Scalping College Basketball Tickets: At many universities, college basketball is intensely popular and, were tickets sold at market prices, many students who wish to attend games would not be able to afford to do so. As a result, universities have come up with non-price rationing mechanisms to allocate basketball tickets.
A. Suppose throughout this exercise that demand curves are equal to marginal willingness to pay curves and no one would ever pay more than $250 for a basketball ticket.
(a) First, suppose only students care about basketball. Draw a demand and supply curve for basketball tickets (to one game) assuming the stadium capacity is 5,000 seats and assuming that supply and (student) demand intersect at $100.
(b) Suppose students have an opportunity cost of time equal to $20 per hour. The university gives away tickets to the game for free to anyone with a valid student ID, but only the first 5,000 students who line up will get a ticket. In equilibrium, how long will the line for basketball tickets be; i.e. how long will students have to wait in line to get a ticket?
(c) What is the deadweight loss from the free ticket policy in (b)? (You can show this on your graph as well as arrive at a dollar figure).
(d) Now suppose that faculty care about basketball every bit as much as students. Unlike students, however, faculty has an opportunity cost of time equal to $100 per hour. Will any faculty attend basketball games under the policy in (b) (assuming students are not allowed to sell tickets to the faculty)?
(e) Now suppose anyone can sell, or “scalp”, his ticket at any price if he obtained one standing in line. Draw a new supply and demand graph — but this time let this be the market for tickets after the university has allocated them using their zero price/waiting-in-line policy. The suppliers are therefore those who have obtained tickets by standing in line, and the supply curve is determined by the willingness of those people to sell their tickets. What would this supply curve look like? Who would be the demanders?
(f) A market such as the one you have just illustrated is called a secondary market — i.e. a market where previous buyers now become sellers. The common policy (often enshrined into law) of not permitting “scalping” of tickets is equivalent to setting a price ceiling of zero in this market. Under this policy, how many tickets will be sold in the secondary market?
(g) How much surplus is being lost through the “no scalping” policy? Is anyone made worse off by allowing scalping of tickets?
(h) In the absence of this policy, how would the mix of people attending the game change?
B. Suppose that the students’ aggregate demand curve for tickets x is p = 250−0.03x and assume throughout that there are no relevant income effects to worry about. Suppose further that the aggregate demand for tickets by faculty is the same as that for students and, as in part A, 5000 seats are available.
(a) What is the aggregate demand function for students and faculty jointly? If the tickets were allocated through a market price, what would be the price?
(b) Suppose that the university only sold tickets to students. What would the equilibrium price be then?
(c) Now suppose the tickets were allocated to those students who waited in line. Do you have to know anything about students’ value of time to calculate the deadweight loss from this allocation mechanism?
(d) Suppose again that students are the only ones who are allocated tickets — and suppose they are prohibited from selling, or “scalping”, them to faculty. Derive the demand and supply curves in the secondary market where students are potential suppliers and faculty are potential demanders.
(e) What would be the price for tickets in this secondary market if it were allowed to operate?
(f) What fraction of the attendees at the game will be faculty?
(g) How large is the deadweight loss from the no-scalping policy? Does this depend on whether students bought the tickets as in (c) or waited in line as in (d)?
(h) Compare the outcome in (a) and (e). Would the composition of the crowd at the basketball game differ between the scenario in which everyone can buy tickets at the market price as opposed to the scenario where students get tickets by waiting in line but can then sell them?