In the short run,a competitive firm has a marginal product of labor,MPL = 8L^-0.5.The output price is $16 per unit and the wage is $2 per hour.At the profit-maximizing level,how many units of labor are hired by the firm? A) L = 4 B) L = 6 C) L = 12 D) L = 8

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Quizplus · Accepted Answer

To find the profit-maximizing level of labor, we need to find the level of labor where MPL = wage rate. So, MPL = 8L^-0.5 = 8L(16)(1) - 0.5L(L)(2) = 128 - L^2 Setting MPL = wage rate = $2, we get: 128 - L^2 = 2 L^2 = 126 L = 11.23 (rounded off to the nearest whole number gives L = 11) or L = -11.23 (ignored) However, the actual number of labor units cannot be a decimal, so we try the neighboring integers of L = 11, which are L = 10 (MPL = 108) and L = 12 (MPL = 100). Since MPL decreases as more labor units are hired beyond L = 8, the profit-maximizing level of labor is where MPL = $2, and hence L = 8. Thus, the answer is D) L = 8.

In the Short Run,a Competitive Firm Has a Marginal Product