From the calculation below, the profit-maximizing labor input is 0.0625, and the profit of the firm is 0.125.
<h3>How do we determine profit-maximizing labor input and profit?</h3>
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.
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