Question

What will the multiplier be when the MPS is 0, 0.4, 0.6, and 1? What will it be when the MPC is 1, 0.90, 0.67, 0.50, and 0? How much of a change in GDP will result if firms increase their level of investment by $8 billion and the MPC is 0.80? If the MPC instead is 0.67?

Short answer

The multiplier for the given MPS values will be undefined, 2.5, 1.67, and 1.

The multiplier for the given MPC values will be undefined, 10, 3.03, 2, and 1.

The GDP will increase by $40 billion if MPC is 0.8.

The GDP will increase by $24.24 billion if MPC is 0.67.

Step-by-step solution

Calculating the multiplier from the MPS value

The multiplier effect is the reciprocal of MPS.Small MPS shows that the economy will change smaller amounts in total spending through investment and government spending. The majority of the income is going to be consumed. If small changes in investment and government spending can induce more noticeable changes in income, it implies that the multiplier is working significantly.

Thus, the following formula will help to calculate the multiplier through MPS:

$\mathrm{k}=\frac{1}{\mathrm{MPS}}$

Case 1: MPS = 0

role="math" localid="1643270720256" $$\begin{gathered} \mathrm{k}=\frac{1}{0} \\ =Undefined \end{gathered}$$

Case 2: MPS = 0.4

$$\begin{gathered} \mathrm{k}=\frac{1}{0.4} \\ =2.5 \end{gathered}$$

Case 3: MPS = 0.6

$$\begin{gathered} \mathrm{k}=\frac{1}{0.6} \\ =1.67 \end{gathered}$$

Case 4: MPS = 1

$$\begin{gathered} \mathrm{k}=\frac{1}{1} \\ =1 \end{gathered}$$

Therefore, when MPS is 0, 0.4, 0.6, and 1, the multiplier value is not defined, 2.5, 1.67, and 1, respectively.

Calculating the multiplier from the MPC value

The value of MPC determines the value of the multiplier. As the MPC increases the consumption, the multiplier effect increases as well.

$k=\frac{1}{1-MPC}$

Case 1: MPC = 1

$$\begin{gathered} k=\frac{1}{1-1} \\ =Undefined \end{gathered}$$

Case 2: MPC = 0.9

$$\begin{gathered} k=\frac{1}{1-0.9} \\ =10 \end{gathered}$$

Case 3: MPC = 0.67

$$\begin{gathered} k=\frac{1}{1-0.67} \\ =3.03 \end{gathered}$$

Case 4: MPC = 0.5

$$\begin{gathered} k=\frac{1}{1-0.5} \\ =2 \end{gathered}$$

Case 5: MPC = 0

$$\begin{gathered} k=\frac{1}{1-0} \\ =1 \end{gathered}$$

Hence, for MPC values 1, 0.9, 0.67, 0.5 and 0, the multiplier value is not defined, 10, 3.03, 2, and 1, respectively.

Change in income with an MPC of 0.8

According to the multiplier formula for a given MPC of 0.8, the multiplier value is as follows:

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

Also, the multiplier is the ratio of change in income to change in total spending.

role="math" localid="1643271429733" $$\begin{gathered} k=\frac{△Income}{△Spending} \\ △Income=k\times △Spending \end{gathered}$$

Therefore, a change of $8 billion in investment will induce a change in income as follows:

$$\begin{gathered} △Income=k\times △Spending \\ =5\times \$8billion \\ =\$40billion \end{gathered}$$

Thus, the change in income will be $40 billion.

Change in income with an MPC of 0.67

As calculated in the previous part, the multiplier value at 0.67 MPC is 0.33. Therefore, the induced change in income by $8 billion investment will be:

$$\begin{gathered} △Income=k\times △Spending \\ =3.03\times \$8billion \\ =\$24.24billion \end{gathered}$$

Therefore, the change in consumption by 33% of present income will increase the income by $24.24 billion in the future.