Question

Consider a firm which produces T-shirts according to Q = L^0.5, where Q denotes output and L is labor input. The domestic wage is w = 2. The firm can sell its output for a given price of p = 1.
(a) Determine the profit-maximizing labor input and the profit of the firm.

Answer 1

From the calculation below, the profit-maximizing labor input is 0.0625, and the profit of the firm is 0.125.

How do we determine profit-maximizing labor input and profit?

From the question, we can obtain:

R = Revenue = Q*P = L^0.5 * 1 = L^0.5

C = Cost = w * L = 2L

P = Profit = R - C = L^0.5 - 2L

To obtain the profit-maximizing labor input, the first derivative of P is taken, equated to zero, and we solve for L as follows:

P' = 0.5L^-0.5 - 2 = 0

0.5L^-0.5 = 2

L^-0.5 = 2 / 0.5

L^-0.5 = 4

L^(-0.5/-0.5) = 4^(-1/0.5)

L = 0.0625 ----> profit-maximizing labor input

The profit (P) of the firm can now be calculated by substituting L = 0.0625 into the P function as follows:

P =  0.0625^0.5 - (2 * 0.0625) = 0.125 --------> Profit of the firm

Learn more about profit function here: brainly.com/question/16866047.

#SPJ1