The owner of a baseball team and local stadium has commissioned a study that sho

Question

The owner of a baseball team and local stadium has commissioned a study that showed the demand by fans for stadium seats (per playing date) to be P = 22 - 0.2Q, where P is the average price of a ticket and Q represents the number of seats (expressed in thousands). The local stadium seats a maximum of 56,000 per game. Suppose the owner offers you 10% of the revenues. If you can only choose a uniform per-ticket price, what is the maximum amount you can earn per game? (Note: Assume that all seats and all games are the same in this problem.

Explanation / Answer

The revenue maximizing price is the price at which demand is unit elastic, which happens to be the midpoint for a linear demand curve. Here we are assuming a linear demand curve, therefore revenue-maximizing price is the midpoint price i.e. half the vertical intercept of the demand curve. Since the vertical intercept is 22, this means price should be charged $11 per seat. At this price owner can sell 55,000 seats, and earn total revenues of $605,000. You should make 10% of ($605,000 - $560,000) for each game, or $4500 per game this coming season.

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