Question

The IS Curve: Assume that the consumption function is given by C= 2000 + 0.6(Y– T) and the investment function is I= 4,000 – 200r, where r is measured in percent, G equals 3000, and T equals 2000.

a)	What is the numerical formula for the IS curve? (Hint:Substitute for C, I, and G in the equation Y= C + I + G and then write an equation for Y as a function of r or r as a function of Y.) Express the equation two ways.
b)	What is the slope of the IS curve? (Hint: The slope of the IScurve is the coefficient of Y when the IScurve is written expressing r as a function of Y.)
c)	If r is one percent, what is I? what is Y? If r is 3 percent, what is I? what is Y? If r is 5 percent, what is I? what is Y?

Answer 1

a) Y = C + I + G

Substituting the values of C, I, T and G in the above equation,

Y = 2000 + 0.6(Y - T) + 4000 - 200r + 3000

Y = 9000 - 200r + 0.6(Y - 2000)

Y = 9000 - 200r + 0.6Y - 1200

Y - 0.6Y = 7800 - 200r

0.4Y = 7800 - 200r

200r = 7800 - 0.4Y

r = (7800 - 0.4Y) / 200

r = 39 - 0.02Y is the answer

0.4Y = 7800 - 200r

Y = (7800 - 200r) / 0.4

Y = 19,500 - 500r is the answer.

b) The slope of the IS curve is -0.02 as can be seen from the equation solved above.

c) r = 1% or 0.01

I = 4000 - 200r = 4000 - 200(0.01) = 4000 - 2 = 3998 is the answer.

Y = 19,500 - 500(0.01) = 19,500 - 5 = 19,495 is the answer.

r = 3% or 0.03

I = 4000 - 200r = 4000 - 200(0.03) = 4000 - 6 = 3994 is the answer.

Y = 19,500 - 500(0.03) = 19,500 - 15 = 19, 485 is the answer.

r = 5% or 0.05

I = 4000 - 200r = 4000 - 200(0.05) = 4000 - 10 = 3990 is the answer.

Y = 19,500 - 500(0.05) = 19,500 - 25 = 19, 475 is the answer.