Refer to columns 1 and 6 in the table for problem 5. Incorporate government into the table by assuming that it plans to tax and spend \(20 billion at each possible level of GDP. Also, assume that the tax is a personal tax and that government spending does not induce a shift in the private aggregate expenditures schedule. What is the change in equilibrium GDP caused by the addition of government?

(1) Real Domestic Output (GDP = DI), Billions	(2) Aggregate Expenditures, Private Closed Economy, Billions	(3) Exports, Billions	(4) Imports, Billions	(5) Net Exports, Billions	(6) Aggregate Expenditures, Private Open Economy, Billions
\)200	\(240	\)20	\(30	-\)10	$230
250	280	20	30	-10	270
300	320	20	30	-10	310
350	360	20	30	-10	350
400	400	20	30	-10	390
450	440	20	30	-10	430
500	480	20	30	-10	470
550	520	20	30	-10	510

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.

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

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

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).