Question

Given a hypothetical consumption function of the form:
Y = C + I0 + G0
C = α + βY^d
Where: Y^d = Y – T
Y = Income
T = Taxes
Compute the equilibrium level of income and consumption

Answer 1

Y = C + I0 + G0

C = α + βY^d

Y^d = Y – T

Y = α + βY^d +I0+G0 = α + β(Y-T)+I0+G0

Y = α + βY-βT+I0+G0

Y(1+β)=α +-βT+I0+G0

Y = (α +-βT+I0+G0)/(1+β)

C = α + β(Y-T) = α + βY-βT=α + (β(α +-βT+I0+G0)/(1+β))-βT