Question

Find the equilibrium interest rate and GDP using this information.

C = a + 0.7(Y – T)

a = 650 – 10r

T = 450 + 0.15Y

I = 800 – 30r

NX = 1000 – 0.10Y

(M/P)^d = 0.35Y – 100r

M^s/P = 1050

Answer 1

In goods market equilibrium, Y = C + I + G + NX [Here, G = 0]

Y = 650 - 10r + 0.7[Y - (450 + 0.15Y)] + 800 - 30r + 1,000 - 0.1Y

Y = 2,450 - 40r + 0.7(Y - 450 - 0.15Y) - 0.1Y

Y = 2,450 - 40r + 0.7(0.85Y - 450) - 0.1Y

Y = 2,450 - 40r + 0.595Y - 315 - 0.1Y

Y = 2,135 - 40r + 0.495Y

(1 - 0.495)Y = 2,135 - 40r

0.505Y = 2,135 - 40r

Y = (2,135 - 40r) / 0.505.........[Equation of IS curve]

In money market equilibrium, (M/P)d = Ms/P

0.35Y - 100r = 1,050

0.35Y = 1,050 + 100r

Y = (1,050 + 100r) / 0.35.........[Equation of LM curve]

In general equilibrium, Y_IS = Y_LM.

(2,135 - 40r) / 0.505 = (1,050 + 100r) / 0.35

0.35 x (2,135 - 40r) = 0.505 x (1,050 + 100r)

747.25 - 14r = 530.25 + 50.5r

215 = 64.5r

r = 3.33

Y = [1,050 + (100 x 3.33)] / 0.35 = (1,050 + 333) / 0.35 = 1,383 / 0.35 = 3,951.43