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    Price as a function of Quantity

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    A park has a capacity to hold 60,000 people on any particular day.

    Using third degree price discrimination - demand for 2 groups (boys & girls)
    Q /6000 + P = 8 Q / 6000 + P = 6
    b b g g

    The hint provided is: Marginal Revenue in the two markets must be equal

    How do I figure out what to charge for admission to the boys and girls respectively?

    © BrainMass Inc. brainmass.com October 9, 2019, 5:59 pm ad1c9bdddf

    Solution Preview

    Let's first set each demand as Price as a function of Quantity:

    For boys (let's call Qb and Pb to their quantity and price)
    Qb/6000 + Pb = 8
    Pb = 8 - Qb/6000

    For girls:
    Qg/6000 + Pg = 6
    Pg = 6 - Qg/6000

    Total profits from the sales of tickets are thus:
    Pb*Qb + Pg*Qg = (8 - Qb/6000)*Qb + (6 - Qg/6000)*Qg =
    = 8Qb - (Qb^2)/6000 + 6Qg - (Qg^2)/6000
    [the ^ symbol means "to the power of"]

    The problem we have to solve is:

    Max 8Qb - (Qb^2)/6000 + 6Qg - (Qg^2)/6000
    Qb, Qg

    subject to
    Qb + Qg = 60,000

    That is: choose how many tickets you want to sell to ...

    Solution Summary

    Price as a function of Quantity is utilized in this case are determined. The marginal revenues in the two markets which must be equal are discussed.