Assume that a hypothetical economy with an MPC of .8 is experiencing a severe recession. By how much would government spending have to rise to shift the aggregate demand curve rightward by $25 billion? How large a tax cut would be needed to achieve the same increase in aggregate demand? Determine one possible combination of government spending increases and tax decreases that would accomplish the same goal.

Given the economy’s MPC of 0.8, the multiplier size for the economy can be calculated in the following manner:

$$\begin{gathered} k=\frac{1}{1-MPC} \\ =\frac{1}{1-0.8} \\ =5 \end{gathered}$$

According to the size of the multiplier, the government spending required to increase the aggregate demand by $25 billion is as follows:

$$\begin{gathered} △G=\frac{△AD}{k} \\ =\frac{\$25billion}{5} \\ =\$5billion \end{gathered}$$

Therefore, $5 billion of government spending is required to shift the aggregate demand curve toward the right by $25 billion.

Another way to increase the aggregate demand is to reduce the taxes because lower taxes will increase private consumption, and thus the demand curve will shift toward the right.

The decline in tax will increase disposable income. However, the whole of the income will not be consumed.So tax deduction will increase consumption multiplies times to MPC.

$5 billion of change in initial spending is required to increase the aggregate demand by $25 billion. The amount of tax reduction needed to increase the consumption by $5 billion can be calculated in the following manner:

$$\begin{gathered} MPC\times taxcut=\$5billion \\ 0.8\times taxcut=\$5billion \\ taxcut=\frac{\$5billion}{0.8} \\ =\$6.25billion \end{gathered}$$

Therefore, a reduction of $6.25 billion in taxes will increase the consumption expenditure by $5 billion, and the aggregate demand will increase by $25 billion.

A tax deduction of $5 billion will increase the consumption as follows:

Consumption = MPC x tax cut

= 0.8 x $5 billion

= $3.2 billion

Therefore, a $5 billion tax deduction will increase private consumption by $3.2 billion.

The remaining required initial spending to produce a shift in the aggregate demand curve by $25 billion has to be satisfied by increased government spending.

New government spending is equal to the difference between $5 billion (that could result in a $25 billion change in AD) and the consumption increase due to price tax.

= $5 billion - $3.2 billion

=$1.8 billion

Therefore, a tax deduction of $5 billion and government spending of $1.8 billion will provide a rightward shift of $25 billion in the aggregate demand curve.