Tuesday, June 8, 2010

Price Discrimination Everywhere: Baseball Edition

Jodi Beggs recently responded to an interesting question on baseball economics on her blog. Here's the question posed to her by a guy named Seth:

I had a topic for you to address that I thought might be good for someone with a behavioral econ background. Tonight is Stephen Strasburg’s MLB debut (#1 uber prospect) for the Nationals. The Nationals will only let you buy tickets for tonight if you buy tickets to 3 other games during the season. You do get one of those games free, plus a Nats hat. Why don’t the Nats just raise their prices for tonight’s game? My guess is that people hate price increases, but I thought I would see if you have some research to back that up or other ideas?

It's an interesting question, and it just so happens that I was planning to write on something directly related to this topic this week. Seth, if you're out there, I'm giving you a two-for-one deal: Two complementary economics answers for the price of one. First, here's Jodi's main point (she has a lot of side points, too... really, check them out here):
Luckily, that explanation is simple- that kid is cool, and people really want to see him. Regardless of whether markets are competitive or not, increased demand leads to higher prices. But Seth points out that the Nationals are being a bit sneaky- they aren’t explicitly raising the ticket prices for the popular game, but they are bundling it with other items. I can’t be sure of what their reasoning is, but my hypothesis is something along the lines of the following: like I said, the marginal cost of one more person at the ballpark is essentially zero since there are a fixed number of seats. (The opportunity cost of the bundled tickets is also zero since the tickets would likely go unsold otherwise.) In addition, once a person is at the ballpark there is a chance that he will buy the $8 draft beers, the $6 cheeseburgers or, if you’re in Boston at least, the $4 Dunkin Donuts iced coffee. These two facts together imply that there is an incentive to get butts in the seats, in which case the bundling strategy is clearly superior to just raising prices.
Basically, Jodi points out that the Nationals were blessed with high demand, so they did what our supply and demand models predict; they raised prices. But, they did so in a smart way. They bundled the high value product with a different product they were having difficulty selling. As Jodi points out, this is a smart idea because it achieves cost savings, filling seats that would otherwise go unfilled.

Bundling is smart for another reason that Jodi didn't mention in her post. Bundling can effectively enable price discrimination (or charging different prices for the same good). The obvious good here is a ticket to watch the phenom, but let's focus on the auxiliary tickets to see more clearly how the Nationals are selling at different prices in this example. Effectively, the Nats can exploit the excess demand for "phenom watching" by using a bundle to charge more than they would have gotten for the ordinary tickets.* If the "phenom watchers" attend the three ordinary games, they will likely sit next to someone who paid half the price for a ticket that they bought in the parking lot before the game. (UPDATE: This is backwards for the price discrimination story. All else equal, the high-phenom demand individuals will feel like they paid a low price for the ordinary tickets. See my correction in the comments.)

An additional consequence of bundling the tickets this way is that the bundle acts as a screening device. Some fly-by-night fans might want to go see the phenom's major league debut, just because it is his major league debut (some people like the spectacle). All else being equal, these fans will tend to have less overall demand than those fans who just love their Nationals. In this sense, the four-ticket bundle will be more attractive to "genuine" fans than it will be to spectacle spectators.**

In case you want to know more about price discrimination, I recently recorded three videos on the topic. Formally, the Nationals are engaging in 2nd degree price discrimination (which is -- appropriately -- the second video in my series). Unlike 1st and 3rd degree price discrimination, the formal theory of 2nd degree PD is a bit hard, but the intuition is just what I've said: use bundles to charge different prices for the same good.

Here are the videos:




If you like these videos, I have 45 more videos on microeconomics at my YouTube channel, which follow (so far) the first six chapters of my book. Check it out if you're interested.

*To be fair, Jodi touched on the price discrimination logic in the story. She just didn't emphasize it. With me being a lover of price discrimination, I felt compelled to write a post emphasizing this feature.

** The team could have different reasons for wanting to screen the audience for genuine fans. Maybe they cheer harder or spend more money at the concession stands.


  1. I found it difficult to make a price discrimination argument because I can't tell how I should allocate prices within the bundle of items. Say I bought one of the ticket bundles for $100 and the face value on each of the tickets is $25- one could say then that it is proper to give a price of $25 to each of the tickets and a price of $0 to the new shiny Nationals hat that comes with the bundle. With this setup, it does in fact seem like I would have paid more for my low-demand tickets than the dude who paid $10 in the parking lot. However, if I can't buy each of the items separately then it's not really clear what the individual prices are. If I base the ticket price allocation on my valuation of the items, I could end up with something like $70 for the high-demand game and $10 for each of the low-demand games (since that is what I could sell the tickets for)...and still $0 for the hat, since, well, it's a Nationals hat.

  2. Good point.

    If two goods are sold together in a bundle, it is difficult to tell what is the right price for individual goods.

    That said, the best way to do it is to net out the value of the other good (your conditional-on-value price allocation). This is right because it acts like a marginal price, and it works for any bundle you can dream up (though sometimes you'll get negative prices).

    The even-split way of doing it is a bit arbitrary, and doesn't make sense for some easy-to-dream-up bundles. For example, I might consider buying a bundle with three things in it: a car, an air freshener, and a set of tires. If I pay $30,000 for this bundle of three goods, it doesn't much make sense to say that I paid $10,000 for the car, $10,000 for the air freshener, and $10,000 for the set of tires.

    With that in mind, you bring up an excellent point about where my original post was exactly backwards. I meant to emphasize how bundling enables price discrimination AMONG THOSE WHO BUY THE BUNDLE. But, I stated it wrong in the post, and I didn't emphasis the most interesting point. Let me state it correctly here.

    Using the right (conditional on value) price allocation, if you are a high phenom demand person, buying the bundle is like paying a low price for the ordinary tickets (because we subtract the value from the bundle price to determine the price for ordinary tickets). If you are (relatively) low phenom demand, buying the bundle is like paying a high price for the ordinary tickets. Among these two types of consumers, people are effectively paying different prices for the same good.

    Finally, I have been thinking about this, and I realized that there is one more thing that can cause the price discrimination argument to unravel. For price discrimination to be viable, resale has to be costly or prohibited. The ballparks of America have vibrant scalping markets, and StubHub is just a click away. So this assumption doesn't seem especially viable.

    Still, if you're willing to stretch, there may be people who have a stubborn distaste for ticket resale. On this group of people, price discrimination through bundling might work.

  3. Tony,

    Thanks for the second answer. I like the screening for fans who would actually want to see more Nationals games story.

    The Nationals have done a lot things to piss off the local fans. Including not showing games on TV for the first couple of year and trying to withhold tax payments. They also let fans think Strasburg was debuting a week earlier, get probably about 10k fans extra for a game last week against the Reds.

    It's funny though the bundle of tickets was 4 games for the price of 3. I think someone who bought the bundle probably paid less for the other non-Strasburg opener games then the person sitting next to them. I live in DC, I haven't found 1/2 price Nationals tickets around the stadium. Most of the ticket sellers (scalpers) I have tried to bargin with in past attempts wouldn't go below face value even on non-marque games. I've checked craigslist and other sites really you might get a 10% discount.

    I'm really leaning toward the Nationals didn't profit maximize last night, but were hoping to build some good will.

  4. If I'm reading you correctly I think your argument has more to do with "perceived value" than true "price discrimination" and doesn't really address Economists Do It With Models push-back.

    If we assume that for most regular games the ticket has a "face value" given by the club of 20 USD, but the "market price" which you can get a ticket from a scalpers that is 50% lower so 10 USD, then we have to following situation:

    Running a scenario with one high-demand "phenomenon" game and one regular game included in a bundle:

    Regular Fan
    If the club are charging 40 USD for the bundle (effectively face value * 2) then the regular fan would purchase the bundle if they see the value of seeing the phenomenon at 30 USD or greater, effectively 40 USD bundle price - 10 USD market value for the regular game

    Phenomenon Fan
    If the club are charging 40 USD for the bundle (effectively face value * 2) then IN PERFECT MARKETS the phenomenon fan would ALSO purchase the bundle if they see the value of seeing the phenomenon at 30 USD or greater, effectively 40 USD bundle price - 10 USD market value for the regular game. The only difference is that they would sell the regular ticket for which they have no interest. Given that we do not live in perfect markets, there will be transaction costs and a percentage of fans will not sell the tickets but just be prepared to pay more for the phenomenon, so they will have to have a marginally higher perceived value for the phenomenon to purchase.

    But there is no price discrimination, the same goods are being sold to each customer segment at the same price, regardless of their perceived value.


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