Pricing to fill the house

ArtsJournal links to this piece from Britain’s Guardian on pricing at the Met (see here for an earlier post of mine on the subject). Tom Service writes:

They filled just 79% of the seats in that huge, red-velvet covered house, and made only 69% of their projected box-office revenue. For all the millions who watched the cinema broadcasts, those are astonishingly low figures for the world’s most expensive opera house. The Met’s general manager, Peter Gelb, admits an experimentation with a more flexible pricing structure, borrowed from Broadway, didn’t work: “We’re learning. I believe in learning from one’s mistakes,” he’s quoted as saying – but even with an apparent pick-up in ticket sales for the early part of the 13/14 season (thanks to an average price reduction of about 10%) it’s astonishing that the world’s most glamorous opera house can be basically be little more than three-quarters full on an average night. (That compares, incidentally, to more than 90% capacity at the Royal Opera House). For all the HD broadcasts and global reach of the Met brand, if you’re not filling your house every night, you’re not creating the kind of atmosphere that audiences want to experience and performers need to play to.

So, how should you price when attendees prefer a full (or near-full) house, because of the atmosphere, and possibly because of improved performance by the players? If these effects are small, we know that it doesn’t always make sense to try to fill the house – the price reductions needed to do so might cause a very large drop in revenues.

But what if the number of attendees does matter? (Studies of museum pricing look in the opposite direction: what are people willing to pay for the benefit of having a smaller crowd? See this study published in Oxford Economic Papers, by Maddison and Foster on the British Museum). There are many products that are similar to the opera case (to the degree it is in fact a matter of significance). We value social networks like Facebook, online dating sites like OKCupid, or smartphone apps like WeChat, the more that we think others are using them. In departing from ‘ordinary’ pricing rules where individual consumers don’t care what others are doing (I bought green beans today at the store and it doesn’t matter to me at all who else bought them today), there are two effects, working in opposite directions – I am willing to pay more for the benefit of using a highly-patronized good if that matters to me (that would push the price up), but the seller wants to keep the price in check if doing so generates more purchases from on-the-fence buyers, who in turn induce other consumers to become interested.

Searching around a bit I found this recent paper by Candogan, Bimpikis, and Ozdaglar in the journal Operations Research, that addresses the pricing problem for ‘network’ goods, but as you can see a problem that on the surface doesn’t sound awfully complex, in fact is very complex. I’m going to work on trying to decipher what’s there…