Question

A Firm has the following production function 𝑸 = 𝟐𝟎𝑳 − 𝟎. 𝟒𝑳 𝟐.

a.Using differential calculus find the unit of labor that maximizes the production.

b. Estimate function of Marginal product of labor.

c. Obtain the Average product of labor.

d. Find the point at which the marginal product of labor is equal to the average cost. 

Answer 1

$Q=20L-0.4L^2,$

$Q=0,$

$L=0~\text{or} ~L=50,$

$Q'=20-0.8L,$

$Q'=0,$

$L=25,$

$Q(25)=250.$