Question

Refer to the accompanying table in answering the questions that follow:

(1) Possible Levels of Employment, Millions	(2) Real Domestic Output, Millions	(3) Aggregate Expenditures (Ca + Ig+ Xn+ G), Millions
90	\(500	\)520
100	550	560
110	600	600
120	650	640
130	700	680

1. If full employment in this economy is 130 million, will there be an inflationary expenditure gap or a recessionary expenditure gap? What will be the consequence of this gap? By how much would aggregate expenditures in column 3 have to change at each level of GDP to eliminate the inflationary expenditure gap or the recessionary expenditure gap? What is the multiplier in this example?

2. Will there be an inflationary expenditure gap or a recessionary expenditure gap if the full employment level of output is $500 billion? By how much would aggregate expenditures in column 3 have to change at each level of GDP to eliminate the gap? What is the multiplier in this example?

3. Assuming that investment, net exports, and government expenditures do not change with changes in real GDP, what are the values of the MPC, the MPS, and the multiplier?

Short answer

1. There will be a recessionary expenditure gap in the economy at full employment of 130 million. The recessionary gap will lead to unemployment and a decline in output.

2. The economy will raise its total spending by $36 billion at each level of GDP to eliminate the recessionary expenditure gap. It will produce a multiplier effect of 1.389. The economy will face an inflationary expenditure gap at $500 billion potential GDP. The economy will have to diminish its total spending by $36 billion at each level of GDP to eliminate the inflationary expenditure gap with the multiplier effect of 1.389.

3. The MPC, MPS, and multiplier values are 0.8, 0.2, and 1.25, respectively.

Step-by-step solution

Step 1. Expenditure gap, consequences, recovery rate, and multiplier at 130 million full employment level

The expenditure gap arises when the actual GDP deviates from the full employment level GDP.

Actual GDP > Full Employment GDP: Inflationary expenditure gap

Actual GDP < Full employment GDP: Recessionary expenditure gap

The actual equilibrium level of GDP is $600 billion (Real GDP=Aggregate expenditure). This level of GDP falls short of the potential GDP level of $700 billion (given by the full employment level of 130 million) by $100 billion. Therefore, the economy will go through a recessionary expenditure gap. At $700 billion in GDP, the expenditure is $680 billion, and there is a gap of $20 billion, which is a recessionary gap.

The consequences of this recessionary expenditure gap will be reduced consumer demand and investments and increased unemployment levels. This will reduce the economy's output, which in turn will reduce the consumer demand and investment further, creating a more severe recession.

The economy has to increase its total spending to cover the recessionary gap of $20 billion at each level of GDP.

An improvement of $40 billion in total expenditure will produce an appraisal of $50 billion in the GDP. Therefore, the MPC will be 0.8 (= 40/50).

Thus, the multiplier for the economy is as follows:

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

Hence, the multiplier is 5.

Step 2. Expenditure gap, recovery rate, and multiplier value at $700 billion of full employment level of GDP

The excess aggregate expenditure beyond the full employment level causes an inflationary expenditure gap. The equilibrium GDP is $600 billion. Thus, the economy will experience an inflationary expenditure gap at $500 billion of full employment GDP.

The maximum total spending received by the economy at full employment of $500 billion is $520 billion, and the economy has to reduce it to $500 billion. Thus, the economy must eliminate $20 billion (=520–500) to remove the inflationary gap.

Since the change in aggregate expenditure and GDP is constant, the multiplier is constant at 5.

Step 3. MPC, MPS, and multiplier at given levels of GDP and total spending

Since the investment, government expenditure, and net exports are constant, the only variable component in the aggregate expenditure is consumption.

Consumption is constantly increasing by $40 billion while income is growing by $50 billion.

$$\begin{gathered} MPC=\frac{∆Consumption}{∆Income} \\ MPC=\frac{40}{50} \\ MPC=0.8 \end{gathered}$$

The MPC is 0.8.

According to the relationship between MPC and MPS,

MPS = 1 – MPC.

MPS = 1 – 0.8

MPS = 0.2

Hence, MPS is 0.2.

The following formula helps to find the multiplier size:

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

Thus, the multiplier is 5.