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New York University *

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111

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Economics

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Jun 26, 2024

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docx

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1

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The owner of a car wash is trying to decide on the number of people to employ based on the following short-run production function and marginal product of labor equation. Short-run production function: Q = 6L - 0.5L^2 Marginal product of labor (MP): MP = 6 - L The owner can hire students on a part-time basis for $4 per hour, while the other workers are paid $5 per hour. Should the owner hire additional workers assuming they keep the current workers? - Part-time students cost $4 per hour. - Current workers are paid $5 per hour. Marginal Product of Labor gives the additional output per additional worker. Hire additional workers if the marginal benefit (additional output) exceeds the marginal cost (additional wages). MP = 6 - L If L = 1, MP = 5. Since the marginal benefit 5 exceeds the marginal cost $4, hiring an additional worker would be beneficial. However, as L increases, MP decreases. If L = 5, MP = 1. In this case, the marginal benefit is less than the marginal cost, so hiring an additional worker may not be beneficial.
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Suppose that a firm's only variable input is labor. The firm increases the number of employees from four to five, thereby causing the weekly output to rise by two units and total costs to increase from $3,000 per week to $3,300 per week. What is the marginal product of hiring five workers instead of four? What is the weekly wage rate earned by the fifth worker?
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