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Math Help - profit functions

  1. #1
    Junior Member
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    profit functions

    1. A firm can price discriminate between two markets. Assume that its TR functions are

    Market 1 TR_1 = 25Q_1 - 2Q_1^2

    Market 2 TR_2 = 17Q_2 - Q_2^2

    and its TC function is TC = 2 + 5Q_1 + 5Q_2

    a. Find the firmís profit function.

    b. Find the output levels needed to maximise profit.
    Use the second-order derivatives to test for a maximum.
    What is the maximum profit?

    What price will the firm charge in each market to maximise its profit?
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  2. #2
    MHF Contributor
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    Profit = TR - TC

    \Pi(Q_1,Q_2) = (25Q_1+17Q_2 -2Q_1^2 -Q_2^2) - (2 + 5Q_1 + 5Q_2)

    b.
    Find the marginal costs/revenues by differentiating the total costs/revenues with respect to the output level of the relevant good.

    Find maximum profit by equating marginal cost = marginal revienue in each market

    Market 1:
    MR_1 = 25 - 4Q_1
    MC_1 = 5

    25-4Q_1 = 5
    Q_1 = 5

    market 2
    MR_2 = 17 - 2Q_2
    MC_2 = 5

    17-2Q_2 = 5
    Q_2 = 6


    I assume you know what a second derivative is so you should be able to do the rest yourself.


    To get the price, use the fact that (Total Revenue / Quantity) = Price.
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