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Pricing with and without price discrimination

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

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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 provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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