Two firms have formed a centralized cartel in order to maximize profit on the market. Their marginal cost curves are: MC_A = 2Q_A and MC_B = 3Q_B. If the marginal revenue curve of the market is MR = 100-0.8Q, what price should the cartel charge? A) P=40 B) P=60 C) P=80 D) P=90

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Quizplus · Accepted Answer

To find the price the cartel should charge, we first need to determine the total quantity supplied by the cartel that maximizes profit. This is done by equating the marginal revenue (MR) to the marginal cost (MC) of the cartel. The total MC of the cartel is the sum of the individual MCs: MC = 2Q1 + 3Q2. Since the firms form a cartel, we assume they act as a single entity, so Q1 + Q2 = Q (total quantity). Without specific information on how the quantity is divided between the two firms, we simplify by treating the total quantity as Q and the total MC as a function of Q. The given MR is 100 - 0.8Q.To maximize profit, set MR = MC. However, without a clear way to combine the individual MCs into a single equation without additional information on how Q is split, we look directly at the MR equation to find the optimal Q and then the price.Given MR = 100 - 0.8Q, to find the quantity that maximizes profit, we would ideally set this equal to the combined MC and solve for Q. However, without the ability to directly combine the MC equations due to the lack of information on the distribution of Q between the two firms, we proceed by recognizing that the optimal output level (Q) and price (P) must be derived from the demand side (since MR is derived from demand), and the cartel's goal is to maximize profit by equating MR to MC.The lack of direct calculation steps from the provided MC equations to solve for Q necessitates an assumption or simplification. Typically, one would solve for Q by setting MR equal to the combined MC, then use the demand curve to find the corresponding P.Given the complexity and the information provided, a direct calculation to find the exact price P without additional steps or assumptions about how to combine the MC equations is not straightforward. The correct answer, based on the information given and typical economic principles, involves recognizing that the cartel's price-setting strategy aims to maximize joint profits by equating MR to the cartel's overall MC, but the specific solution would require additional steps or information not provided in the question. Thus, the answer provided is based on the understanding of economic principles rather than a detailed calculation from the given equations.

Two Firms Have Formed a Centralized Cartel in Order to Maximize