Question

Assume that the consumption schedule for a private open economy is such that consumption C = 50 + 0.8Y. Assume further that planned investment Ig and net exports X_n are independent of the level of real GDP and constant at Ig = 30 and Xn = 10. Recall also that, in equilibrium, the real output produced (Y) is equal to aggregate expenditures: Y = C + I_g + X_n.

1. Calculate the equilibrium level of income or real GDP for this economy.

2. What happens to equilibrium Y if Ig changes to 10? What does this outcome reveal about the size of the multiplier?

Short answer

1. The equilibrium level of income is 450.

2. If I_g changes to 10, the equilibrium level of income is 350, and the multiplier is 5.

Step-by-step solution

Step 1. Explanation for part (a)

At equilibrium, the real GDP (Y) is equal to the aggregate expenditures (Y = C + I_g + X_n).Placing the given values of C, I_g, and X_n will provide the equilibrium income as follows:

$$\begin{gathered} C=50+0.8Y \\ {I}_g=30 \\ {X}_n=10 \\ Y=C+I_g+X_n \\ Y=50+0.8Y+30+10 \\ 0.2Y=90 \\ Y=450 \end{gathered}$$

Therefore, the equilibrium level of real GDP is 450.

Step 2. Explanation for part (b)

If the gross investment changes to 10, the equilibrium real GDP equation will be as follows:

$$\begin{gathered} Y=50+0.8Y+10+10 \\ 0.2Y=70 \\ Y=350 \end{gathered}$$

Thus, the equilibrium real GDP will decline to 350. This output indicates that a decline in investment by 20 has reduced the income by 100.

Thus, the multiplier size is:

$$\begin{gathered} k=\frac{∆Y}{∆I} \\ k=\frac{100}{20} \\ k=5 \end{gathered}$$

It shows that a decrease in investment has reduced the income 5 times (= 100/20) the reduction in investment. Therefore, the multiplier is 5.