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    Equilibrium Output in a Duopolist Market

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    Assume that 2 companies(C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function:


    Where Qc and Qd are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are

    TCc=25,000 + 100Qc
    TCd=20,000 + 125Qd

    Assume that the firms act independently as in the Courtnot model(ie, each firm assumes that the other firm's output will not change).

    a.) Determine the long equilibrium output and the selling price of each firm.
    b.) Determine the total profits for each firm at the equilibrium output found in part (a).

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    Solution Preview

    First calculate the Qc assuming that it takes the Qd as given.
    The marginal cost for Firm C =MCc= 100
    The Revenue function for firm C=TRc=(600-Qc-Qd)*Qc
    Marginal Revenues for firm C=MRc=600-2Qc-Qd
    For profit ...

    Solution Summary

    This solution describes the steps to calculate long run equilibrium output and selling price for each of the given firms. It also calculates total industry profits.