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6 July, 09:30

Firm A and firm B compete in the same market by simultaneous quantity competition. Firms can choose any quantity Q ≥ 0. The inverse market demand curve is P (Q) = 40-2Q. Both firms have cost functions C (Q) = 2Q2, implying a marginal cost function of MC (Q) = 4Q.

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  1. 6 July, 09:48
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    Hi dear, the question you posted is not complete, but, not to worry I will be posting some important things for you to be able to solve this kind of question.

    Explanation:

    From the question, we are given that; inverse market demand curve is P (Q) = 40-2Q and the two (Both) firms have cost functions C (Q) = 2Q2. Also, marginal cost function of MC (Q) = 4Q.

    The kind of questions that one can expect to be asked are;

    (1). The maximization problem for both firms and determine the optimal price and quantity products produced.

    The solution is;

    P (q) q - C (q) = (40 - 2q) q - 2q2.

    Therefore, we have;

    40 - 2q∗ - 4 = 0

    or

    q∗ = 36/4.

    Given q∗ = 7/4, the two firms charge price will be;

    p∗ = 40 - q∗ = 44/4 = 11.

    (2). How much profit does the two firms make?

    => 11 * 7/4 = 77/4.
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