Chapter 16, Problem 1FRQ

a)

To determine

The question requires us to determine the value of the marginal propensity to consume.

Answer to Problem 1FRQ

The marginal propensity to consume is 0.8.

Explanation of Solution

Marginal propensity to consume (MPC) represents a change in consumption when disposable income increases changes. It is a fraction of each additional $1 in the disposable income that is consumed.

  $\text{MPC = }\frac{\text{Change in consumer spending}}{\text{Change in disposable income}}$

Given, the consumption spending function,

  $\text{C=\$1}\text{.5}\text{trillion+0}{\text{.8Y}}_{\text{D}}$

Here,

• $1.5 trillion is the autonomous consumption level
• The marginal propensity to consume is 0.8 which represents the slope of the consumption function.
• ${\text{Y}}_{\text{D}}$ is the disposable income.

The marginal propensity to consume is 0.8.

b)

To determine

The question requires us to determine the level of aggregate consumer spending when disposable income is zero.

Answer to Problem 1FRQ

The aggregate consumer spending will be $1.5 trillion.

Explanation of Solution

Autonomous consumption is the bare minimum level of consumption spending a person consumes even when disposable income is zero.

When disposable income is zero, the aggregate consumer spending will be $1.5 trillion.

c)

To determine

The question requires us to determine the level of aggregate consumer spending when disposable income is $4 trillion.

Answer to Problem 1FRQ

The value of aggregate consumer spending is $4.7 trillion.

Explanation of Solution

Given,

Current disposable income = $4 trillion

Consumption spending function, $\text{C=\$1}\text{.5}\text{trillion+0}{\text{.8Y}}_{\text{D}}$

The aggregate consumption spending is:

  $\begin{array}{c}\text{C=\$1}\text{.5}\text{trillion+0}{\text{.8Y}}_{\text{D}}\\ \text{=\$1}\text{.5}\text{+trillion+}\left(\text{0}\text{.8×\$4}\text{trillion}\right)\\ \text{=\$1}\text{.5}\text{+trillion+\$3}\text{.2}\text{trillion}\\ \text{=\$4}\text{.7}\text{trillion}\end{array}$

The value of aggregate consumer spending is $4.7 trillion.

d)

To determine

The question requires us to determine the value of the spending multiplier.

Answer to Problem 1FRQ

The value of the spending multiplier is 5.

Explanation of Solution

The spending multiplier shows the impact of change in aggregate spending on the real GDP. The expression for spending multiplier is the following:

  $\frac{\text{ΔY}}{\text{ΔAS}}\text{=}\frac{\text{1}}{\text{1-MPC}}$

Given, MPC = 0.8

Spending multiplier is:

  $\begin{array}{c}\frac{\text{ΔY}}{\text{ΔAS}}\text{=}\frac{\text{1}}{\text{1-MPC}}\\ \text{=}\frac{\text{1}}{\text{1-0}\text{.8}}\\ \text{=}\frac{\text{1}}{\text{0}\text{.2}}\\ \text{=5}\end{array}$

Therefore, the value of spending multiplier is 5.

e)

To determine

The question requires us to determine the value of real GDP.

Answer to Problem 1FRQ

The real GDP will change by $25 billion

Explanation of Solution

Change in real GDP when aggregate spending rises by $5 billion:

  $\begin{array}{c}\text{ΔY=}\frac{\text{1}}{\text{1-MPC}}\text{×ΔAS}\\ \text{=}\frac{\text{1}}{\text{1-0}\text{.8}}\text{×\$5}\text{billion}\\ \text{=5×\$5}\text{billion}\\ \text{=\$25}\text{billion}\end{array}$

So, real GDP will change by $25 billion when aggregate spending increases by $5 billion.