Question

Assuming the level of investment is \(16 billion and independent of the level of total output, complete the following table and determine the equilibrium levels of output and employment in this private closed economy. What are the values of the MPC and MPS?

Possible Levels of Employment, Millions	Real Domestic Output (GDP = DI), Billions	Consumption, Billions	Saving, Billions
40	\)240	$244
45	260	260
50	280	276
55	300	292
60	320	308
65	340	324
70	360	340
75	380	356
80	400	372

Short answer

The table with all the complete values is as follows:

Possible Levels of Employment, Millions	Real Domestic Output (GDP = DI), Billions	Consumption, Billions	Savings, Billions
40	$240	$244	-$4
45	260	260	0
50	280	276	4
55	300	292	8
60	320	308	12
65	340	324	16
70	360	340	20
75	380	356	24
80	400	372	28

The equilibrium level of output is $340 billion, and the equilibrium employment level is 65 million.

The value of MPC is 0.8, and the size of MPS is 0.2.

Step-by-step solution

Step 1. Equilibrium level of output and employment

A private closed economy is in equilibrium when the aggregate expenditure, resulting from planned investment and consumption, equals the real domestic output. Aggregate expenditure becomes equal to the real domestic output if the portion of saved income becomes equal to the investment.

Since the investment is constantly $16 billion, the aggregate expenditure values for each respective level of domestic output and consumption are shown below according to the formula AE = C + I.

Saving is the part of income that is not consumed.If a person earns $100 per month and consumes only $80, the remaining $20 is their savings.

Therefore, savings can be calculated as follows:

S = DI – C

As per the above formula, the level of savings at each income level is presented in the table given below:

Possible Levels of Employment, Millions	Real Domestic Output (GDP = DI), Billions	Consumption, Billions	Savings, Billions (S)	Aggregate Expenditure ( C + 16)
40	$240	$244	-$4	$260 (=244+16)
45	260	260	0	276
50	280	276	4	292
55	300	292	8	308
60	320	308	12	324
65	340	324	16	340
70	360	340	20	356
75	380	356	24	372
80	400	372	28	388

Since the real domestic output equals aggregate expenditure and savings is equal to the investment of $16 billion at $340 billion of GDP, the aggregate level of output and employment is $340 billion and 65 million, respectively.

Calculation for the value of MPC

MPC is the fraction of the change in income that is consumed.

$MPC=\frac{∆Consumption}{∆Income}$

For instance, if income increased by $50 and consumption increased by $10, then the MPC will be 5 (= 10/50).

The above formula for MPC helps to get the values of MPC at different disposable incomes. The values for MPC for each change in income are as follows:

Possible Levels of Employment, Millions	Real Domestic Output (GDP = DI), Billions	Consumption, Billions	Change in consumption (𝛥C)	Change in DI (𝛥DI)	MPC (=𝛥C/𝛥DI)
40	$240	$244	-	-	-
45	260	260	16	20	0.8
50	280	276	16	20	0.8
55	300	292	16	20	0.8
60	320	308	16	20	0.8
65	340	324	16	20	0.8
70	360	340	16	20	0.8
75	380	356	16	20	0.8
80	400	372	16	20	0.8

The value of MPC is constant throughout the table because the change in income and consumption remains constant. The value of MPC is 0.8.

Calculation of the value of MPS

MPS is the fraction of change in income not consumed.

$MPS=\frac{∆Saving}{∆Income}$

Suppose a person’s earnings increased from $100 to $120 and savings increased from $20 to $22. The change of $20 in income has increased the savings by $2. Therefore, their MPS is 0.1 (= 2/20).

The values of MPS at each level of income are shown below:

Possible Levels of Employment, Millions	Real Domestic Output (GDP = DI), Billions	Consumption, Billions (C)	Savings, Billions (S)	Change in savings (𝛥s)	Change in DI (𝛥DI)	MPS (=𝛥S/𝛥DI)
40	$240	$244	-$4	-	-	-
45	260	260	0	4	20	0.2
50	280	276	4	4	20	0.2
55	300	292	8	4	20	0.2
60	320	308	12	4	20	0.2
65	340	324	16	4	20	0.2
70	360	340	20	4	20	0.2
75	380	356	24	4	20	0.2
80	400	372	28	4	20	0.2

The value of MPS is 0.2, which is constant throughout the data because income and savings have increased at a steady rate.