Principles of Economics, 7th Edition (MindTap Course List)
Principles of Economics, 7th Edition (MindTap Course List)
7th Edition
ISBN: 9781285165875
Author: N. Gregory Mankiw
Publisher: Cengage Learning
Question
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Chapter 30, 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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Students have asked these similar questions
Assuming the nominal interest rate is positive, ceteris paribus, which of the following statements is correct? a. If the nominal interest rate is 4 percent and the inflation rate is 3 percent, then the real interest rate is 7 percent. b. When the inflation rate is positive, ceteris paribus, the real interest rate will be less than the nominal interest rate. c. When the inflation rate is zero, ceteris paribus, the nominal interest rate will be less than the real interest rate. d. If the nominal interest rate is 5 percent and the inflation rate is 2 percent, then the real interest rate is -3 percent.
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