suppose the production function in medieval Europe isY =2k^0.5L^0.5, where K is

Question

suppose the production function in medieval Europe isY =2k^0.5L^0.5, where K is the amount of land and L is the amount of labor. The economy begins with 100 units of land and 100 units of labor. Use a calculator and equations to find a numerical answer to each of the followingquestions.

(1) How much output does the economy produce?

(2) What are the wage a

nd the rental price of land?

(3)What share of output does labor receive?

(4) If a plague kills half of the population, what is the new level of output?

(5) What is the new wage and rental price of land?

(6) What share of output does labor receive now?

Explanation / Answer

ANs 1)

Y=2K^0.5L^0.5 and K=100 and L=100

Y=2(100)^0.5*(100)^0.5=200 units

Ans B)

MPL=real wage

MPL=dY/dL=(K/L)^0.5=(100/100)^0.5=1

Real Wage =1 unit

MPK=(L/K)^0.5=1

Rental Price of Landis 1 unit

Ans C)

Share of output for Labor is wL/Y=100*1/200=50%

Ans D)

If Plague kills half population then New level of output will be

Y=2(100)^0.5*(50)^0.5

Y=20*50^0.5=141.42

Ans 5)

Now Wage is (K/L)^0.5=(100/50)^0.5=1.41

Rental price of land will be the same

ANs 6)

Share of output for alabour is =1.41*50/200=35.25%

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