Given the demand function P = 35 - 4Q, the marginal revenue function MR = 36 - 8Q, and marginal cost MC = 4, what is the profit-maximizing price?

Given the demand function P = 35 - 4Q, the marginal revenue function MR = 36 - 8Q, and marginal cost MC = 4, what is the profit-maximizing price?

• A. 16
• B. 19
• C. 21
• D. 25

Answer: (B)

Profit is maximized where marginal revenue equals marginal cost. Set MR equal to MC: 36 − 8Q = 4, which gives Q = 4. The price corresponding to this output comes from the demand function: P = 35 − 4Q, so P = 35 − 4(4) = 19. Therefore, the profit-maximizing price is 19. At quantities below 4, MR exceeds MC, suggesting more profit can be earned by producing more; above 4, MR is below MC, so producing more would reduce profit. The intersection at Q = 4 is the optimum.

Profit is maximized where marginal revenue equals marginal cost. Set MR equal to MC: 36 − 8Q = 4, which gives Q = 4. The price corresponding to this output comes from the demand function: P = 35 − 4Q, so P = 35 − 4(4) = 19. Therefore, the profit-maximizing price is 19. At quantities below 4, MR exceeds MC, suggesting more profit can be earned by producing more; above 4, MR is below MC, so producing more would reduce profit. The intersection at Q = 4 is the optimum.