Finding the Profit-Maximizing Employment Level via Differentiation

Simplifying the Profit Function

Deriving a Single-Variable Profit Function

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?

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?

Rationale for Simplifying the Profit Function

Critiquing a Profit Maximization Approach

Critiquing a Profit Maximization Method

A manager wants to determine the number of employees that will maximize the company's profit. The manager has a profit equation that depends on both the number of employees and the wage paid, as well as a separate equation showing that the required wage depends on the number of employees hired. Arrange the following steps in the correct logical order to solve this problem.

Analyzing a Flawed Profit Calculation