A survey (pdf) by Anthony Krautmann and David Berri has found that most fans in many popular sports pay less for their tickets than conventional economic theory would predict.

Which poses the question: are team owners therefore irrational?

Not necessarily. There are (at least?) four justifications for such apparent under-pricing.

Lots of things in the real world are underpriced. Most popular concerts and sporting contests lose some volume of revenue to aftermarket transactions on sites like StubHub and SeatGeek. It's nearly impossible to get a reservation at some of the most popular restaurants in San Francisco like State Bird Provisions. There's a waiting list for NOMA Sydney that's 27,000 people long.

If you were pricing to maximize revenue, to match supply and demand exactly, you'd boost prices or perhaps auction off all the seats. What would NOMA Sydney have to charge until its waiting list dropped to zero? I can't even begin toguess, but would it surprise you if it was well north of $2,000 a head for dinner?

Given all of that, I was curious to see what this author thought might explain football ticket underpricing.

The first argument is that underpricing tickets leaves more revenue to be gathered through ancillary sales like souvenirs or overpriced concessions. Without data, I'm skeptical. My instinct is that concession and souvenir sales are less elastic with ticket prices than hypothesized.

The second point is that it's better to have a full stadium for team morale and to influence the officiating. But again, you could sell tickets via a mechanism like a Dutch Auction and maximize revenue while still filling the stadium.

The other two arguments are more convincing.

Thirdly, higher ticket prices can have adverse compositional effects: they might price out younger and poorer fans but replace them with tourists – the sort who buy those half-and-half scarves and should, therefore be shot on sight. This increases uncertainty about longer-term revenues: a potentially life-long loyal young supporter is lost and a more fickle one is gained. It also diminishes home advantage: refs are more likely to give dodgy decisions in front of thousands of screaming Scousers than in front quiet Japanese tourists.

I went to a couple games at the old Chicago Stadium, during Jordan's early years with the Bulls, and that place was loud. When they moved to the United Center and the ticket prices went way up, the crowd felt different. More wealthy, and definitely not as loud. It could just be the acoustics of the new space, but anecdotally, I saw fewer fans standing and screaming. Also, the rise of the smartphone means more of the dead moments in a game are filled with people scrolling on their phones, quietly.

Fourthly, high ticket prices can make life harder for owners. They raise fans’ expectations: if you’re spending £50 to see a game you’ll expect better football than if you spend just £10: I suspect that a big reason why Arsene Wenger has been criticised so much in recent years is not so much that Arsenal’s performances have been poor but because high prices have raised expectations.

It's hard to lower prices. Some sports teams may have done it at some point, but I've never seen it. You can raise prices when the team is good and on the rise, but those prices tend to stick when the team declines, and that's when stadiums start to empty out.

Saison is the restaurant in San Francisco that feels closest to pricing to match supply and demand. When I first moved to San Francisco, I had a meal there for $79. The next time there, the meal price had jumped over $100. Then the next time, it was up to $149. Later I heard the tasting menu had risen yet again to $248. The last time I went, thankfully on some banker's expense account, the price was $398 for dinner.

The dining room is usually full, but it's usually possible to get a table the same week. It feels like they've finally reached a price that about as close as you can get to where the supply and demand curves meet. Since the number of seats and turns is limited each night, perhaps this is revenue maximizing pricing, but the margin of error is razor thin.

My guess is that optimal pricing is somewhere below the price that matches supply and demand perfectly. Always being sold out adds a feeling of exclusivity, and no one knows how sold out you are, so being just sold out may be as good from a perception standpoint as being having a massive waiting list.

At the same time, I have a sneaking suspicion continuing to raise the price of a dinner would actually raise demand at some high end restaurants. There may be some Veblen-like qualities to restaurant pricing.