Archive for category Buffets and Risk
Monday Microeconomic Muse: Buffets, Part Three: How Do Buffets Deal With Asymmetric Information?
Posted by The Marginalist in Buffets and Risk, Microeconomic Muses on April 20th, 2009
This is part three of the “Buffet” series. To read part one, click here. To read part two, click here.
That’s right
YUP. Microeconomic Muses are on Mondays now. I decided that posting one every other day would mean I’d eventually run out of them. Onwards!
Recap
LAST time, I talked about the influence of asymmetric information and adverse selection in buffets. I concluded that in a very simple model of a buffet, the low-cost people (people who eat less) get driven, eventually leaving the buffet owner with only the people who eat a lot of food. I don’t want to reexplain everything here, so if you missed it, links are at the beginning.
Today I’m going to revisit the question I posed at the end of part two: Why hasn’t adverse selection ruined buffets?
What went wrong?
LET’S first think about what exactly made adverse selection such a bad thing for buffets.
- Adverse selection drives out the profitable customers (those who eat little)
- Adverse selection retains the high risk customers (those who are likely to eat a lot)
- You can’t price based on how much people will eat (asymmetric information)
So these are the problems buffets have to think about when they counter adverse selection. Here are some ideas I have about what the solutions are.
1. Keep the low-risk customers in
The reason why you need the low-risk customers (the people who eat little) to stay in is that these are the people you’ll be making your biggest profit off of, and they’ll offset the losses from the big eaters. But how do you keep a low-risk customer in when they’ll get less food then they pay for?
The way we’ve been looking at buffets so far is that customers look at the amount of food they know they’re going to consume. But the trick is to make the buffet no longer about the quantity of food. In other words, change the incentives for people to come and eat at your buffet.
Incentive: Something that makes someone do something, or at least want to do something.
One obvious incentive is the quality of the food. For example, the place I visited had awesome food. Everything there was great — I felt that I wasn’t paying for the quantity of the food, I was paying for that great steak.
Another way to change the incentives of the customers is to make it not only about the food. For example, I absolutely loved Fogo de Chao’s atmosphere, and the service was very friendly and personal (one of the waiters struck up a conversation with me about wrestling — I happened to be wearing my state wrestling shirt).
Lastly, make going to your buffet a group thing. I have low-risk buffet goers and high-risk buffet goers in the same social group, and we go to Old Country every now and then as a social thing.
2. Improve your chances
Another way is to simply lower the average expected value of your customers. Fogo de Chao gave us an assortment of free sides that were all cheap to make and full of starches. Starches, I hear, fill you up — and by giving us “free” sides, they reduced the amount of meat (the expensive stuff) that we’d eat.
So, how would a buffet go about doing this? One way is to, like Fogo de Chao, just put the dishes right in front of us. In more conventional buffets, I would place starchy, cheap foods first in line (or wherever the customers are more likely to visit). Customers will fill their plates (and their stomachs) with the food that comes at a lower cost to you before getting to the good (and expensive) food!
Basically, in our roulette metaphor (part one), you’re decreasing the chance of people actually winning this bet.
3. Price discriminate
Another way to get around this is to end asymmetric information. Basically, you’d try to charge each person a different amount based on how much they will eat. Wait a minute, you cry! Didn’t you just say that buffet goers know their type, but the buffet owner doesn’t?
True, you can’t know for sure how much any one person is going to eat. But you can know that certain demographics of people will eat more or less than others. Seniors and children will eat less than adults, for example. So you charge adults more than seniors and children, which allows you to keep more people in your market.
But you have to do this really carefully. For example, you can’t discriminate based on racial demographics or by sex — that would be too blatant. If you discriminate on age, you can at least claim to just be being nice to old folks and kids!
Charging different people based on their demographic group is known as price discrimination.
Price Discrimination: When a business charges different demographic groups different prices based on their willingness to pay different prices. Not the same as discriminating against people because you don’t like them.
Price discrimination shows up in a lot of other places — movie theater and museum tickets are a big one.
Buffets, Part Two: Asymmetric Information and Adverse Selection
Posted by The Marginalist in Buffets and Risk, Microeconomic Muses on April 14th, 2009
Recap
IN the last post, I wrote about the similarities between casinos and buffets. Both casinos and buffets basically make a bet every time they invite someone in; however, by inviting large numbers of people in, they can more accurately predict what their expected payouts are going to be, and make a predictable profit that way.
At the end of the post, I asked,
Given that, how are casinos not like buffets?
And that’s the topic of today’s post — the soup and salad of this series.
Let’s revisit gambling
LET’S say you’re running a betting game at a carnival that goes something like this: the gambler pays $1 and chooses heads or tails on coin flip, and if he or she wins, she gets two dollars back.
When analyzing risk, economists like to separate people into different “types.” In this game, one type of person is the winner; he/she will guess the coin flip correctly. The other type will be the loser; he/she will guess incorrectly. You can separate people into different “types” for any game you’ll find at a casino (or a carnival).
In the gambling world, no one really knows their type, and the casino owners don’t know the gamblers’ types. That is, no one knows whether or not they’ll be a winner or a loser (let’s ignore poker and other strategic games for now). But that changes in a buffet.
Buffet-goers know their type
WHEN someone walks into a buffet, they know how hungry they are, and they have an idea of how much they’ll eat. Jonny knows he’ll eat the buffet out of house and home, but I (during wrestling season) know I won’t eat more than a plateful of food.
To economists, this type of situation is known as asymmetric information.
Asymmetric Information: Asymmetry occurs when one side of a trade or bet knows information that the other side does not. Occurs in insurance, buffets, and college admissions.
That’s the main difference between the buffet and the casino; the buffet is in an asymmetric situation, and the casino is not. The real interesting about asymmetry is that sometimes it creates poor outcomes for everyone.
Pretend you’re going to open a buffet.
LET’S also pretend that ten people are interested in your buffet. One person will eat $10 worth of food, the next, $20, and so on, up to Andy, eats up to $100 worth of food.
Unfortunately, you don’t know how much each person is going to cost you, so you have to charge everyone the same price. This is the result of the asymmetry of your buffet!
Let’s ignore profit for now, and say you charge just enough to cover your costs. The total cost to you will come up to $550, which means you have to charge everyone $55. But what does that do to your customers?
$55 is a great deal for the football players who’ll eat $60, $70, $80, $90, and $100 worth of food. But everyone who’ll eat less food than that will realize it’s not such a good idea, and they’ll head over to Old Country, so now you’re only left with the customers who’ll eat more than $55 worth of food — you’re left with the bad bets.
Knowing this, you can figure out that the average cost of the buffet-goers to you — the average expected value of the customers, will increase. So you’ll have to raise your price again to cover these costs. But again, you don’t know the exact types of the remaining customers, so you’ll have to charge the average.
The average cost of the remaining customers is $80 dollars, so you charge $80. But this drives away the customers who’ll eat $60 and $70 worth of food! You’re left with Messieurs. $80, $90, and $100.
So you calculate again — you charge $90 and drive away Mr. $80. Then you charge $95 and drive away Mr. $90 (I’m assuming, perhaps wrongly, that only men will eat this much food. Now that would be an interesting thing to research).
Soon you’re left with Mr. $100, and you’re charging $100. But your original customer base is essentially gone.
What we’ve discovered is a case of Adverse selection. Adverse selection is something that scares economists because it basically closes off a risk-based product to a majority of the market (the buffet-goers) and reduces the ability of firms (the buffets) to provide that product to the market.
Adverse Selection: A vicious cycle in which asymmetric information filters out the profitable customers of a risk-based business until only the most risk-intense customers are left.
A note on this model
THE specific amounts of food people will eat and the specific numbers of people is largely irrelevant for the concept; I only chose these numbers because they’re easy to work with. If you use other mixes of diverse types of buffet-goers, you’ll get the same result.
The key to understand the imaginary examples and models I’m going to use in this blog is to remember that they’re purely used to demonstrate concepts, not to be taken seriously as models of specific real life situations.
The models that economists use almost always started out as basic models like the one I’ve explained above. To fit specific situations, economists figure out what their models are missing, and go from there until they create accurate and precise models of human behavior.
Well, this model is obviously incorrect…
RIGHT. Buffets are still in business, and serve people other than the most gluttonous of gluttons. Why? That’s in the main course of this meal series (yes, that metaphor is getting old).
Tomorrow: “Buffets, Part Three: How Buffets Deal with Adverse Selection.”
And a couple more things….
THANKS to everyone who’s reading this so far. Help me out and tell your friends about this, yeah? Facebook, word-of-mouth, and anything else is greatly appreciated.
Also, a regularly updated Glossary of Terms is available in the sidebar.
Buffets, Part One: The Law of Large Numbers
Posted by The Marginalist in Buffets and Risk, Microeconomic Muses on April 13th, 2009
Introduction
IN Chicago, I ate at this great Brazillian Steak Buffet called Fogo de Chao.
Fogo de Chao. Brother at the left.
I have nothing but kind words for this place — these were the best steaks I’ve ever tasted, the service was wonderful (one of the waiters struck up a conversation with me about wrestling), and the dining experience itself is worth going there for (chefs walk around with cuts of steak and slice off portions for you).
But this ain’t a restaurant review… this part one another microeconomic muse. Bon appetit.
Let’s look at casinos first (I promise this will be relevant)
Let’s say you run a casino. At the roulette table (click the link to learn about roulette), you charge $1 for each play, and pay out $35 for each time someone bets on one number. The odds of winning this game is 1:37, or 1/38. So about once every 38 times, you (the casino owner) can expect to pay $35 out. However, the other 37 times, you can expect to win $1.
When we talk about making bets and risky decisions, economists like to think about the expected value of a risk. Wikipedia describes this as “integral of the random variable with respect to its probability measure.” (This, by the way is why math is important for economists.) I have no idea what this means (and, given the reading base of this blog, neither do you!). I define it as:
Expected Value: Imagine if you played a risk-based game an infinite number of times. Your expected value of that game is the average payout of the game. Think of it as a weighted average of all the possible outcomes of a game.
I don’t want to go too far into the math, but just remember that the expected value of a bet is basically the amount you can expect to win or lose, on average. It turns out that the expected value of roulette is 5.3 cents (the casino owner will win 5.3 cents, on average, per play).
Back to pretending you’re the casino owner. Imagine if you only play one roulette game. On that one game, you could lose $35! If you only play a few games, you run the risk of ruining your casino in those few games.
But imagine if you play a thousand games. It’s more and more likely, as you play more games, that you’ll get closer and closer to paying out 1/38 of the time, and winning the rest of the 37 times. Again, I don’t want to go too far into the math here, but as you play more and more games, it’s much easier to predict how many times you’ll win — you can predict your average expected wins with many plays. This is known as the law of large numbers.
The Law of Large Numbers: As the number of plays on a bet get larger, the average payout of those bets gets closer and closer to the average expected value of the bet.
Ironically, by betting more often, you can reduce your risk!
Yes, this has something to do with buffets.
Buffets are kind of like casinos in this way. When a buffet takes a customer, they’re essentially betting that the value of the food that a customer eats won’t exceed the amount that they paid to get into buffet. Basically, Old Country Buffet is hoping you won’t eat more than the $10 you paid to get in.
Now, let’s say 1/7 of these customers will be like my friend Jonny, who’ll eat, say, $30 worth of food. The rest (6/7) will be normal people and eat about $2 worth of food. Jonny is like the casino player who wins $35, and the rest are the chumps who just lost money on this bet.
(Note: Of course, there are people who’ll eat food valued at other costs, like $5, $10, $20, etc, but let’s keep it simple for now).
Just like the casino owner, the buffet owner needs to think about the average expected value of this bet She needs to find the average value of food that she thinks the average buffet-goer will eat. Based on that expected average value, she needs to charge a little bit more than that.
Now if you do the math, in our example above, each customer will eat, on average, $6 of food. The buffet owner will make, on average, $4 per person.
And, like in the casino, the law of large numbers applies here. If she seats one table a night, she could ruin her business if a table full of Jonnys show up. But if she seats three hundred tables a night, she can reasonably expect that very close to 1/7 of these are fully of Jonnys and the rest are normal buffet-goers. By serving a large number of people, she can ascertain that her average profit will be pretty darn close to $4 per head.
Given that, how are casinos not like buffets?
But there’s a twist to the bets that buffets are making that casinos don’t have to face. Think about it, then read about it in my next post — “Buffets Part Two.” This was just, say, the bread on the table before the real meal.