Question

Suppose the economy of a country is derived by the following equation.Derive the I-S equation

Y= C+I +G+X (income Identity)

C=75+0.72Yd (Consumption)

I= 100 - 500r (Investment)

X= 100 - 0.12Y -500r (Net Exports)

Answer 1

$Y= C+I +G+X\\Y=(75+0.72Yd)+(100-500r)+(100-0.12Y-500r)\\Y=75+0.72Yd+100-500r+100-0.12Y-500r\\Y=275+0.72Yd-100r-0.12Y\\Y-0.72Y+0.12Y=275-100r\\0.4Y=275-1000r\\Y=\frac{275-1000r}{0.4}\\Y=687.5-2500r$