.4
0.26	13
0.28	11.2
0.3	9

As it can be seen from the above table, value of seignorage revenue gets maximized at the inf1ation rate of 0.18.

Economics Concept Introduction

Introduction:

Inflation is the persistent increase in price level over a short period of time.

c)

To determine

Maximum amount of seignorage revenue.

Answer to Problem 8NP

The maximum amount of seignorage that is earned is 16.2 units.

Explanation of Solution

Given Information:

L = 0.2Y-500i

L = M/P

Y = 1000

r = 0.04

i = r + inflation(p)

Where,

i is the nominal interest rate

r is the real interest rate

M is the nominal money supply

L is the real money demand

Inflation	Revenue
0	0
0.02	3.4
0.04	6.4
0.06	9
0.08	11.2
0.1	13
0.12	14.4
0.14	15.4
0.16	16
0.18	16.2
0.2	16
0.22	15.4
0.24	14.4
0.26	13
0.28	11.2
0.3	9

The maximum amount of seignorage that is earned is 16.2 units by referring to above table.

Economics Concept Introduction

Introduction:

Total revenue is calculated by multiplying price into Quantity. It is the sale amount which is earned.

d)

To determine

Graphical representation of inflation rates, maximum value of inflation and revenue when Y = 1000 and r 0.08.

Answer to Problem 8NP

Revenue of seignorage is maximized (at the value of 12.8) at inflation rate of 0.16.

Explanation of Solution

Given Information:

L = 0.2Y-500i

L = M/P

Y = 1000

r = 0.08

i = r + inflation(p)

Where,

i is the nominal interest rate

r is the real interest rate

M is the nominal money supply

L is the real money demand

At equilibrium L = M/P, therefore,

For Y = 1000 and r = 0.08 gives the result as:

  $\frac{M}{P}=160-500\pi$

  $R=\pi \frac{M}{P}$

  $R=\pi (160-500\pi )$

  $R=160\pi -500{\pi }^2$

Table-2

Inflation	New Revenue
0	0
0.02	3
0.04	5.6
0.06	7.8
0.08	9.6
0.1	11
0.12	12
0.14	12.6
0.16	12.8
0.18	12.6
0.2	12
0.22	11
0.24	9.6
0.26	7.8
0.28	5.6
0.3	3

  

Revenue of seignorage is maximized (at the value of 12.8) at inflation rate of 0.16.

Economics Concept Introduction

Introduction:

Inflation is the persistent increase in price level over a short period of time.