Chapter 9, Problem 2.4P

Subpart (a):

To determine

Government spending multiplier.

Explanation of Solution

The government spending multiplier is calculated as follows:

$\begin{array}{c}\text{Govt}\text{. spending multiplier=}\frac{1}{\text{MPS}}\\ =\frac{1}{\text{0}\text{.1}}\\ =10\end{array}$

The government spending multiplier is 10.

Economics Concept Introduction

Concept introduction:

Marginal propensity to save (MPS): The ratio of change in saving when there is a change in disposable income.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate.

Subpart (b):

To determine

Government spending multiplier.

Explanation of Solution

The government spending multiplier is calculated as follows:

$\begin{array}{c}\text{Govt}\text{. spending multiplier=}\frac{1}{\text{1}-\text{MPC}}\\ =\frac{1}{\text{1}-\text{0}\text{.6}}\\ =\frac{1}{0.4}\\ =2.5\end{array}$

The government spending multiplier is 2.5.

Economics Concept Introduction

Concept introduction:

Marginal propensity to consume (MPC): Marginal propensity to consume refers to the sensitivity of change in the consumption level due to the changes occurred in the income level.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate.

Subpart (c):

To determine

Government spending multiplier.

Explanation of Solution

The government spending multiplier is calculated as follows:

$\begin{array}{c}\text{Govt}\text{. spending multiplier=}\frac{1}{\text{MPS}}\\ =\frac{1}{\text{0}\text{.25}}\\ =4\end{array}$

The government spending multiplier is 4.

Economics Concept Introduction

Concept introduction:

Marginal propensity to save (MPS): The ratio of change in saving when there is a change in disposable income.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate.

Subpart (d):

To determine

Tax multiplier.

Explanation of Solution

The tax multiplier is calculated as follows:

$\begin{array}{ccc}\text{Tax multiplier}& =& -\frac{\text{MPC}}{\text{1}-\text{MPC}}\\ & =& -\frac{0.5}{1-0.5}\\ & =& -\frac{0.5}{0.5}\\ & =& -1\end{array}$

The tax spending multiplier is -1.

Economics Concept Introduction

Concept introduction:

Marginal propensity to consume (MPC): Marginal propensity to consume refers to the sensitivity of change in the consumption level due to the changes occurred in the income level.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate.

Subpart (e):

To determine

Tax multiplier.

Explanation of Solution

The tax multiplier is calculated as follows:

$\begin{array}{ccc}\text{Tax multiplier}& =& -\frac{\text{1}-\text{MPS}}{\text{MPS}}\\ & =& -\frac{1-0.2}{0.2}\\ & =& -\frac{0.8}{0.2}\\ & =& -4\end{array}$

The tax spending multiplier is -4.

Economics Concept Introduction

Concept introduction:

Marginal propensity to save (MPS): The ratio of change in saving when there is a change in disposable income.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate.

Subpart (f):

To determine

Tax multiplier.

Explanation of Solution

The MPS is calculated as follows:

$\begin{array}{c}\text{MPS=}\frac{1}{\text{Govt}\text{. spending multiplier}}\\ =\frac{1}{\text{8}}\\ =0.125\end{array}$

The MPS is 0.125.

The tax multiplier is calculated as follows:

The tax spending multiplier is -7.

Economics Concept Introduction

Concept introduction:

Marginal propensity to save (MPS): The ratio of change in saving when there is a change in disposable income.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate.

Subpart (g):

To determine

Government spending multiplier.

Explanation of Solution

The MPS is calculated  using tax multiplier as follows:

$\begin{array}{ccc}\text{Tax multiplier}& =& -\frac{\text{1}-\text{MPS}}{\text{MPS}}\\ -5& =& -\frac{1-\text{MPS}}{\text{MPS}}\\ 5\text{MPS}& =& 1-\text{MPS}\\ \text{MPS}& =& \frac{1}{6}\\ & =& 0.167\end{array}$

MPS is 0.167.

The government spending multiplier is calculated as follows:

$\begin{array}{c}\text{Govt}\text{. spending multiplier=}\frac{1}{\text{MPS}}\\ =\frac{1}{0.167}\\ =6\end{array}$

The government spending multiplier is 6.

Economics Concept Introduction

Concept introduction:

Marginal propensity to save (MPS): The ratio of change in saving when there is a change in disposable income.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate.

Subpart (h):

To determine

Applying balanced budget multiplier.

Explanation of Solution

If government purchases and taxes increases by $500 billion simultaneously, the output also increases by $500 billion since the balanced budget multiplier effect of 1 is applicable in this case.

Economics Concept Introduction

Concept introduction:

Balanced Budget Multiplier: Balanced Budget Multiplier refers to the ratio of change in the equilibrium GDP to the change in government spending where the government spend is offset by change in taxes.