Essentials of Economics (MindTap Course List)
Essentials of Economics (MindTap Course List)
7th Edition
ISBN: 9781285165950
Author: N. Gregory Mankiw
Publisher: Cengage Learning
Question
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Chapter 22, Problem 6PA

Subpart (a):

To determine

Real interest rate before and after the tax.

Subpart (a):

Expert Solution
Check Mark

Explanation of Solution

Before the tax real interest rate is calculated using the formula:

Real interest rateBefore tax=Nominal interest rateBefore taxinflation rate (1)

Substitute the respective values in equation (1) to calculate the real interest rate.

Real interest rateBefore tax=105=5

Thus, before the tax real interest rate is 5%.

The reduction in the nominal interest rate (Reduction NI) due to 40% tax is given as follows:

Reduction in NI = 40100× Nominal interest rate= 0.4×10= 4

Thus, reduction in nominal interest rate due to tax is 4%.

After the tax nominal interest rate is calculated using the formula:

Nominal interest rateAfter tax=(Nominal interestBefore taxReduction in normal interest) (2)

Substitute the respective values in equation (2) to calculate the nominal interest rate.

Nominal interest rateAfter tax=104=6

Thus, after the tax nominal interest rate is 6%.

After the tax real interest rate is calculated using the formula:

Real interest rateAfter tax=Nominal interest rateAfter taxinflation rate (3)

Substitute the respective values in equation (3) to calculate the real interest rate.

Real interest rateAfter tax=65=1

Thus, after the tax real interest rate is 1%.

Economics Concept Introduction

Concept introduction:

Inflation: It is an increase in the general price level of goods and services in an economy over a period.

Nominal interest rate: It is the interest rate that measures the change in dollar amounts.

Real interest rate: It is the interest rate adjusted with inflation, which is measured by the difference between nominal interest rate and inflation rate.

Subpart (b):

To determine

Real interest rate before and after the tax.

Subpart (b):

Expert Solution
Check Mark

Explanation of Solution

Substitute the respective values in equation (1) to calculate real interest rate before tax.

Real interest rateBefore tax=62=4

Thus, before the tax real interest rate is 4%.

The reduction in the nominal interest rate (Reduction NI) due to 40% tax is given as follows:

Reduction in NI = 40100× Nominal interest rate= 0.4×6= 2.4

Thus, reduction in nominal interest rate due to tax is 2.4%.

Substitute the respective values in equation (2) to calculate the nominal interest rate after tax.

Nominal interest rateAfter tax=62.4=3.6

Thus, after the tax nominal interest rate is 3.6%.

Substitute the respective values in equation (3) to calculate the real interest rate after tax.

Real interest rateAfter tax=3.62=1.6

Thus, after the tax real interest rate is 1.6%.

Economics Concept Introduction

Concept introduction:

Inflation: It is an increase in the general price level of goods and services in an economy over a period.

Nominal interest rate: It is the interest rate that measures the change in dollar amounts.

Real interest rate: It is the interest rate adjusted with inflation, which is measured by the difference between nominal interest rate and inflation rate.

Subpart (c):

To determine

Real interest rate before and after the tax.

Subpart (c):

Expert Solution
Check Mark

Explanation of Solution

Substitute the respective values in equation (1) to calculate the real interest rate before tax.

Real interest rateBefore tax=41=3

Thus, before the tax real interest rate is 3%.

The reduction in the nominal interest rate (Reduction NI) due to 40% tax is given as follows:

Reduction in NI = 40100× Nominal interest rate= 0.4×4= 1.6

Thus, reduction in nominal interest rate due to tax is 1.6%.

Substitute the respective values in equation (2) to calculate the nominal interest rate after tax.

Nominal interest rateAfter tax=41.6=2.4

Thus, after the tax nominal interest rate is 2.4%.

Substitute the respective values in equation (3) to calculate the real interest rate after tax.

Real interest rateAfter tax=2.41=1.4

Thus, after the tax real interest rate is 1.4%.

From the results, it can be inferred that the after-tax real interest rate is much lower than the before-tax real interest rate.

Economics Concept Introduction

Concept introduction:

Inflation: It is an increase in the general price level of goods and services in an economy over a period.

Nominal interest rate: It is the interest rate that measures the change in dollar amounts.

Real interest rate: It is the interest rate adjusted with inflation, which is measured by the difference between nominal interest rate and inflation rate.

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