91Ó°ÊÓ

Since the government spending at each level of GDP is $20 billion, the aggregate expenditure is AE = C + I_g + NX + G.

Since the multiplier (as calculated in problem 5) is 5, a change of 20 billion government spending will increase the equilibrium GDP by $100 billion.

Increase in GDP = 5 × $20 billion

Increase in GDP = $100 billion

Aggregate expenditures at each level of GDP are given below:

Therefore, the equilibrium GDP due to increased government spending is $450 billion.

As the taxes imposed are personal taxes, private consumption will decline, according to the MPC.

$$\begin{gathered} k=\frac{1}{MPS} \\ 5=\frac{1}{MPS} \\ MPS=0.2 \\ MPC=1-0.2 \\ MPC=0.8 \end{gathered}$$

$$\begin{gathered} MPC=∆Consumption×∆Tax \\ MPC=0.8×\$20billion \\ MPC=\$16billion \end{gathered}$$

Therefore, the personal taxes of $20 billion at each level of GDP reduce consumption by $16 billion at each level of GDP.

A decline in consumption of $16 billion will increase the GDP by the multiplier times.

Increase in GDP = 5 × $16 billion

Increase in GDP = $80 billion

In this example, the government spending increased the aggregate expenditure in the public open economy by $100 billion, which is equal to GDP at $450 billion. Taxes will reduce this GDP by $80 billion. Thus, the equilibrium is at $370 billion ($450 billion - $80 billion).