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    Calculating the profit maximizing price and quantity

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    Assume a monopolist with the following demand and cost relationships.
    Q = 400 - 20P
    TC = 10 + 5Q + Q^2 (Where "^" means "to the power of")

    Calculate the following:
    Profit maximizing price
    Profit maximizing quantity
    TR, TC, and Profit at profit maximizing Q and P.

    © BrainMass Inc. brainmass.com March 4, 2021, 11:16 pm ad1c9bdddf
    https://brainmass.com/economics/pricing-output-decisions/calculating-profit-maximizing-price-quantity-408996

    Solution Preview

    Demand curve:
    Q = 400 - 20P
    Rearranging:
    20P = 400 - Q
    P = 20 - 0.05Q

    Total Revenue:
    TR = PQ
    TR = (20 - 0.05Q)Q
    TR = 20Q - ...

    Solution Summary

    Detailed calculations of a monopolist's profit maximizing price and output given its Demand and Total Cost functions.

    $2.49

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