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8 December, 07:16

A monopolist faces a demand curve given by: P = 105 - 3Q, where P is the price of the good and Q is the quantity demanded. The marginal cost of production is constant and is equal to $15. There are no fixed costs of production. How much output should the monopolist produce in order to maximize profit?

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  1. 8 December, 10:04
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    Answer: 15

    Explanation:

    For profit to be maximized by a monopolist, the marginal revenue and marginal cost must be gotten.

    P = 105-3Q

    MC = 15

    Since total revenue is price * quantity, TR = P*Q = (105-3Q) Q

    = 105Q-3Q^2

    MR = 105-6Q

    Since we've gotten marginal revenue and marginal cost, we equate both together.

    MR=MC

    105-6Q = 15

    6Q = 105-15

    6Q=90

    Divide both side by 6

    6Q/6 = 90/6

    Q = 15

    The quantity that will maximise profit is 15
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