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 quantity should Firm A produce? A) Q=20 B) Q=30 C) Q=40 D) Q=50

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Quizplus · Accepted Answer

To maximize profit in a cartel, the firms will equate the market's marginal revenue (MR) with the marginal cost (MC) of the cartel, which is the sum of the marginal costs of the individual firms. Given the marginal cost functions MC_A = 2Q_A and MC_B = 3Q_B, and the market's marginal revenue curve MR = 100 - 0.8Q, we first find the total quantity Q that maximizes profit by setting MR equal to the total MC (MC of Firm A + MC of Firm B).However, without the explicit formula for how the total quantity Q is split between Firm A and Firm B, we directly cannot find the quantity produced by Firm A. The given information is insufficient to directly calculate Firm A's production quantity without assumptions about how the total quantity is divided between the firms. Given the marginal cost functions, if we were to assume the firms share the market equally or based on their marginal costs, we would still need more information to accurately divide the total quantity (Q) between Firm A and Firm B. The correct approach involves solving for the total quantity Q that equates the market's MR to the combined MC of both firms, then determining Firm A's share based on additional information, which is not provided. Thus, without further details on how the total quantity is split or additional steps, we cannot accurately calculate Firm A's production quantity from the provided options. The explanation provided does not match the expectation of selecting one of the given choices directly because it highlights the lack of sufficient information to solve for Firm A's production quantity based on the given marginal cost functions and marginal revenue curve alone.

Two Firms Have Formed a Centralized Cartel in Order to Maximize