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    Pricing with and without price discrimination

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    Indoor Water Park caters to both locals and out-of-state visitors. The demand for day-passes to the water park for each market segment is independent of the other market segment. The marginal cost (which also equals the average variable cost) of providing service to each visitor is $5 per day. Its fixed costs are $10,000 per day. Assume the daily demand curves for the two market segments are give by:

    Locals: Qloc = 3000 - 200 P
    Out of town: Qout = 3000 - 100 P

    a. If Indoor Water Park charges one price to all patrons, what is the profit maximizing price and quantity? What will be Indoor's total profits?

    b. If Indoor Water Park changes a different price to locals than it does to out-of-town visitors, what price and quantity will be set for each market segment? What will be Indoor's total profits?

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    https://brainmass.com/economics/microeconomics/pricing-with-without-price-discrimination-219876

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    Solution:

    a. If Indoor Water Park charges one price to all patrons, what is the profit maximizing price and quantity? What will be Indoor's total profits?

    Total demande Q= Qloc + Qout
    Q=3000-200P+3000-100P
    =6000-300P
    300P=6000-Q
    P= (6000-Q)/300

    Total revenue, TR = P*Q= (6000-Q)*Q/300= (6000Q-Q^2)/300
    Marginal revenue = d (TR)/dQ= (6000-2Q)/300

    For profit maximization MR=MC

    (6000-2Q)/300=5
    6000-2Q=1500
    2Q=6000-1500
    Q=4500/2=2250

    P= ...

    Solution Summary

    Solution describes the steps for caculating profit maximizing price and quantity with and without price discrimination policy.

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