Chapter 1.3, Problem 39E

a.

To determine

To find: MPC.

Answer to Problem 39E

0.86

Explanation of Solution

Given information:

The variables represents as follows:

  $\begin{array}{l}x=\text{Nation's disposable income}\\ y=\text{Personal consumption expenditure}\end{array}$

$x$ (billions of dollars)	$y$ (billions of dollars)
56	50
76	67.2

MPC = Marginal propensity to consume

When MPC is 0.7, the value of $\Delta x\text{ and }\Delta y$ is 1 and 0.7 respectively.

Calculation:

Since 0.7 MPC means, the value of $\Delta x=1$ and $\Delta y=0.7$ . We can evaluate this MPC value as follows:

  $\begin{array}{c}\text{MPC}=\frac{\Delta y}{\Delta x}\\ =\frac{0.7}{1}\\ =0.7\end{array}$

Thus, the equation for MPC can be written as follows:

  $\begin{array}{c}\text{MPC}=\frac{\Delta y}{\Delta x}\\ =\frac{y_2-y_1}{x_2-x_1}\end{array}$

Put the values of x and y in the above equation to evaluate MPC as follows:

  $\begin{array}{c}\text{MPC}=\frac{\Delta y}{\Delta x}\\ =\frac{62.5-50}{76-56}\\ =\frac{17.2}{20}\\ =0.86\end{array}$

Thus, the value of MPC is 0.86.

b.

To determine

To find: the additional dollars spend by the average family.

Answer to Problem 39E

  $\$1552.3$

Explanation of Solution

Given information:

The variables represents as follows:

  $\begin{array}{l}x=\text{Nation's disposable income}\\ y=\text{Personal consumption expenditure}\end{array}$

$x$ (billions of dollars)	$y$ (billions of dollars)
56	50
76	67.2

Marginal propensity to consume, MPC = 0.86

The condition given is that x increases $1805.

Calculation:

The equation of MPC is as follows:

  $\text{MPC}=\frac{y}{x}$

Plug in the given values to evaluate y as shown below.

  $\begin{array}{c}0.86=\frac{y}{\$1805}\\ 0.86\left(\$1805\right)=y\\ \$1552.3=y\\ y=\$1552.3\end{array}$

Thus, the additional consumption expenditure of an average family increases by $\$1552.3$ .

c.

To determine

To find: MPS.

Answer to Problem 39E

0.14

Explanation of Solution

Given information:

MPC = Marginal propensity to consume

MPS = Marginal propensity to save

  $\text{MPS}=1-\text{MPC}$

MPC = 0.86

Calculation:

Put the value of MPC in the given equation to evaluate MPS as follows:

  $\begin{array}{c}\text{MPS}=1-\text{MPC}\\ =1-0.86\\ =0.14\end{array}$

Thus, the MPS is 0.14.

d.

To determine

To find: the additional dollars saved by the average family.

Answer to Problem 39E

  $\$252.7$

Explanation of Solution

Given information:

The variables represents as follows:

  $\begin{array}{l}x=\text{Nation's disposable income}\\ y=\text{Personal consumption expenditure}\end{array}$

$x$ (billions of dollars)	$y$ (billions of dollars)
56	50
76	67.2

Marginal propensity to save, MPS = 0.14

The condition given is that x increases $1805.

Calculation:

The equation of MPS is as follows:

  $\text{MPS}=\frac{y}{x}$

Plug in the given values to evaluate y as shown below.

  $\begin{array}{c}0.14=\frac{y}{\$1805}\\ 0.14\left(\$1805\right)=y\\ \$252.7=y\\ y=\$252.7\end{array}$

Thus, the additional consumption saving of an average family increases by $\$252.7$ .