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    Economics (Theoretical)

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    Suppose you are a monopolist operating two different plants at different locations. Both plants produce the same product; Qsub1 is the quantity produced at plant 1 and Qsub2 is the quantity produced at plant 2. We face the inverse demand function of :
    P=500-2Qsubm, where Qsubm is the market demand. The cost functions for the two plants respectively are:
    Csub1= 25+2Qsub1squared and Csub2= 20+Qsub2Squared

    1. What is the marginal revenue and marginal cost functions?
    2. What are the profit maximizing quantities for each plant and their price in the marketplace?
    3. How much profit will the firm make?

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    Solution Preview

    1. denote sub1 as 1 and sub2 as 2, subm as m for easier reading

    P = 500-2Qm
    C1 = 25 + 2Q1^2
    C2 = 20 + Q2^2

    Total revenue = price X quantity = (500-2Qm)Qm = 500Qm - ...

    Solution Summary

    The expert determines what the marginal revenues and marginal cost functions are for a monopolist operating two different plants. How much the profits the firm will make is determined.