The data in columns 1 and 2 in the table below are for a private closed economy.

1. Use columns 1 and 2 to determine the equilibrium GDP for this hypothetical economy.

2. Now open up this economy to international trade by including the export and import figures of columns 3 and 4. Fill in columns 5 and 6 and determine the equilibrium GDP for the open economy. What is the change in equilibrium GDP caused by the addition of net exports?

3. Given the original \(20 billion level of exports, what would be net exports and the equilibrium GDP if imports were \)10 billion greater at each level of GDP?

4. What is the multiplier in this example?

(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
250	280	20	30
300	320	20	30
350	360	20	30
400	400	20	30
450	440	20	30
500	480	20	30
550	520	20	30

In a private closed economy, for a stable GDP, the total spending generated by the output should be exactly equal to the GDP (real domestic output).

Since the real domestic output at the $400 billion level of GDP is equal to the aggregate expenditure at that level ($400 billion). The equilibrium GDP for the hypothetical economy is $400 billion.

The net exports determine the net spending from abroad after deducting the cost of imports.

Net Exports = Exports – Imports

An open private economy involves transactions with foreign economies. Thus, the aggregate expenditure for an open private economy includes net exports also.

AE = C + I_g+ NX

The values of net exports and aggregate expenditure, private open economy at various levels of GDP are as follows:

The equilibrium for a private closed economy was $400 billion GDP, which shifted to $350 billion for a private open economy. Therefore, the net exports reduced the equilibrium GDP by $50 billion (=$400 - $350).

Since the imports increased by $10 billion at each level of GDP, with exports being constant, net export and aggregate expenditure have declined. The values of new net exports and new aggregate expenditure at each level of GDP are as follows:

Since the aggregate expenditure and real domestic output are equal to $300 billion, the equilibrium GDP is $300 billion, and net exports are -$20 billion.

Since the aggregate expenditure has changed by $40 billion and GDP revised by $50 billion, the MPC will be:

$$\begin{gathered} MPC=\frac{∆AE}{∆GDP} \\ =\frac{40}{50} \\ =0.8 \end{gathered}$$

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

The multiplier by the given formula is calculated as below:

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

Therefore, the multiplier is 5.