Question

Suppose that an initial \(10 billion increase in investment spending expands GDP by \)10 billion in the first round of the multiplier process. If GDP and consumption both rise by \(6 billion in the second round of the process, what is the MPC in this economy? What is the size of the multiplier? If, instead, GDP and consumption both rose by \)8 billion in the second round, what would have been the size of the multiplier?

Short answer

The MPC is 0.6.

The multiplier size is 2.5.

If the consumption had increased by $8 billion, the multiplier size would have been 5.

Step-by-step solution

MPC of the economy after the first round of the multiplier process

Out of $10 billion GDP increased in the first round of the multiplier process, $6 billion are consumed. So the change in consumption is $6 billion by the shift of $10 billion in income.

The proportion of change in income compared to the change in income is:

$$\begin{gathered} \mathit{M}\mathit{P}\mathit{C}\mathbf{=}\frac{\mathbf{△}\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{s}\mathbf{u}\mathbf{m}\mathbf{p}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}}{\mathbf{△}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}} \\ =\frac{6}{10} \\ =0.6 \end{gathered}$$

Thus, the MPC is 0.6.

Multiplier size in the second round

With an MPC of 0.6, the GDP increases by $6 billion. So the multiplier is:

$$\begin{gathered} \mathit{k}\mathbf{=}\frac{\mathbf{1}}{\mathbf{1}\mathbf{-}\mathbf{M}\mathbf{P}\mathbf{C}} \\ =\frac{1}{1-0.6} \\ =2.5 \end{gathered}$$

The size of the multiplier in the second round is 2.5.

Multiplier size in the second round with a shift of $8 billion consumption

If the consumption increases by $8 billion in the second round, the MPC in the second will be:

$$\begin{gathered} MPC=\frac{△\mathrm{Consumption}}{△\mathrm{Income}} \\ =\frac{8}{10} \\ =0.8 \end{gathered}$$

With an MPC of 0.8, the multiplier will be:

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

Hence, the multiplier is 5.