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    Cournot Oligopoly

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    Cournot Oligopoly

    . Two firms compete on the quantity they produce of good a single com¬modity. They face a demand function

    p= f(x)

    where p is the price at which they will sell the good, which depends on the total quantity produced, x= x1 + x2 (x1 is the quantity produced by firm i = 1, 2). Let the demand be linear:
    p = β - γ(x1+ x2)

    The production cost for firm i is
    C (xi) = -α (xi) ^2
    and its revenues are
    pxi

    . Problem Set:

    - Write the maximization problem of each firm (maximizing prof¬its, revenues minus costs), its best reply function and the Nash equilibrium quantities x1 and x2
    - Write the problem of a single monopolist firm, that is, a firm choosing x1 + x2 and facing the same demand, cost and revenue functions.
    - Is total quantity x1 + x2 larger or smaller in the monopolist case?
    And total profits?

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    https://brainmass.com/economics/oligopoly/cournot-oligopoly-29839

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    Cournot Oligopoly

    Two firms compete on the quantity they produce of good a single com¬modity. They face a demand function

    p= f(x)

    where p is the price at which they will sell the good, which depends on the total quantity produced, x= x1 + x2 (x1 is the quantity produced by firm i = 1, 2). Let the demand be linear:
    p = β - γ(x1+ x2)

    The production cost for firm i is
    C (xi) = -α (xi) ^2
    and its revenues are
    pxi

    . Problem Set:

    - Write the maximization problem of each firm (maximizing prof¬its, revenues minus costs), its best reply function ...

    Solution Summary

    Cournot Oligopoly is demonstrated.

    $2.19