Suppose that the inverse market demand for an upcoming Bruce Springsteen concert at Philadelphia's 20,000 seat Wachovia Center is p = 1000 - 0.04 Q. Mr. Springsteen and his promoters consider whether to auction the tickets to the concert. The auction works as follows. An auctioneer orders the bids from highest to lowest; and the price of each ticket equals the 20,000th highest bid. The tickets go to the highest bidders. In the auction, assume that each person bids his or her willingness-to-pay.
a. What is the price of the tickets? What is the market consumer surplus?
b. Instead, suppose that Mr. Springsteen, for the benefit of his fans, decides to sell each ticket for $100. Based on the demand function, there are 22,500 people who are willing to pay $100 or more. So, not everyone who wants to see the concert at the $100 price can purchase a ticket. Of these 22,500 people, suppose that each of the 20,000 people who actually acquire tickets has a lower willingness-to-pay than each of the 2,500 people who do not. What is the consumer surplus?
c. Suppose Bruce Springsteen's objective in choosing whether to auction the tickets or to set a price of $100 is to maximize the market consumer surplus. Which does he choose: an auction or a $100 price?