Critiquing a Profit Maximization Approach
An economics student is tasked with setting up a firm's profit-maximization problem. The firm's profit (π) is given by the function π = 50N^(1/2) - wN, where N is the number of employees and w is the wage. The firm has determined that to ensure worker productivity, the wage must be linked to the number of employees by the function w = 5 + 0.2N.
The student proposes the following first step: "To find the optimal number of employees, I will take the derivative of the profit function with respect to N, treating w as a constant, and set it to zero. This will give me the profit-maximizing condition."
Evaluate the student's proposed first step. Is their reasoning correct? Explain why or why not, and describe the correct initial step that should be taken to express profit in a form that can be maximized with respect to a single variable.
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Science
Economy
CORE Econ
Social Science
Empirical Science
Economics
Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.6 The firm and its employees - The Economy 2.0 Microeconomics @ CORE Econ
Evaluation in Bloom's Taxonomy
Cognitive Psychology
Psychology
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A firm's profit (π) is determined by its revenue and labor costs, represented by the function π = 100N - N² - wN, where N is the number of employees and w is the wage. To ensure employees work effectively, the firm must pay a wage according to the function w = 10 + 0.5N. To find the profit-maximizing level of employment, the first step is to express profit as a function of only N. Which of the following equations correctly represents the firm's profit as a function of N alone?
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