Consider the following production function Q KLS Explain th

Consider the following production function: Q = K?LS. Explain the special characteristics of this production function. How is it different from a Linear production function? How is it different from a Leontief production function? (8 marks) Assuming that the firm hires 10 units of capital and 20 units of labour, use the production function given in part a to compute the average and marginal products of labour. (8 marks) Explain how the firm would use the marginal product of labour to determine the profit maximizing quantity of labour which the firm would hire. (4 marks) 1, a. b. c.

Solution

1/a

These are constant return to scale

Linear function are only one time differential and continuous

Leontif function are not continuous and L shaped

Ans 2

APL=Q/L =K^(2/3)*L^(1/3)/L=10^(2/3)*20^(1/3)/20=0.5^(2/3)

MPL=dQ/dL=1/3(K/L)^2/3=1/3*(0.5)^(2/3)

Ans 3

Profit maximising condition when MRS=Pl/Pk=Ml/Mk=0.25

There fore=Pl=0.25 Pk