Question

The next several questions refer to the case of an economy with the following equations: Y = 50K0.3L0.7 with K=100 and L=100 G=1000, T=1000 I = 2000- 1000r C = 200 + 0.5(Y-T) real money demand: (M/P)d = 0.2Y - 1000r nominal money supply: M = 3200 (Assume a closed economy: Y = C + I + G. Assume the economy is in the long run equilibrium.) Compute the aggregate price level (P) ?

Answer 1

When K = L = 100,

Y = 50 x (100)^0.3(100)^0.7 = 50 x 100 = 5,000

Goods market is in long-run equilibrium, when Y = C + I + G

Y = 200 + 0.5(Y - 1000) + 2000 - 1000r + 1000

5000 = 3200 + 0.5 x (5000 - 1000) - 1000r [Since Y = 5000 computed above]

5000 = 3200 + 2500 - 500 - 1000r

5000 = 5200 - 1000r

1000r = 200

r = 0.2

From money market long-run equilibrium, (M/P)d = (M/P)s

3200 / P = (0.2 x 5000) - (1000 x 0.2)

3200 / P = 1000 - 200

3200 / P = 800

P = 4