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    Help with profit-maximizing quantity and price

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    A monopolist has demand and cost curves given by:
    Quantity demand = 10000 - 20P
    TC = 1000 + 10Q + .05Q^2

    a. Find the monopolist's profit-maximizing quantity and price.
    b. Find the monopolist's profit.

    I tried to do the problem but kept coming up with a negative number for the monopolist's profit. Are my number's correct?

    P = 10 - .05Q
    TR = 10Q - .05Q^2
    Q = 99.5
    P = $5.03 (nearest cent) or $5.00 (nearest 10 cents)

    What should I use as the wholesale price?

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    https://brainmass.com/economics/macroeconomics/profit-maximizing-quantity-price-104242

    Solution Preview

    a. Find the monopolist's profit-maximizing quantity and price.

    We write the demand into:
    P = 500-.05Q
    Then TR = P*Q = 500Q - .05Q^2
    It should be noticed that the firm is a monopolist and is facing a downward ...

    Solution Summary

    The expert examines profit-maximizing quantity prices.

    $2.19