Question

Given Y = C + I + G c = Co + bY, I = Io and G = Go Where Co = 135, b = 0.8, Io = 75, and Go = 30
(i) Find the equation for the equilibrium level of income in the reduced form,
(ii) Solve the equilibrium level of income

Answer 1

At equilibrium :

Y = C

From the question lets do the substitution.

Y = C + 75 + 30

C = 135 + 0.8Y

i) Lets make C the subject of the equation in the first equation.

C = Y - 75 - 30

The equilibrium equation is :

Y - 75 - 30 = 135 + 0.8Y

ii) Lets solve for y now.

Y - 0.8Y = 135 + 75 + 30

0.2Y = 240

Y = 240/0.2

Y = 1200

The equilibrium income is 1200

Answer 2

At equilibrium :

X = C

From the question lets do the substitution.

X = C + 75 + 30

C = 135 + 0.8X

i) Lets assume C from the first equation.

C = X - 75 - 30

The equilibrium equation is :

X - 75 - 30 = 135 + 0.8X

ii) Lets solve for X now.

X - 0.8X = 135 + 75 + 30

0.2X = 240

X = 240/0.2

X = 1200

The equilibrium income is 1200