Question

Price Discrimination

Promoters of a major college basketball tournament estimate that the demand for tickets on the part of adults is given by Q^A = 5,000 – 10P_A, and that demand for tickets on the part of students is given by Q^S = 10,000 – 100P_S. The promoters wish to segment the market and charge adults and students different prices. They estimate that the marginal and average total cost of seating an additional spectator is constant at $10 (i.e. there are no fixed costs).

1. If the promoters segment the market and charge adults and students different prices, what is the profit maximizing quantity that should be sold to each segment and what price should be charged for each segment? What is the total profit generated when the promoter segments the market?
2. Suppose the CEO of the tournament decides that price discrimination hurts the public image of the tournament and decides to charge everyone the same price. Calculate the profit maximizing number of tickets and the price of tickets when there is no price discrimination. What is the total profit generated when the promoter does not segment the market?

Answer 1

If promoters segment the market and charge different prices:

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Profit maximizing price and quantity for adults: MR = MC

Here, Q^A = 5,000 – 10P_A

Thus MR = 5000 - 20P_A

Equate MR = MC

5000 - 20P = 10

4990 = 20P

P = $249.5

Thus, Q = 2505 seats

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Profit maximizing price and quantity for students: MR = MC

Q^S = 10,000 – 100P_S

Thus, MR = 10,000 - 200P_S

Equate MC = MR

10,000 - 200P = 10

9990 = 200P

P = $49.95

Thus, Q = 3995 seats

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Total Profit = TR - TC

Take TR and TC for both students and adults as under:

= [(249.95 x 2505) + (49.95 x 3995)] - [(2505 x 10) + (3995 x 10)]

= [626124.75 + 199550.25] - [25050 + 39950]

= 825675 - 65000

Profits = $760,675

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If promoters charge the same prices:

The demand curves get aggregated:

Q= (5,000 – 10P) + (10,000 – 100P)

Q = 15,000 - 110P

Thus, MR = 15,000 - 220P

Equate MR = MC

15,000 - 220P = 10

14990 = 220P

P = $68.14

Thus, Q = 7505 seats

Total Profit = TR - TC

= (68.14 x 7505) - (10 x 7505)

Profits = $436,340.7

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It can be clearly seen that price discrimination (by segmenting the market) leads to a much higher profit.