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Math Help - Payoff matrix and profit maximising help

  1. #1
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    Payoff matrix and profit maximising help

    Hi there,

    I need to revise for my upcoming examinations but the teacher has failed to put up solutions for the following two questions. I would be grateful for any help on this. many thanks.

    <b>Question 1</b>
    Consider the cost functions faced by a duopoly comprising two firms: A and B:

    CA = 12 + qA, where CA denotes cost in dollars and qA is the quantity in kilograms

    Firm B:
    CB = 12 + qB , where CB denotes cost in dollars and qB is the quantity in kilograms

    The demand function is given by
    P = 100 Q, where Q = industry output = qA + qB

    REQUIRED:
    a) Calculate the profit maximising level of output qA and qB for firms A and B, respectively.

    b) Calculate the price P at the above level of output.

    c) Calculate the profits made by each of the firms, Firm A and Firm B

    d) If Firm A holds output at qA = 23, and Firm B also keeps output at qB = 23, Calculate the profits made by each of the firms, Firm A and Firm B

    e) Point out the salient aspects of a comparison between output and profit levels in (c) and (d)
    above.

    f) Is the output level qA = qB = 23 a Nash equilibrium?



    <b>Question 2</b>

    Consider the following payoff matrix between two bakeries:

    Please click here to see the table:
    http://img849.imageshack.us/img849/659/shanti.png

    Choose the best answer from the list below, and give reasons for your choice:

    a) The Nash equilibrium is not a pareto optimum
    b) The Nash equilibrium is a pareto optimum
    c) Airline As dominant strategy is to cut price
    d) Airline B has no dominant strategy.


    Once again, many thanks in advance for anyone who can help.
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  2. #2
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    post your attempt
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  3. #3
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    Quote Originally Posted by SpringFan25 View Post
    post your attempt
    Not made an attempt. Don't really know wheere to start
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  4. #4
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    (1) looks like a cournot duopoly question (if it isn't, then ignroe this post).

    a) Calculate the profit maximising level of output qA and qB for firms A and B, respectively.
    assume that Qa is fixed. can you find the profit maximising output Qb? This is the reaction function for firm b.

    Do the same thing (with Qb fixed) to find the reaction function of A

    Then solve the reaction functions simultaneously to find the profit maximising levels Qa, Qb.
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