Question

The next several questions refer to the case of an economy with the following equations:

Y = 50K^0.3L^0.7 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 nomianl wage (W)

Answer 1

Substituting L = 100 nd K = 100 in production function,

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

Profit is maximized when MPL = (W/P)

MPL = Y/L = 50 x (K/L)^0.3 = 50 x (100/100)^0.3 = 50 x 1 = 50

W/P = 50

Goods market is in equilibrium when Y = C + I + G

Y = 200 + 0.5(Y - 1000) + 2000 - 1000r + 1000 [Substituting Y = 5000 as derived above]

5000 = 3200 + 0.5 x (5000 - 1000) - 1000r

5000 = 3200 + 2500 - 500 - 1000r

5000 = 5200 - 1000r

1000r = 200

r = 0.2

In money market equilibrium, Rea money demanded equals Real money supplied (M/P). When M = 3200,

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

3200 / P = 1000 - 200

3200 / P = 800

P = 4

Therefore,

W = P x (W/P) = 4 x 50 = 200