20 You are given the following shortrun production function

20. You are given the following short-run production function for the firm: Q = 24L – (0.01)( L2 ), where L = number of workers hired per day, Q = output per day. The firm is a perfect competitor in both the output & input (i.e. labour) markets. The price of output is $10.00 per unit and labour costs $20.00 per day, the number of workers hired per day by the firm will be:

A) 100 B) 200 C) 400 D) 600 E) 800 F) 900 G) 1000 H) 1100 I) 1300 J) None of the above

need detail calculation? thank you?

Solution

A firm hires that number of workers corresponding to which marginal revenue product of labor equals wage rate or labor cost.

Production function is as follows -

Q = 24L - 0.01L²

Calculate the marginal product of labor -

MPL = dQ/dL = d(24L - 0.01L²)/dL = 24 - 0.02L

Calculate marginal revenue product of labor -

MRPL = MPL * Price = (24 - 0.02L) * 10 = 240 - 0.2L

Equating MRPL and labor cost

240 - 0.2L = 20

0.2L = 220

L = 220/0.2 = 1,100

The number of workers hired per day by the firm will be 1,100 workers.

Hence, the correct answer is the option (H).