Why are rugby world cup tickets so expensive?

Stuff last week ran a poll in their sports section that was guaranteed to get any economist excited. It asked, “What would you rate as a fair price for a mediocre seat at the Rugby World Cup final next year?”

Why is that exciting? Because, assuming “fair price” is the same as “willingness to pay” (WTP), the answers to this survey let us observe the demand curve directly. It’s not often we have the data to calculate a real live demand curve. That requires knowledge of what various types of consumers are actually willing to pay for a product, and such knowledge is hard to come by. Not having that knowledge is costly, as we’ll see later.

Here’s the data from the Stuff poll. When I grabbed it (yes, I did this manually. You’re welcome) there were 7143 responses – a good-sized sample for New Zealand.

Price Responses
1000 274
750 204
500 839
250 1168
200 893
150 945
100 1207
50 755
25 858

From this we can construct the demand curve – a simple plot of price against tickets sold at that price (except the other way around, because economists are strange like that).

The demand curve has its usual downward-sloping shape, because the higher the price is, the fewer people want to buy tickets. So if the tournament organisers charge $1000 per ticket, they’ll sell less than 300, at least to this group of people; if they charge $25 per ticket, they’ll sell the full 7143, being the 858 people who felt that $25 was a “fair price” together with all the other people who would have happily paid more.

The slope of the demand curve gives us an idea of the price elasticity of demand – the sales lost each time we increase the price by 1%. Although the demand curve looks elegantly concave, the elasticity of demand actually varies significantly between price points. The 100% price increase from $25 to $50 costs only 12% of the sales at that price, whereas the 100% price increase from $250 to $500 is worth 47% of sales. The higher willingness-to-pay consumers are also significantly more sensitive to price changes, and increasing the price that high up the demand curve makes them drop out of the market in large numbers.

So how should the organisers price the tickets? It’s safe to increase the price from $25, because those consumers are pretty insensitive to price, but not so safe to increase it from $250. Where’s the sweet spot?

As the good old theory of the firm tells us, it’s exactly where the price elasticity of demand is equal to 1. That way, you’re getting the most you can out of your price-insensitive consumers – you’ve increased the price as much as you can for them – while still coming close to charging your price-sensitive consumers the high price they’re willing to pay. Happily for us the Stuff survey came quite close to hitting that price point exactly – we can see from the chart above that the price elasticity of demand is closest to 1 when the price per ticket moves from $200 to $250. The best price lies somewhere between those two points (you’d need more granular data to tell where exactly).

To prove that this is the sweet spot, here’s the chart of total revenue for each price. You can see that it’s maximised at $200.

So why are RWC tickets so expensive? Sure, the organisers could sell more tickets by charging less – but that would leave them with lower revenue. It makes sense to charge more, even if that results in some empty seats in the stadium.

Of course, seat availability, price rationing, and how to think about marginal cost in the context of a major event like this, is a whole post in its own right…

There’s one other thing we can tell from this data though, and that’s the cost to the ticket seller of not being able to tell what a particular customer is willing to pay. In a perfect world the seller would change the price for each individual customer, charging them $500 if they’re happy to pay $500 and $50 if that’s all they’ll part with. That would mean more sales – every customer with a non-zero willingness to pay would buy a ticket – and also more revenue – the high-end customers would end up paying every penny of what they’re willing to. Instead, the seller has to charge the same price to everyone, which cuts out all the consumers with a willingness-to-pay below the sale price, and leaves the rich guys having paid a lot less than they might have.

The “potential revenue” that comes from charging every customer their exact WTP is the area under the demand curve. In the current example, it’s around $1.6 million.

By charging $200 per ticket, the sellers are freezing out 3765 people who would have paid less than that, for a lost revenue of $321,000. They’re also under-charging 2485 people who would have paid more, for lost revenue of $642,000.

The $321,000 is gone forever, no one gets it. But the $642,000 goes to all the high-WTP consumers who got what they consider a great deal at a price of $200. They get to enjoy it in the form of consumer surplus; they’ll get a total of $1.3 million of happiness out of the game, but they only had to pay a collective $676,000 for it.

What does this mean? If only there was some way of telling, credibly, what a person is willing to pay, there could have been another $321,000 of value created by the RWC final (within this group of people). All those low-WTP consumers could have enjoyed the final, and the organisers could have got more revenue out of them. Which is great, so long as (a) there was no shortage of seats (unlikely), and (b) the consumers happy to pay the regular price don’t feel ripped off and try ways to get the lower price (also unlikely).

In practice, there are almost always more high-WTP consumers than seats available, so the organisers can charge the higher, revenue-maximising price to everyone without losing out. And that’s why RWC tickets are so expensive.

(The poll was originally on this article, but of course it’s gone now. Why was I reading that rubbish? I have no idea.)