Macroeconomics
Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
Publisher: PEARSON
Question
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Chapter 15, Problem 8NP

a)

To determine

To plot:Graphical representation of inflation rates.

a)

Expert Solution
Check Mark

Answer to Problem 8NP

  Macroeconomics, Chapter 15, Problem 8NP , additional homework tip  1

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=0.2Y500(r+π)

  L=0.2(1000)500(0.04+π)

  L=20020500π

  L=180500π

Since at equilibrium L = M/P, therefore,

  MP=180500π …..(1)

Formula to calculate seignorage revenue is:

  R=πMP

Substituting equation (1) in the above equation to get

  R=πMP

  R=π(180500π)

  R=180π500π2

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

    InflationRevenue
    00
    0.023.4
    0.046.4
    0.069
    0.0811.2
    0.113
    0.1214.4
    0.1415.4
    0.1616
    0.1816.2
    0.216
    0.2215.4
    0.2414.4
    0.2613
    0.2811.2
    0.39

  Macroeconomics, Chapter 15, Problem 8NP , additional homework tip  2

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.

b)

Expert Solution
Check Mark

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

    InflationRevenue
    00
    0.023.4
    0.046.4
    0.069
    0.0811.2
    0.113
    0.1214.4
    0.1415.4
    0.1616
    0.1816.2
    0.216
    0.2215.4
    0.2414.4
    0.2613
    0.2811.2
    0.39

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.

c)

Expert Solution
Check Mark

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

    InflationRevenue
    00
    0.023.4
    0.046.4
    0.069
    0.0811.2
    0.113
    0.1214.4
    0.1415.4
    0.1616
    0.1816.2
    0.216
    0.2215.4
    0.2414.4
    0.2613
    0.2811.2
    0.39

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.

d)

Expert Solution
Check Mark

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:

  MP=160500π

  R=πMP

  R=π(160500π)

  R=160π500π2

Table-2

    InflationNew Revenue
    00
    0.023
    0.045.6
    0.067.8
    0.089.6
    0.111
    0.1212
    0.1412.6
    0.1612.8
    0.1812.6
    0.212
    0.2211
    0.249.6
    0.267.8
    0.285.6
    0.33

  Macroeconomics, Chapter 15, Problem 8NP , additional homework tip  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.

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