Question

Suppose that the production function for the Gonan Island economy is Y = AK^0.25L^0.75. Suppose also that                            A = 2, K = 100,000, and L = 60,000.

1. Calculate the following:
2. 1. The real GDP
3. 2. The real wage
4. 3. The real rental cost of capital
5. 4. The share of income that goes to labor

Answer 1

i)

Real GDP Y is given as

Y=A*K^0.25*L^0.75

Set A=2, K=100000, L=60000

Y=2*100000^0.25*60000^0.75=136346.32

ii)

Y=A*K^0.25*L^0.75

MPL=dY/dL=0.75*A*K^0.25*L^(-0.25)

Set A=2, K=100000, L=60000

MPL=0.75*2*100000^0.25*60000^(-0.25)

We know that MPL=real wage rate=1.70432905 or say 1.70

iii)

Y=A*K^0.25*L^0.75

MPK=dY/dK=0.25*A*K^(-0.75)*L^0.75

Set A=2, K=100000, L=60000

MPK=0.25*2*100000^(-0.75)*60000^0.75=0.34086581

We know that MPK=real rental cost of capital=0.34086581 or 0.34

iv)

Total wage bill=L*w=1.70432905*60000=102259.74

Share of income that goes to labor=L*w/Y=102259.74/136346.32=0.75