A company can produce and sell f(L) tons of a product per month using L hours of labor per month. The wage of the workers is w dollars per hour, and the finished product sells for p dollars per ton.
(a) The function f(L) is the company’s production function. Give the units of f(L).What is the practical significance of f(1000) = 400?

(b) The derivative f'(L) is the company’s marginal product of labor. Give the units of f'(L). What is the practical significance of f'(1000) = 2?
(c) The real wage of the workers is the quantity of product that can be bought with one hour’s wages. Show that the real wage is w∕p tons per hour.
(d) Show that the monthly profit of the company is

π(L) = pf(L) − wL.

(e) Show that when operating at maximum profit, the company’s marginal product of labor equals the real wage:

Transcribed Image Text:

f'(L) = " Р