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Math Help - Profit maximising monopolist

  1. #1
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    Profit maximising monopolist

    Demand curves for two markets are q1 = 100 - p1 and q2 = 75 -p2/2. Total costs = q2/2

    Suppose the monopolist can price discriminate between the two markets, how much will the monopolist sell, and at what prices?

    Now suppose price discrimination is not possible, find the profit maximising price and the quantities it will sell?



    Can anyone please hel pme with this question? Iv looked over and over online and textbooks but i cannot find it

    Thanks
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  2. #2
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    Re: Profit maximising monopolist

    are you sure you typed the cost function correctly?
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    Re: Profit maximising monopolist

    Total cost function C(q) = q2/2
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  4. #4
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    Re: Profit maximising monopolist

    so it costs nothing to supply q1 then? does that sound right to you :P

    anyway, the marginal cost of supping market 1 is 0, the marginal cost of supplying market 2 is 0.5. If i remember my micro, Set MC=MR in both markets to get the price discriminating output.
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  5. #5
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    Re: Profit maximising monopolist

    apologies its q^2/2
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  6. #6
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    Re: Profit maximising monopolist

    there may be a faster way but you should alsways get the right answer by setting up the profit maximisation problem:

    The price discriminator must choose a quantity to supply to each market:

    \max_{q_1,q_2} TR(q_1,q_2) - TC(q_1,q_2)

    \max_{q_1,q_2} p_1q_1 + p_2q_2 - (q_1+q_2)^2

    use the demand functions to substitute the prces for quantities and solve.
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  7. #7
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    Re: Profit maximising monopolist

    Thanks got that part done. The next part of the question is -

    Suppose it is now possible for anyone to transport the good from 1 market to the other at zero transportation costs. Find the profit max monoolists's optional price and the quantities it will sell in the 2 markets at this price.
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  8. #8
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    Re: Profit maximising monopolist

    oops, i got the total cost function wrong. i should have written

    \max_{q_1,q_2} p_1q_1 + p_2q_2 - 0.5(q_1+q_2)^2

    ​part 2
    Anyway, there are several way to approach part 2.
    either: recognise that p1 = p2 in this situation. As such you can express q2 as a function of q1, to get a maximisation problem with a single choice variable (q1).

    or:
    replace the demand curve TR(q1,q2) with the total insutry demand curve TR(q), and solve the problem as you would for a non-proce discriminating monopolist.
    for part 2....the company will see the total industry demand curve. To get this you have to add up the demand curves along the quantity axis...then set up a new optiisation problem.
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  9. #9
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    Re: Profit maximising monopolist

    help me out here .. which would be easiest
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  10. #10
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    Re: Profit maximising monopolist

    using the 2nd option and p1 = p2 = p

    If I add the demand f
    q1 = 100-p and q2 = 75 - p/2
    100-p+75-0.5p = q
    175 - 1.5p = q

    Am I starting to get there?
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  11. #11
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    Re: Profit maximising monopolist

    looks right to me
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  12. #12
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    Re: Profit maximising monopolist

    Thank you ... what next?
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  13. #13
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    Re: Profit maximising monopolist

    you have a demand function: 175 - 1.5p = q
    and a cost function: 0.5q^2

    now find the profit maximising level of output in the usual way
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