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4 August, 21:33

A monopolist with constant average and marginal cost equal to 8 (AC = MC = 8) faces demand Q = 100 - P, implying that its marginal revenue is MR = 100 - 2Q.

Its profit-maximizing quantity is:

a) 8 b) 46 c) 50 d) 92

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  1. 4 August, 21:57
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    b) 46

    Explanation:

    Provided that

    AC = MC = 8

    Q = 100 - P

    Or P = 100 - Q

    MR = 100 - 2Q

    So the total revenue would be

    = Price * Quantity

    So if we put the values of p in the total revenue so the equation would be

    = 100 * Q - Q^2

    Now we have to take the differentiation with respect to marginal revenue which equal to

    = d (Total revenue) : d (Quantity)

    If we differentiated than the value would come

    = 100 - 2Q

    And

    We know that

    MR = MC

    100 - 2Q = 8

    2Q = 92

    Q = 46
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