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    Equlibrium Price/Output/Profit

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    Two firms, ABC, Inc and XYZ, Co. produce video systems. The industry demand function for video systems is P = 100 - 2 (Q1 + Q2), where Q2 is the output for ABC, Inc. and Q2 is the output for XYZ, Co. The total cost function are TCa = 50 + 80Qa and TCb = 60 +90Qb, respectively.

    a. If each firm sets its output to maximize its profits, assuming the other firm holds its output constant, what is the equilibrium price? (Show Work)

    b. What will be the output for each firm? (Show Work)

    c. What will be the profit for each firm? (Show Work)

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    Solution Preview

    We first write the profit functions for both firms. Remember that profit = revenue- cost = price X quantity - total cost

    firm A

    profit = PQa - TC(Qa) = (100 - 2Qa - 2Qb)Qa - 50 - 80Qa = 100Qa - 2Qa^2 - 2QaQb - 50 - 80Qa
    = 20Qa - 2Qa^2 - 2QaQb - 50

    now we take ...

    Solution Summary

    Equilibrium price, output and profits are examined. Maximization of profits are determined for each firm.