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    Demand and Cost Functions

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    6. You are the manager of a monopoly, and your demand and cost functions are
    given by P = 480 - 8Q and C(Q) = 500 + 4Q2, respectively.

    - What price-quantity combination maximizes your firm's profits
    - Calculate the maximum profits.
    - Is demand elastic, inelastic, or unit elastic at the profit-maximizing price
    quantity combination?
    - What price-quantity combination maximizes revenue?
    - Calculate the maximum revenues.

    © BrainMass Inc. brainmass.com October 10, 2019, 2:22 am ad1c9bdddf
    https://brainmass.com/economics/monopolies/demand-and-cost-functions-of-a-monopoly-374262

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    (a) R(Q) = PQ = (480 - 8Q)Q = 480Q - 8Q^2
    Profit = R(Q) - C(Q) = 480Q - 8Q^2 - 500 - 4Q^2 = -12Q^2 + 480Q - 500
    For maximum profit, the derivative of the profit function = 0
    -24Q + 480 = 0
    Therefore Q = 20
    P = 480 - 8(20) ...

    Solution Summary

    This solution shows all the steps for calculating a series of problems based on a companies demand and cost functions.

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