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    Profit maximization for a shop using the MR= MC method

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    Joe's Barber Shop has a daily total cost function of

    TC = 100 + 4Q + Q^2

    and the daily demand for his services is

    Q = 50 - 2P

    What is the profit maximizing price that Joe should charge for his services?

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    Solution Preview

    Joe's maximum profit occurs where Marginal Revenue (MR) = Marginal Cost (MC).

    Demand curve:
    Q = 50 - 2P
    2P = 50 - Q
    P = 25 - ...

    Solution Summary

    This solution shows how to calculate the profit-maximizing output and price for a barber shop that operates as a monopolistic competitor.