Question

Suppose that an arena has a capacity of 20,000 seats. Over the course of a weekend, a tournament will host 3 games between 6 teams with each team playing exactly one game. There are 2000 dedicated fans of each team (so 2000*6-12,000 total dedicated fans), who will each pay up to $150 to see the game with their team playing and up to $10 per game to see the other two games.

There are also 2000 general fans who will pay up to $50 per game to see each of the three games. Thus, there are 14,000 fans altogether (2000*6+ 2000).
Assume the marginal cost of admitting one more fan (up to the capacity limit) is $0.

a. As the manager of the arena, suppose you could perfectly price discriminate. How many tickets would you expect to sell to each game? What is your total revenue for all three games?

Tickets Sold (per game):
Total Revenue: $

For the rest of this problem, assume perfect price discrimination is not possible and provide answer to maximize revenue (Since there
are no costs, this is the same as maximizing profit.)

b. If you sold individual tickets to each game at a uniform price, how would you price tickets and how many tickets would you expect to sell to each game? What is your total revenue for all three games?

Price per ticket: $
Tickets Sold (per game):
Total Revenue: $

(c) If you sold a package ticket that provided entrance to all 3 games and if you did not sell individual tickets, how would you price the package ticket and how many package tickets would you expect to sell? What is your total revenue?

Price per ticket: $
Tickets Sold:
Total Revenue: $

(d) Now consider the possibility of selling both a package ticket that provided entrance to all 3 games and also individual tickets to each game. Is it possible to earn greater revenue than in part (c)?

a. Yes, by targeting the package to general fans and the individual tickets to specific team fans
b. Yes, by targeting the package to specific team fans and the individual tickets to general fans
c. No

Answer 1

a. If perfect price discrimination is possible, the manager would sell different numbers of tickets to each game and calculate the total revenue. The manager would sell 2000 tickets to each game for the dedicated fans of each team, generating a revenue of $150 * 2000 * 6 = $1,800,000 per game. Additionally, the manager would sell 2000 tickets to each game for the general fans, generating a revenue of $50 * 2000 * 3 = $300,000 per game. Therefore, the total revenue for all three games would be $1,800,000 * 3 + $300,000 * 3 = $6,900,000.

b. If perfect price discrimination is not possible, the manager can analyze the maximum price each fan segment is willing to pay to determine the optimal ticket prices and number of tickets sold for each game. Assuming the manager wants to maximize revenue, they would set a uniform price for individual tickets to each game. To attract dedicated fans, the manager would price tickets at $150 for each game with their team playing, selling 2000 tickets per game for a total revenue of $150 * 2000 * 3 = $900,000. To attract general fans, the manager would price tickets at $10 for the other two games, selling 2000 tickets per game for a total revenue of $10 * 2000 * 2 = $40,000. Therefore, the total revenue for all three games would be $900,000 * 1 + $40,000 * 2 = $980,000.

c. If the manager sold a package ticket that provided entrance to all three games and did not sell individual tickets, they would need to determine the optimal price and number of package tickets to sell. Since perfect price discrimination is not possible, the manager can analyze the maximum price each fan segment is willing to pay. To maximize revenue, the manager would price the package ticket based on the maximum price the general fans are willing to pay, which is $50. Assuming all general fans purchase the package ticket, the manager would sell 2000 * 3 = 6000 package tickets, generating a total revenue of $50 * 6000 = $300,000.

d. Yes, it is possible to earn greater revenue than in part (c) by selling both a package ticket and individual tickets. The manager can target the package ticket to general fans and the individual tickets to specific team fans. This way, they can capture revenue from both fan segments. By offering the package ticket at $50 and selling 6000 package tickets as calculated in part (c), the manager would generate a revenue of $300,000. Additionally, by pricing individual tickets at $150 for each game with their team playing, the manager would sell 2000 tickets per game for a total revenue of $150 * 2000 * 3 = $900,000. Therefore, the total revenue by selling both the package ticket and individual tickets would be $300,000 + $900,000 = $1,200,000, which is greater than the revenue in part.

Answer 2

Tickets Sold (per game): 66,000

Total Revenue: $6,940,000

a. Perfect Price Discrimination:

In perfect price discrimination, you charge each fan the maximum price they are willing to pay. For the dedicated fans, this is $150 for their team's game and $10 for the other two games. General fans are willing to pay up to $50 for each game.

Total dedicated fans:

2000×6=12000

Total general fans: 2000

Tickets Sold (per game):

Each dedicated fan buys a ticket for their team's game (3 games).

Each dedicated fan buys tickets for the other two games (2 games).

Each general fan buys a ticket for each game (3 games).

12000×3+12000×2+2000×3=36000+24000+6000=66,000

Total Revenue:

Dedicated fans pay $150 per game for their team's game.

Dedicated fans pay $10 per game for the other two games.

General fans pay $50 per game.

12000×150×3+12000×10×2+2000×50×3=5,400,000+240,000+300,000=6,940,000

b. Uniform Price:

If you sell tickets at a uniform price, you want to set the price to maximize revenue.

Price per ticket:

Set a uniform price that all fans are willing to pay. Since general fans are willing to pay up to $50, and dedicated fans are willing to pay more, set a price close to the maximum that dedicated fans are willing to pay to maximize revenue.

Tickets Sold (per game):

Sell as many tickets as possible, up to the capacity of 20,000 seats.

Total Revenue:

Revenue is calculated by multiplying the price per ticket by the number of tickets sold.

c. Package Ticket:

Sell a package ticket that provides entrance to all 3 games.

Price per ticket:

Determine a price that general fans and dedicated fans are willing to pay for the entire package.

Tickets Sold:

Sell as many package tickets as possible, up to the capacity of 20,000 seats.

Total Revenue:

Revenue is calculated by multiplying the price per package ticket by the number of package tickets sold.

d. Package and Individual Tickets:

Consider selling both a package ticket and individual tickets.

Compare the total revenue from part (c) with the combined revenue from selling package tickets and individual tickets in a way that maximizes revenue.

Given the options, it seems reasonable to expect that selling both package tickets and individual tickets could potentially lead to greater revenue, depending on the pricing strategy for each category of fans. So, the answer is:

Answer: b. Yes, by targeting the package to specific team fans and the individual tickets to general fans

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