Question

Suppose C = 40 + 0.8YD, T = 50, I = 60, G = 40, X = 90, M = 50 + 0.05Y

(i) Find equilibrium income.

(ii) Find the net export balance at equilibrium income.

(iii) What happens to equilibrium income and the net export balance when the government purchases increases from 40 to 50?

Answer 1

Given, C = 40 + 0.8YD

T = 50

I = 60

G = 40

X = 90

M = 50 + 0.05Y

(i) Equilibrium level of income

Y = C + c (Y - T) + I + G + X - M - mY

Y = $\frac{\text{A}}{1-c+M},$
Here A = C - cT + I + G + X - M

$=\frac{\text{C - cT + I + G + X + M}}{1-c+m}$

= $\frac{40-0.8\times 50+60+40+90-50}{1-0.8+0.05}$

= $\frac{140}{0.25}$

= $\frac{140}{25}\times 100$

= 560

(ii) Net exports at equilibrium income

NX = X - M - mY

= 90 - 50 - 0.05 $\times$ 560

= 40 - 28

= 12

(iii) If G increases from 40 to 50,

= $\frac{\text{C - cT + I + G + X - M}}{\text{1 - c + m}}$

= $\frac{40-0.8\times 50+60+50+90-50}{1-0.8+0.05}$

= $\frac{40-40+60+50+40}{0.25}$

= $\frac{150}{0.25}=\frac{150}{25}\times 100=600$

Net export balance:

NX = X - M - mY

= 90 - 50 - 0.05 $\times$ 600

= 40 - 30 = 10