Chapter 28, Problem 6P

To determine

Concept Introduction:

Marginal Propensity to Consume (MPC): It is the proportion of amount which the consumer pays for consumption of goods and services, and it does not include the savings of the consumer.

Formula to calculate money multiplier:
$\text{Money}\text{Multiplier}=\frac{1}{1-\text{MPC}}$ (I)

Here:

• MPC in marginal propensity to consume.

Formula to calculate recessionary/inflationary gap:

$\text{Recessionary}\text{Gap}/\text{Inflationary}\text{Gap}=\text{Potential}\text{Output}-\text{Real}\text{Output}$ (II)

Negative value shows inflationary gap whereas positive value shows recessionary gap.

Formula to calculate required change in government purchases:

$\text{Change in Government Purchases}=\left(\frac{\begin{array}{l}\text{Recessionary}\text{Gap}\\ \text{/Inflationary}\text{Gap}\end{array}}{\text{Money}\text{Multiplier}}\right)$ (III)

Formula to calculate transfer per dollar:

$\text{Transfer}\text{per}\text{Dollar}=\frac{\text{MPC}}{1-\text{MPC}}\times \$1$ (IV)

Here:

• MPC in marginal propensity to consume.

Formula to calculate change in the government transfers:

$\text{Change}\text{in}\text{Government}\text{Transfers}=\frac{\text{Recessionary}\text{Gap/Inflationary}\text{Gap}}{\text{Transfer}\text{per}\text{Dollar}}$ (V)

a. Change in government spending and government transfer.

Given:

Real GDP equals $100 billion.
Potential output equals $160 billion.
Marginal propensity to consume is 0.75.

Substitute 0.75 for MPC in (I):
$\begin{array}{c}\text{Money}\text{Multiplier}=\frac{1}{1-0.75}\\ =\frac{1}{0.25}\\ =4\end{array}$

Substitute $160 billion for potential output and $100 billion for real output in (II):

$\begin{array}{c}\text{Recessionary}\text{Gap}=\$160\text{ billion}-\$100\text{ billion}\\ =\$60\text{ billion}\end{array}$

Substitute $60 billion for recessionary gap and 4 for money multiplier in (III):

$\begin{array}{c}\text{Change in Government Purchases}=\frac{\$60\text{billion}}{4}\\ =\$15\text{billion}\end{array}$

Substitute 0.75 for MPC in (IV):

$\begin{array}{c}\text{Transfer}\text{per}\text{Dollar}=\frac{0.75}{1-0.75}\times \$1\\ =\frac{0.75}{0.25}\times \$1\\ =3\times \$1\\ =\$3\end{array}$

Substitute $60 billion for recessionary gap and $3 for transfer per dollar in (V):

$\begin{array}{c}\text{Change}\text{in}\text{Transfers}=\frac{\$60\text{billion}}{\$3}\\ =\$20\text{billion}\end{array}$

Therefore, there is a rise in government spending by $15 billion and there should be increase in government transfers by $20 billion.

Explanation of Solution

Conclusion:

Thus, rise in government spending is by $15 billion and government transfers by $20 billion.

b. Effect on Real GDP when MPC is 0.5.

Given:

Real GDP equals $250 billion.
Potential output equals $200 billion.
Marginal propensity to consume is 0.5.

Substitute 0.75 for MPC in (I):
$\begin{array}{c}\text{Money}\text{Multiplier}=\frac{1}{1-0.5}\\ =\frac{1}{0.5}\\ =2\end{array}$

Substitute $160 billion for potential output and $100 billion for real output in (II):

$\begin{array}{c}\text{Inflationary}\text{Gap}=\$200\text{ billion}-\$250\text{ billion}\\ \text{=}-\$50\text{ billion}\end{array}$

Substitute $60 billion for recessionary gap and 4 for money multiplier in (III):

$\begin{array}{c}\text{Change in Government Purchases}=\frac{-\$50\text{billion}}{2}\\ =-\$25\text{billion}\end{array}$

Substitute 0.75 for MPC in (IV):

$\begin{array}{c}\text{Transfer}\text{per}\text{Dollar}=\frac{0.5}{1-0.5}\times \$1\\ =\frac{0.5}{0.5}\times \$1\\ =1\times \$1\\ =\$1\end{array}$

Substitute $60 billion for recessionary gap and $3 for transfer per dollar in (V):

$\begin{array}{c}\text{Change}\text{in}\text{Transfers}=\frac{-\$25\text{billion}}{\$1}\\ =-\$25\text{billion}\end{array}$

Therefore, there is a fall in real GDP by $50 billion and there should be a decrease in government transfers by $25 billion.

Conclusion:

Thus, a fall in real GDP by $50 billion and decrease in government transfers by $25 billion.

c. Effect on Real GDP when MPC is 0.8.

Given:

Real GDP equals to $180 billion.
Potential output equals to $100 billion.
Marginal propensity to consume is 0.8.

Substitute 0.8 for MPC in (I):
$\begin{array}{c}\text{Money}\text{Multiplier}=\frac{1}{1-0.8}\\ =\frac{1}{0.2}\\ =5\end{array}$

Substitute $100 billion for potential output and $180 billion for real output in (II):

$\begin{array}{c}\text{Inflationary}\text{Gap}=\$100\text{ billion}-\$180\text{ billion}\\ \text{=}-\$80\text{ billion}\end{array}$

Substitute $80 billion for recessionary gap and 5 for money multiplier in (III):

$\begin{array}{c}\text{Change in Government Purchases}=\frac{-\$80\text{billion}}{5}\\ =-\$16\text{billion}\end{array}$

Substitute 0.8 for MPC in (IV):

$\begin{array}{c}\text{Transfer}\text{per}\text{Dollar}=\frac{0.8}{1-0.8}\times \$1\\ =\frac{0.8}{0.2}\times \$1\\ =4\times \$1\\ =\$4\end{array}$

Substitute $80 billion for recessionary gap and $4 for transfer per dollar in (V):

$\begin{array}{c}\text{Change}\text{in}\text{Transfers}=\frac{-\$80\text{billion}}{\$4}\\ =-\$20\text{billion}\end{array}$

Therefore, there is a fall in real GDP by $80 billion and there should be a decrease in government transfers by $20 billion.

Conclusion:

Thus, there is a a fall in real GDP by $80 billion and a decrease in government transfers by $20 billion.