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    Two production plants with cost functions

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    A monopoly has two production plants with cost functions C1 = 50 + 0.1 Q12 and C2 = 30 + 0.05 Q22. The demand it faces is Q=500 - 10P. What is the profit maximizing level of output?

    a. Q1 = 62.5; Q2 = 125
    b. Q1 = 125; Q2 = 62.5
    c. Q1 = Q2 = 125
    d. Q1 = Q2 = 62.5

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    Solution Preview

    First of all, I'm assuming from your question that the cost functions have the quantity produced squared rather than multiplied by 2. When you wrote 50 + 0.1 Q12, I'm assuming this means 50 + 0.1 Q1^2 (where ^ means 'to the power of').

    In order to find the answer, we must set up the monopolist's problem. It has to choose Q1 and Q2 (the output of each plant) such that its profits are maximized. We already know its ...

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