Verifying a Profit Maximization Recommendation
An external consultant has advised a firm to produce 25 units of its product, claiming this quantity maximizes profit because it is where the firm's marginal revenue equals its marginal cost. As an internal analyst, you are asked to verify this recommendation by directly analyzing the firm's profit function. Based on your analysis, is the consultant's recommendation correct? Justify your conclusion by calculating the profit-maximizing quantity using this alternative method.
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Demonstrating Equivalent Profit Maximization Methods
Verifying a Profit Maximization Recommendation
A firm's total revenue function is R(Q) = 15Q - Q², and its total cost function is C(Q) = 2Q. Which of the following equations, when solved for Q, will yield the profit-maximizing output level?
A firm is trying to find its profit-maximizing output level. It correctly calculates that at an output of Q=50, the slope of its total revenue curve is $7 and the slope of its total cost curve is also $7. Based on this information, the firm can conclude that the slope of its profit function at Q=50 is zero.
The Mathematical Equivalence of Profit Maximization Rules
A firm's total revenue is given by the function R(Q) and its total cost by the function C(Q). The firm's profit is given by Π(Q) = R(Q) - C(Q). To find the profit-maximizing level of output, a manager can use two equivalent approaches: setting the derivative of the profit function to zero (Π'(Q) = 0) or setting marginal revenue equal to marginal cost (MR = MC). Match each mathematical expression with its correct economic term.
Applying Equivalent Profit Maximization Methods
Reconciling Profit Maximization Approaches
Diagnosing an Error in Profit Maximization