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    assume duopolists face damnd curve of P=125-Q, where Q is total market demand. each firm has a marginal cost of 25.
    1. find reaction for both firms
    2. find cournot equilibrium quantities and price
    3. find stackelberg '' ''
    4. cartel equilibrium quantity and price ?
    5. find bertrand '' ''
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    1. find reaction function for both firms
    Q(1) = 50 - 0.5Q(2)
    Q(2) = 50 - 0.5Q(1)

    2. find cournot equilibrium quantities and price
    Q(1) = Q(2) = 100/3 so total Q = 200/3
    Price = 175/3
    Profit for each firm = 10,000/9

    3. find stackelberg
    Suppose firm 1 moves first which will have an advantage over another
    Q(1) = 50 and Q(2) = 25 so total Q = 75
    Price = 50
    Profit firm 1 = 1250 Profit firm 2 = 625

    4. cartel equilibrium quantity and price
    They will produce 50 units in total (25 for each firm) Price = 75
    Profit (in total) = 2500 (1250 for each firm)

    5. find bertrand
    If non-differentiation then firms will charge Price = MC which is 25 and they will earn zero economic profit.
 
 
 
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