Question

National Income — Work It Out: Question 1 Suppose the production function in an economy is Y = K0.5L0.5, where K is the amount of capital and L is the amount of labor. The economy begins with 36 units of capital and 4 units of labor. Round answers to two places after the decimal when necessary. d. If a sudden immigration quadruples the size of the population, while the capital stock is unchanged, what is the new level of output? new output: 24 units e. What is the new wage and rental price of labor? new wage: unit(s) of output new rental price: unit(s) of output f. What is the new share of output labor receives? share out output to labor: %

Answer 1

d)

Given

Y=K^0.5L^0.5

K=36

New L=4*4=16

So,

Y=36^0.5*16^0.5=24 units

e)

Y=K^0.5L^0.5

Marginal product of labor=MPL=dY/dL=0.5*K^0.5*L^(-0.5)

Set K=36 and L=16

Marginal product of labor=MPL=0.5*36^0.5*16^(-0.5)=0.75

Real wage=MPL=3/4 units or say 0.75 units

Marginal product of capital=MPK=dY/dK=0.5*K^(-0.5)*L^0.5

Set K=36 and L=16

Marginal product of capital=MPK=0.5*36^(-0.5)*16^0.5=1/3

Real rental price=MPK=1/3 units or say 0.33 units

f)

Total wage bill=wage*Number of labor units=0.75*16=12 units

New share of output labor receives=total wage bill/output=12/24=50%

Share out output to labor: 50%