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    Demand, Marginal Revenue, Profits for a Monopolist

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    2. Suppose you are the manager of Alpha Enterprises, a firm that holds a patent that makes it the exclusive manufacturer of bubble memory chips. Based on the estimates provided by a consultant, you know that the relevant demand and cost functions for bubble memory chips are Q = 25 - .5P; C = 50 + 2Q.

    a. What is the firm's inverse demand function?
    b. What is the firm's marginal revenue when producing 4 units of output?
    c. What level of output would maximize profits?
    d. At what price would you maximizing profits?
    e. What will be the dollar level of your profits?

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    Solution Preview

    A. Q = 25 - 0.5P --> 0.5P = 25 - Q --> P = 50 - 2Q
    B. Revenue = P * Q = (50 - 2Q) * Q = 50Q - 2Q^2
    Marginal revenue = 50 - 4Q ...

    Solution Summary

    This solution looks at the inverse demand function, marginal revenue, maximum profits for a firm with a patent (monopolist).