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    Calculating the optimal profit levels

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    1. Customers to Live Theaters, Inc. can be divided into two groups: seniors and everyone else. The inverse demand curves for each of the two groups are given below. The marginal cost (which equals the average variable cost) of serving an additional patron, either senior or everyone else, is equal to $4. Fixed costs are equal to $1000.

    Ps = 80 - Qs
    Pe = 100 - 2Qe

    Where Ps and Pe denote, respectively, the prices charged to seniors and everyone else and Qs and Qe denote the number of seniors and the number of all other customers served.

    a. What is Live Theaters' total revenue function? What is its total cost function? Its total profits function?

    b. What are the profit maximizing levels of price and output if Live Theaters, Inc. engages in third degree price discrimination? Show that MRe = MRs = MC

    c. What are profits associated with this option?

    d. If Live Theaters charges one price to all patrons, what would it be? How many customers would it serve? What would be its profits?

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    Solution Preview

    a. What is Live Theaters' total revenue function? What is its total cost function? Its total profits function?

    Total Revenue from seniors=TRs=Ps*Qs=(80-Qs)*Qs=80Qs-Qs^2
    Total Revenue from all others=TRe=Pe*Qe=(100-2Qe)*Qe=100Qe-2Qe^2
    Total Revenue from both segments=TRs+TRe=80Qs-Qs^2+100Qe-2Qe^2

    Total Cost=TC=1000+4*(Qs+Qe)

    Total Profit=Total Cost-Total Revenue
    =80Qs-Qs^2+100Qe-2Qe^2-1000-4*(Qs+Qe)
    =80Qs-Qs^2+100Qe-2Qe^2-1000-4Qs-4Qe
    ...

    Solution Summary

    Solution describes the steps to calculate optimal profit levels with and without third degree discrimination.

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