Question

Given the following information

      G = 300

      T = 200

      C = 220 + .6 (Y-T)

      I = 100 – 4r

      M^d = .75Y – 6r

      M^s = 735

a.   Derive the IS and LM curves. Calculate the equilibrium values of Y and r.

b.   Suppose that G is reduced until the budget deficit is eliminated. Calculate the new equilibrium values of Y and r. Explain the intuition of what happened, providing an IS/LM graph to illustrate.

Answer 1

(a)

In goods market equilibrium, Y = C + I + G

Y = 220 + 0.6(Y - 200) + 100 - 4r + 300

Y = 620 + 0.6Y - 120 - 4r

0.4Y = 500 - 4r

Y = 1250 - 10r (Equation of IS curve)

In money market equilibrium, Md = Ms.

0.75Y - 6r = 735

0.75Y = 735 + 6r

Y = 980 + 8r (Equation of LM curve)

In equilibrium, Y_IS = Y_LM.

1250 - 10r = 980 + 8r

18r = 270

r = 15

Y = 1250 - (10 x 15) = 1250 - 150 = 1100

(b)

If budget deficit is zero, it means T = G = 200.

From IS equation,

Y = 220 + 0.6(Y - 200) + 100 - 4r + 200

Y = 520 + 0.6Y - 120 - 4r

0.4Y = 400 - 4r

Y = 1000 - 10r (Equation of new IS curve)

Equating with LM equation,

1000 - 10r = 980 + 8r

18r = 20

r = 1.11

Y = 1000 - (10 x 1.11) = 1000 - 11.1 = 988.9

It is seen that both Y and r have decreased. This is because a decrease in G will shift the IS curve leftward, which lowers both real interest rate and output.

In following graph, IS0 and LM0 are initial IS and LM curves intersecting at point A with initial equilibrium interest rate r0 and initial equilibrium output (GDP) Y0. When government spending decreases, IS0 shifts left to IS1, intersecting LM0 at point B with lower interest rate r1 and lower GDP Y1.