Two firms have formed a centralized cartel in order to maximize profit on the market. Their marginal cost curves are: MC₁ = 2Q₁ and MC₂ = 3Q₂. If the marginal revenue curve of the market is MR = 100-0.8Q, what quantity should the profit maximizing cartel produce? A) Q=20 B) Q=30 C) Q=40 D) Q=50

Question

Quizplus · Accepted Answer

To maximize profit, the cartel's marginal cost (MC) must equal its marginal revenue (MR). The total MC for the cartel is the sum of the individual MCs: MC = 2Q + 3Q = 5Q. Setting this equal to the given MR equation (100 - 0.8Q) and solving for Q gives: 5Q = 100 - 0.8Q, which simplifies to 5.8Q = 100, and further to Q = 100 / 5.8, resulting in Q = approximately 17.24 for each firm, but since the question seems to imply a total quantity (and possibly a misinterpretation in calculation steps due to the symbols used), the correct approach for total Q considering both firms' production would actually involve correctly interpreting the given equations and solving for the total Q that equates MR to MC for the entire cartel, not individually. However, without the precise algebraic manipulation based on the given equations, the intended answer seems to aim for a scenario where the total quantity produced by the cartel is determined by equating the cartel's total marginal cost to the market's marginal revenue, which typically involves solving for Q in the equation MR = MC. The provided options and the context suggest a misunderstanding in the calculation or interpretation process, as the correct calculation should equate the cartel's combined MC to the MR and solve for Q, reflecting the total output that maximizes profit for the cartel.

Two Firms Have Formed a Centralized Cartel in Order to Maximize