In Problem 5, you found the profit that a promoter of a major college basketball tournament would earn if he were to segment the market into adults and students. Suppose that the promoter's CEO decides that price discrimination presents a poor public image, and announces that everybody will be charged the same price. His resident economist (you) is tasked with figuring out what that price should be.
a. Find the total demand for tickets by adding the demand curves of adults and students.
b. Derive the inverse demand curve for tickets, as well as the associated marginal revenue curve associated with that demand.
c. Find the profit-maximizing quantity of tickets and the corresponding price.
d. Determine the promoter's profit.
e. Compare the promoter's profit when he tries to price for the entire market, to his profit when he simply charges the adult price from the previous problem. Is it better for the promoter to price for the entire market and almost fill the arena, or to price for adults only and have a lot of empty seats?
Problem 5:
Promoters of a major college basketball tournament estimate that the demand for tickets on the part of adults is given by Qad = 5,000 - 10P, and that the demand for tickets on the part of students is given by Qst = 10,000 - 100P. 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.
a. For each segment (adults and students), find the inverse demand and marginal revenue functions.
b. Equate marginal revenue and marginal cost. Determine the profit-maximizing quantity for each segment.
c. Plug the quantities you found in (b) into the respective inverse demand curves to find the profit-maximizing price for each segment. Who pays more, adults or students?
d. Determine the profit generated by each segment, and add them together to find the promoter's total profit.
e. How would your answers change if the arena where the event was to take place had only 5,000 seats?