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

Goods market is in equilibrium when

Y = C + I + G + NX

Plugging in given values and equations,

Y = (650 - 10r) + 0.7{Y - (450 + 0.15Y)} + (800 - 30r) + (1,000 - 0.1Y) [Since G = 0]

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

Y = 4,227.72 - 79.21r .........[Equation of IS curve]

Money market is in equilibrium when Money demand = Money supply.

(M/P)d = Ms/P

0.35Y - 100r = 1,050

0.35Y = 1,050 + 100r

Y = (1,050 + 100r) / 0.35

Y = 3,000 + 285.71r .........[Equation of LM curve]

General equilibrium is achieved when Y_IS = Y_LM.

4,227.72 - 79.21r = 3,000 + 285.71r

364.92r = 1,227.72

r = 3.36

Y = 3,000 + (285.71 x 3.36) = 3,000 + 960 = 3,960