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    Cinema Theater 3rd-Degree Price Discrimination

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    Cinema Theater has estimated the following demand functions for its movies:

    Daytime demand, Qd = 400 - 50Pd
    Nighttime demand, Qn = 200 - 20Pn
    The marginal cost of serving another customer is $5 and its fixed costs are $100.

    a. If the theater uses third degree price discrimination, what price will it charge for daytime tickets? How many will be sold?
    b. If the theater uses third degree price discrimination, what price will it charge for nighttime tickets? How many will be sold?
    c. What is the profit associated with using third degree price discrimination?
    d. If the theater does not use price discrimination and charges the same price to all customers, what is that price and how many tickets will be sold?
    e. What happens to profit when the theater does not engage in third degree price discrimination? How much does it rise or fall?

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    Solution Preview

    a) Third degree price discrimination means charging different prices to different types of customers - in this case, daytime customers and nighttime customers.

    Cinema Theater's profits are maximized when Marginal Revenue (MR) = Marginal Cost (MC).

    We are told that MC = 5.

    To find MR, first we must determine Total Revenue (TR).

    From the demand curve:
    Qd = 400 - 50Pd
    Rearranging:
    50Pd = 400 - Qd
    Pd = (400 - Qd)/50
    Pd = 8 - 0.02Qd

    TRd = PdQd
    TRd = (8 - 0.02Qd)Qd
    TRd = 8Qd - 0.02Qd^2

    MRd is the derivative of TRd.
    MRd = 8 - 2(0.02Qd)
    MRd = 8 - 0.04Qd

    To maximize daytime profit, let ...

    Solution Summary

    This solution shows how Cinema Theatre can use third-degree price discrimination between daytime customers and nighttime customers to charge different prices and maximize its profits. All mathematical calculations are shown in detail.

    $2.49

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