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Math Help - Finding conditions for a monopolist not to price discriminate

  1. #1
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    Finding conditions for a monopolist not to price discriminate

    A monopolist sells in two markets. The demand curve for the monopolistís product is x1 = a1 - b1 p1 in market 1 and x2 = a2 - b2 p2 in market 2, where and are the quantities sold in each market, p1 and p2 are the prices charged in each market. The monopolist has zero marginal costs. Note that although the monopolist can charge different prices in the two markets, it must sell all units within a market at the same price.

    (a) Under what conditions on the parameters (a1, b1, a2, b2) will the monopolist optimally choose not to price discriminate? (Assume interior solutions.)

    So i figured out: -2b1 a1 - 2b2 a2 > 0 and c>0 for this part.


    (b) Now suppose that the demand functions take the form Xi = Ai Pi ^-bi, for i = 1,2, and the monopolist has some constant marginal cost of c>0. Under what conditions will the monopolist choose not to price discriminate? (Assume interior solutions.)

    I need some help with this part, I don't really know how to start

    thanks in advance!
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  2. #2
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    im not sure where you got "c>0" from in your first answer. I hope that does not mean "marginal cost > 0" because you are told that the marginal cost is zero.


    One method for part b would be to:

    start by finding the profit if the company DOES price discriminate (find the profit maximising price in both markets).

    Then find the total demand function (D = x1 + x2 = .....) and find the most profit that can be made if a single price is set for the whole market.

    Then identify the conditions needed for the profit to be higher in the second case.


    However, i would have thought that was the same method you would have used in part a?
    Last edited by SpringFan25; July 27th 2010 at 10:01 AM.
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