Harry Potter and the chamber of scalpers

The Economist had an interesting story this week about ticket scalping, particularly related to the new stage show Harry Potter and the Cursed Child. Scalping is a regular favourite topic for economics teachers, as I have noted before. From The Economist story:

TICKETS to “Harry Potter and the Cursed Child”, the latest, on-stage instalment in the magically lucrative series, have proved harder to grasp than the golden snitch. After 250,000 tickets released on August 4th sold out within hours, fans’ disappointment turned to outrage as stubs with a face value of £15-70 ($20-90) started popping up on resale websites for more than £8,000.

In line with the howls of outrage, the play’s producers called the secondary ticket market an “industry-wide plague” and asserted their contractual right to refuse entry to people turning up with a resold ticket...

Rather than allowing touts to profit, the play’s producers could take a cue from “Hamilton”, a wildly successful Broadway musical, and raise prices for the premium seats until demand falls in line with supply (even at up to $849 per ticket, some argue that “Hamilton” is too cheap). But the Potter producers seem to be more worried about impecunious wizarding fans losing out than about the prospect of touts swiping surplus.

If you are trying to provide tickets at below-equilibrium prices to fans, then you have to expect the entrepreneurial types to buy some (maybe most) of those tickets for re-sale to fans who are willing to pay more than the face price but would have missed out otherwise. The interesting thing is that the actions of the ticket scalpers doesn't change economic welfare in total, they simply redistribute the welfare.

Consider the diagram below. The supply of tickets to the Harry Potter show S0 is fixed at Q0 - if the price rises, more tickets cannot suddenly be made available because the capacity of the theatre is fixed (note the diagram assumes that the marginal cost of providing tickets up to Q0 is zero).

Demand for tickets is high (D0), leading to a relatively high equilibrium price (P0). However, tickets are priced at P1, below the equilibrium (and market-clearing) price. At this lower price there is excess demand for tickets (a shortage) - the quantity of tickets demanded is Qd, while the quantity of tickets supplied remains at Q0.

With the low ticket price P1, the consumer surplus (the difference between the price the consumers are willing to pay, and the price they actually pay) is the area ABCP1. Producer surplus (essentially the profits for the theatre) is the area P1CDO. Total welfare (the sum of producer and consumer surplus) is the area ABCDO. At the higher price P0 due to the actions of scalpers (buying at P1 and selling at P0), the consumer surplus decreases to ABP0, while producer surplus remains unchanged. The scalpers gain a surplus (or profit) of the area P0BCP1, and total welfare (the sum of producer and consumer surplus, and scalper surplus) remains ABCDO. So the ticket scalpers don't reduce total welfare - their actions don't result in a deadweight loss.

If the ticket sellers want to cut out the scalpers, they need to either raise prices (so that the scalpers can no longer profit), or undertake costly measures to destroy the secondary market for tickets. From The Economist article:

Restricting the secondary market is possible, but only with great effort. The government’s review reported that the Glastonbury model, where festival-goers must show proof of identity alongside their ticket, works, but only because the organisers have such tight control over everything about the process, from ticketing to the venue.

I note that the NFL has its own ticket exchange, where ticket holders can on-sell their tickets to other fans (other sports teams are increasingly doing the same). This doesn't stop the scalping, it just shifts it online and allows the teams to take a cut. Perhaps theatre companies need to do the same. If you can't beat them, join them?