Question

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

a) Find equilibrium income

(b) Find the net export balance at equilibrium income

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

Answer 1

C = 40 + 0.8YD

T = 50

I = 60

G = 40

X = 90

M = 50 + 0.05Y

(a) Equilibrium level of income

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

 `Y = A/(1 - C + m)` Where, A = C − CT + I + G + X − M

`= (C - cT + I + G + X - M)/(1 - c + M)`

`= (40-0.8xx50+60+40+90-50)/(1 - 0.8 + 0.05)`

`=(40-40+60+40-90-50)/(1-0.75)`

`140/0.25=140/25 xx100`

= 560

(b) Net exports at equilibrium income

NX = X − M − mY

= 90 − 50 − 0.05 × 560

= 40 − 28 = 12

(c) When G increase from 40 to 50,

`"Equilibrium income"  (Y)=(C - cT + I + G + X -M)/(1 - c + m)` 

`= (40-0.8xx50+60+50+90)/(1 - 0.8+0.05)` 

`= (40- 40 + 60 + 50+90)/(0.25)`

`= 150/0.25 = 150/25 xx 100 = 600`

Net export balance at equilibrium income

NX = X − (M − mY)

= 90 − 50 + 0.05 × 600

= 40 − 30 = 10