New York City announces that it will celebrate the 400th anniversary of the Dutch settlement of New Amsterdam (now NYC) with a concert in Madison Square Garden on January 1, 2024. The artists will be Rihanna and DJ Khaled. The city calculates that it can just sell out the 20,000 seats at $300 a ticket, but it decides that to make the concert affordable to more people, it will charge only $200 per ticket. Clearly, this will cause excess demand. Therefore, the city announces that the box office will open five days before the concert, at noon. People can line up ahead of time; each person in line can buy ONE ticket only, while supplies last (first come, first served). Once the box office opens, the sales happen infinitely fast, so all tickets are sold instantly at noon. People can line up and buy tickets and then sell them online to others.

(a) If the competitive rate of compensation for lining up is $8 an hour, when will the lineup start to form? Should people arrive gradually or all at once?

(b) With the information given, can you compute social surplus? Can you compute the loss of social surplus resulting from the government charging $200 per ticket instead of $300 per ticket? Show how, if you can, or explain why you can’t.

(c) Suppose that people were sure the weather would be good during the lineup. But unexpectedly, an hour after the lineup begins, it starts pouring rain and it’s obvious it will rain all day. This doubles the competitive rate for lining up, to $16 an hour. What happens? And does the rain change the surplus of those who ultimately attend the concert, or of those who line up?