Ketchup Economics Explained

Last week I wrote about a controversial field of gastronomic economics: ketchup economics. OK, you caught me. This field of economics does not exist. Perhaps it should. How then, was I able to quote Larry Summers discussing the findings and controversies in this field at such length in a reputable journal (link here for those with JSTOR access, citation here or here)? Larry was using ketchup economics as a metaphor to understand financial economics.

Broadly speaking, there are two main fields of finance. One, asset pricing is concerned with what it sounds like. How much should a stock, bond, or option be worth given the (uncertain) payouts it promises (dividends, coupon payments, etc.) that it promises in the future? The other, corporate finance, is concerned with how firms' investments are chosen and financed. Should the firm finance itself with equity (e.g., issuing stock in an IPO or SEO), debt (e.g., bank loan or bonds), or some combination?

Larry Summer's view is that these fields are not asking the most interesting questions. For asset pricing, how much should the overall stock market be worth? For corporate finance, what kind of investments should a firm make? Instead, both asset pricing and corporate finance spent a lot of time answering the financial analog of the Summers' ketchup finding that "two quart bottles of ketchup invariably sell for twice as much as one quart bottles of ketchup." In fact, two Nobel prizes (one in asset pricing, one in corporate finance) have been given out for answering questions along these lines. The Black-Scholes option pricing formula shows that the price of an option can be calculated in terms of the price (and other attributes, chiefly volatility) of a stock and a bond (e.g., the interest rate), just as the value of a large bottle of ketchup can be calculated in terms of the price of two smaller bottles of ketchup. The Modigliani-Miller theorem shows that the total value of a company (the sum of the value of a firm's stocks and bonds) is independent of their proportions, just as the price of a certain amount of ketchup will be independent of whether it is sold in two small bottles or one large one.

I'm happy to report that there has been some progress in finance in countering these concerns in the 20 years since Summers first raised them. For example, consumption-based asset pricing shows how the overall level and movement of stock prices can be linked to people's consumption. Instead of just valuing assets relative to one another, we can think about the overall level of asset prices and also connect these levels to the value these assets provide in people's lives.

Bringing Food Into Camden Yards

Public Service Announcement: According to the Baltimore Orioles website (see "Articles Not Permitted Into Ballpark") and my own experience, you can bring food and non-alcoholic beverages into the ballpark (but no glass bottles or coolers). Given the very high prices for food inside the park and the length of baseball games, bringing your own food is a wise move.

Tickets to see the Orioles at Camden Yards were cheaper than I expected (we had excellent $15 seats at games against the Red Sox). Clearly, ticket sales are the loss leader that gets people into the stadium to buy food, alcohol and souvenirs. Note that there are many many businesses with this model. Many motels break even or lose money on low room rates in order to make it up on telephone use charges, expensive mini-bar drinks and snacks, and (pay-per-view) porn. Movie theaters break even or lose money on ticket sales but then make money on concessions. Firms sell printers at artificially low prices to make money on toner cartridges. In each of these cases, the visible and expected fee is kept low to get people to the point where they will choose to buy the (perhaps unanticipated or unconsidered) add-on good at an extremely high markup. Note that in all of these cases, it is possible to enjoy cheap initial fees without paying the high markup for secondary services. If you know about these fees, you can use your cell phone in the hotel room, eat before you go the movies, or do your large printing jobs on economy mode (or at work). People who do this get a great deal, as they enjoy the artificially low initial fee (cheap hotel room) but can avoid or minimize the artificially high secondary fee (room telephone charges). Many firms exploit the fact that we don't think about doing these things until it is too late (e.g., we've already arrived at the movie theater or our printer is out of toner). Given this odd pricing by some firms, you might think that other firms would have an incentive to advertise that they don't have annoying pricing schemes. I'd be willing to pay an extra $1 to go to a movie theater that had reasonably priced popcorn and soda. Xavier Gabaix and David Laibson have an interesting paper in which they show why this doesn't happen. In a nutshell, educated consumers (those who know and plan for the fact that movie popcorn is expensive by eating beforehand) don't want to go to a theater with cheap popcorn (because it costs more since they are no longer being subsides by dupes who buy expensive popcorn); uneducated consumers are no longer profitable once they become educated to the popcorn scam so it doesn't make sense to remind them of it.

Camden Yards is a bit unusual in allowing food from the outside. I suppose their reasoning is that many people simply wouldn't go to the game if they were told they couldn't bring in outside food. It is worth noting that most people don't bring food to the game even though they are permitted to. I suspect people don't know they can bring in food, or they forget that they can bring in food. The Orioles don't publicize the fact that outside food is permitted. You have to infer it from the cryptic passage I linked to above.

You see some effort by other firms to educate fans about this fact as they approach the ballpark. I heard a guy with a megaphone exhorting me to buy his peanuts outside the stadium and telling me how much cheaper they were than the ones inside. However, such advertising was limited and for good reason. An educated consumer is by definition not going to be too profitable because you are educating them to the fact that they can bring in cheap outside food. Why spend money to educate a consumer to buy your low-margin product? (Cheap peanuts are barely profitable to sell even if you don't spend on advertising.) The result of all this is that most people don't plan ahead by packing dinner when they come to the game; many probably don't think about the possibility until they get to the park and notice a few people who have done it.

Gastronomic Economics on the First Day of Class

Today is the first day of class.

As any of you who have taken economics classes know, it is common to draw graphs where the x-axis is the amount of one good you consume and the y-axis is the amount of another good you consume. (The more you consume of one good the less money you have left over for the other.)

This gastronomic economists is seeking suggestions about pairs of gastronomically related goods. "Beer" and "pizza" is the standard pair, but I think we can be more creative. (Guns and butter is also common but guns are unrelated to food; my first class used drugs and everything else as the two goods.) Please leave comments with creative food-related goods pairs of goods I can use in class. Particularly welcome would be creative food-related pairs that are compliments or substitutes. Examples of superior, normal, inferior, and Giffen food-related goods are also welcome.

Ketchup Economics

Today's post is about what is, in my view, the most important sub-field of gastronomic economics: the economics of ketchup. An excellent survey was written in 1985 in a top journal by Larry Summers (Harvard economics professor, former Secretary of the Treasury, and former President of Harvard). In his article (link here for those with JSTOR access, citation here or here), Larry summarized the main findings of ketchup economics as follows:

Nonetheless ketchup economists have an impressive research program, focusing on the scope for excess opportunities in the ketchup market. They have shown that two quart bottles of ketchup invariably sell for twice as much as one quart bottles of ketchup except for deviations traceable to transaction costs, and that one cannot get a bargain on ketchup by buying and combining ingredients once one takes account of transaction costs. Nor are there gains to be had from storing ketchup, or mixing together different quality ketchups and selling the resulting product. Indeed, most ketchup economists regard the efficiency of the ketchup market as the best established fact in empirical economics. (Summers, p. 634, again full citation here)

Personally, I feel that ketchup economics - while interesting and important - has received too much attention relative to other relatively under-studied fields in gastronomic economics (e.g., restaurant economics). Still, in the wake of the popularity of Freakonomics it should come as no surprise that a piece by Malcolm Gladwell about ketchup aimed at non-economists garnered so much attention. Given the interesting and thoughtful articles that Gladwell has written about the economics of other fields such as SUVs and moral hazard in health insurance (both articles I have assigned to my students), it is disappointing that he seemed to miss so completely the importance and subtlety of ketchup. I would throw tomatoes at him, but as an economist I just can't bear to waste such a valuable asset.

Unfairness of Splitting the Bill

This is part three on the economics of splitting the bill:
Part I - The inefficiency of splitting the bill
Part II - The inequality of splitting the bill
Part III - The unfairness of splitting the bill (this post)

In her comment to my post on the inequality of splitting the bill, Lise notes that people with smaller appetites or cheaper tastes suffer when you split the bill evenly. Notwithstanding the alleged trend for women to order steaks on dates (TimesSelect), she believes that women will suffer on average from splitting the bill. Note that this is not an efficiency issue; it persists even when people don't order more when they split the bill.

So why do we split 50-50 when it isn't "fair"? Peyton Young (who recently moved from Johns Hopkins to Oxford) has written several papers and a survey article on this topic. If we wanted people who ordered more to pay more, it would be natural for each person to pay their share. This is hard to get exactly right without a calculator and a fair bit of effort, as the bill doesn't calculate the tax on each item or cluster the bill. We like 50-50 because it is easy.

Of course, there are times when 50-50 isn't particularly easy. To me, splitting a $45 bill into $20 and $25 seems easier than splitting $22.50 each. This suggests another answer, which is that 50-50 is the default. If you aren't going to go with 50-50, then this requires a discussion of what the right proportions are in every case. This negotiation is rather costly, and could easily spoil an otherwise pleasant meal. Even if 50-50 isn't right in a specific case, deviating from it opens a can of worms few of us want to deal with.

While the stakes (steaks?) aren't too high in the case of restaurant meals, there are settings with larger consequences where people stick to an "unfair" 50-50. (Peyton Young discusses the proportion of crops that go to the farmer in sharecropping as an example.) Here, it seems that 50-50 is an anchor-point for negotiations.

Is this a big deal in the case of dinner? Even if 50-50 isn't the right split in a given case, in many situations it is probably right on average. I may order more than my companions at one meal; I may order less at another meal. As long as this nets out over the long run, who cares? Lise's concern was that it doesn't net out on average for women, who order less on average. This may be so, but this begs the question of whether the unfairness to women of splitting the bill nets out against the social norm that men pay for dinner on dates with women. And this begs the question of how men paying for dinner nets out against other gendered costs (e.g., clothing) and differences in income. This is a can of worms I don't want to open, and definitely a dangerous one to open on a dinner date regardless of who is paying.

Inequality of Splitting the Bill

A few days ago, I blogged about the inefficiency of splitting the bill. (Cliff notes version: when you split the bill, your dining companions bear much of the cost of your ordering more. This gives you an incentive to order more than you would otherwise.)

Today, the inequality of splitting the bill. I should probably explain this. When I was a graduate student, I had a opposite-sex roommate. We are both foodies, and would frequently go out to eat together. When the bill came, we would each put down a credit card. We split the bill evenly. So far, not too interesting.

Half the time, the bill turned out to be odd (not even, e.g., $46.13). In this case, it wasn't possible to split the bill exactly. It was common to see the bill split $23.06 and $23.07, and also $23.00 and $23.13. One of us had to pay more. I (a male) and not my roommate (a female) was always given the larger amount to pay. This happened far too often to be explained by chance. I wish I had recorded these data, but we split the bill in this fashion this dozens of times; the outcome was always (or perhaps almost always) the same.

In our case, it was easy to match credit cards to patrons (one name is typically female, the other typically male). Based on this mini and accidental experiment, I guess men nearly always pay the extra penny. Economically, this extra penny isn't a big deal; it it dwarfed by the higher cost that women are forced to pay for a variety of sevices (e.g., dry-cleaning). Over the course of our meals, the difference probably added up to less than the cost of a latte at Starbucks.

Psychologically, I think this is kind of interesting. Did servers think I was more able to pay? That I wanted to pay more? That paying more (or all) was my "role"? I wonder what will turn up based on differences in race; I wonder if gender differences are larger or smaller if the dinner looks like a work function, a date, or a social gathering.

I'd love to get actual data on this, so if you feel like it please help me out with an experiment.

Who can participate? You can participate if:

1. you go out to dinner at a place that takes credit cards;
2. you go with other people and are willing to "split the bill", putting down one credit card per person;
3. some of your party could be reasonably identified from others in your party based on the names on your credit cards. This identification could be based on race, gender, or even age. (This would work well if Jennifer Smith (female) and John Jones (male) went out, or Jennifer Smith (Caucasian) and Jennifer Wong (Asian), or Mildred Smith (age 85) and Jennifer Jones (age 30). This need not work perfectly, as I'm sure there are plenty of Jennifer Smiths who are of Asian descent and plenty of Jennifer Wongs who are not.); and,
4. the final bill turns out not to be evenly divisible by the number of people in your party. For example, the bill is odd for a table of two.
   

How to participate?

1. If you get a bill that is not evenly divisible (e.g., $46.13 bill for two people), each person should put down a credit card with their name on it (which implicitly identifies whose credit card goes with each person).
2. If asked, say you want to "split the bill" or "split the bill evenly". Do not mention that this isn't possible to the penny.
3. Make a note of the following information and email it to me:

• The location of the restaurant, name of the restaurant, and the date you went.
• Your best guess about the age, race/ethnicity, and gender of the server (or the person who you think dealt with your credit card information), if possible.
• The name, age, race/ethnicity, and gender of each person in your party. Approximate ages/ethnicites are fine if you don't want to ask your dinner date's age or ethnic background. We just want to know what a server might guess about these things by looking at you and your names.
• The total bill amount (without tip) and how this amount was allocated among the people in your party.
• Where on the table (near which person, etc) did the server place the bill? Did the server ask you what you wanted done with the cards you put down?
• Did your dinner look to the server like an a) date, b) work function, c) social gathering of friends, or d) other (please explain)?
  

Thank you in advance.

Inefficiency of Splitting the Bill

Have you ever been to a restaurant with a large group of people and split the bill, so everyone pays the same amount? Most of us have; it is common among my friends. Under these circumstances, have you ever been temped to order more than you otherwise might? After all, if you spend an extra $1, you only pay $1 x 1/N (where N is the number of people in your group). Have you seen your friends order things (e.g., one more $10 cocktail, the lobster) you think they wouldn't otherwise when you are splitting the bill? Again, they alone get the benefit of the food and everyone shares in paying for it.

The first person who expressed concern about this to me (in 1998) was Sarah Reber, an economist with excellent economic intuition. Sarah's guess was that this problem was particularly severe for (alcoholic) drinks, and less severe for food. I hadn't given it much thought, but recently found out about this paper by Uri Gneezy, Ernan Haruvy and Hadas Yafe which provides nice evidence that this is a problem. The authors found groups of people going to a restaurant. At the beginning of the meal, they were randomly told that a) they would each pay for their own meal, b) that they would split the total bill equally, or c) that the person running the experiment would pick up the tab. People spent least in (a) when they bore the full cost of ordering more; they spent less in (b) when they bore only some of the cost of ordering more; they spent least in (c) when they bore none of the costs. So people spend more when their friends pick up much of the cost of this extra ordering. They don't take into account the harm they do their friends by ordering more.

The efficient outcome is obtained if everyone pays for themselves, so people bear the full cost of their food (which makes sense given that they also get the full benefit of eating). So why is it so common to split the bill? One answer is that it is easier. It is always hard to figure out each person's share of the tax and tip. Another is that it is awkward to suggest that everyone pays for themselves. If you took the harm you did to your friends by ordering more (when you are splitting the bill) into account when ordering, there would be no problem with splitting the bill. Suggesting that you want everyone to pay for themselves is effectively accusing your friends of not caring about your welfare. Now that's an awkward conversation.

Pricing Power of Baltimore Restaurants

I want to begin this post with two stylized facts about Baltimore restaurants relative to other cities.
1. On average, nice Baltimore restaurants are more expensive than comparable restaurants in other cities.
2. On average, nice Baltimore restaurants are easier to get into (a.k.a. emptier) than comparable restaurants in other cities.

These two observations seem pretty clear to me after just a few months in Baltimore (and having spent lots of time in more than a few major cities for comparison). I'm going to use them as the starting point for this discussion, but I welcome thoughts on either point. If either of these is wrong, my theory (which attempts to explain them) is probably wrong too.

Can we explain these two facts with a single unified explanation? Why doesn't a restaurant cut prices to get fuller? Given the fixed costs of running a restaurant, this would certainly be worth doing if a small price cut would substantially increase the number of customers. The fact that we don't see much of this (judging by the high prices and empty restaurants) implies that in Baltimore you wouldn't get a big increase in customers with a small decrease in price. In other cities, you see lower prices and fuller restaurants because empty restaurants can increase their number of customers more dramatically with small price drops. In other words, Baltimore's restaurant patrons have a more inelastic demand for a given restaurant than patrons in other cities.

Why are Baltimore restaurant patrons more inelastic demanders of dinners than patrons in other cities? The obvious answer here is that larger and richer cities have room in their markets for more nice restaurants of any given type and therefore more competition. The Baltimore restaurant market is less competitive and "thinner" so restaurant owners have more pricing power. Thai Restaurant in Waverly charges much higher prices than similar restaurants elsewhere because you have to Mount Vernon (and arguably to the DC suburbs) to get good Thai food nearby. I'm willing to pay $3 to avoid this commute, and Waverly doesn't have a big enough market to support two Thai restaurants. Therefore, the one Thai restaurant can raise prices a bit knowing our other options are limited.

Using Zagat Data to Pick Restaurants

As a foodie economist, one of the few things that makes my mouth water more than a good meal is good data about restaurants. The basest form of such data are the restaurant hygiene ratings I blogged about recently. For a foodie economist (though not an epidemiologist), more interesting data would include information about a restaurants cost and quality.

Zagat collects just such data. As you probably know, Zagat includes data about the location, type of food, hours of a variety of restaurants in most metropolitan areas. More interestingly, it asks readers/eaters to post their evaluation of restaurant cost and quality (in terms of food, decor, and service). Zagat aggregates these evaluations into scores for cost, food, decor, and service for the restaurants it includes. (They also include blurbs with witty and punny remarks about the restaurants, but as an economist I'm not sure what to do with these.)

So given all this data, how do you pick a restaurant? You want to find one that is "good" but also a "good deal." This restricts you to restaurants on the price-quality frontier, but how do you identify these? Below, please see instructions for doing this. I haven't done it because:

a) Step 1 below would take a fair bit of effort;
b) I couldn't get a good publication out of it; and,
c) Without Zagat permission (which I don't have) I suspect that it's not legal to use their data.

I should say at the outset that this idea is not unique to me. This is what any decent economist would tell you to do if they thought about it. In fact, I think this is pretty much what Orley Ashenfelter does to choose wines and what was done in this paper by Olivier Gergaudy, Linett Montano Guzmanz, and Vincenzo Verardi to pick French restaurants (which was written about in a July 13th, 2006 New York Times article by fellow foodie-economist-blogger Tyler Cowen). I suspect other researchers have done this as well. (If you are an economist or statistician who has written a paper which does this or something like it, please let me know and I'll add a link to it here.)

Step 1: Enter Zagat data. Put it in a spreadsheet, with each restaurant in its own row. Columns would have "Restaurant Name", Cost, Food, Decor, Service, Neighborhood, City, Cuisine, and perhaps some of the other attibrutes (open late, etc.) Zagat includes. Convert this data into the applied statistical software of your choice, in my case STATA.

Step 2: Generate dummy variables for location (either city or neighborhood) and cuisine. There is one of these for each location or cuisine, and they take on a value of 1 if the restaurant is in that location (or of that cuisine) and zero otherwise. You will want to lump together any categories that are similar but with few observations. (I'd put Lao food in with the Thai category unless there are a lot more Lao restaurants on Zagat than I expect. In Baltimore, you would want to lump together nearby or similar neighborhoods into groups. You want at least 20 values of "1" for each dummy variable, but given the large number of cities in the data this shouldn't be too hard.) You may also want to create a polynomial function of food, decor, and service, by creating variables like food², decor², or even food×decor.

Step 3: Run an OLS (ordinary least squares) regression to predict "cost" with food, service, decor (and perhaps the squared and cubed and cross-multiplied versions of these variables), location dummies, and cuisine dummies. Collect the "residuals" from this regression. Multiply them by negative one and call them "value".

Step 4: Choose a restaurant with a very high (highly positive) value (or equivalently a strongly negative residual). This restaurant is cheap for how good it is, what kind of food it is, and where it is located. You can then look for the restaurant in your preferred price range, neighborhood, or cuisine type with the best value.

(Optional Step 5: Make your own personal value measure to your taste by calculating your own residuals. If you particularly value decor but don't care about food, you can make your own residuals by using different coefficients on those variables than the one given by the regression. Don't do this unless you know enough statistics/econometrics that you can scale your adjustments properly or this will go badly.)

I'm surprised that Zagat doesn't put up a list of the restaurants in each city with the best value by this criteria. They do have a list of good deals, but they obviously use another criteria, as their "good deal" picks are invariably cheap and come from cuisines (e.g., coffee shop, pizza) where all the prices are low. The cuisine dummy variables I discussed fix this problem.

(N.B. 1: Tim and Nina Zagat, call me. We can improve your lists of preferred restaurants. Or you could add a list of "economist picks" online or have several statisticians/economists each of us post our preferred lists. It would make all the great data in your guides more useful and actionable. You could add in a tool to come up with customized picks based on an idiot-proof user interface that let's people do Step 5. They would enter in the relative importance they place on various attributes and would get individual-specific ratings.)

(N.B. 2: This would make a good undergraduate senior thesis, particularly if you set up Step 5.)

Economics of Restaurant Hygiene

Since this is a blog by an economics professor about restaurants, I thought I'd talk about some of the economics research about restaurants. My favorite paper on this subject is "The Effects of Information on Product Quality: Evidence from Restaurant Hygiene Grade Cards," by Ginger Jin (University of Maryland) and Philip Leslie (Stanford University).

The research asks about the importance of restaurant hygiene, and more importantly what we know about hygiene. We all like to eat in restaurants where the place where we eat (which we see) and the place where food is prepared (which we don't see) are both clean. I think many of us are worried about what happens in the kitchen, and some of us probably stay away from restaurants we are particularly worried about. Local health inspectors routinely inspect restaurants (including the kitchen) for cleanliness and safety, occasionally fining or closing the worst restaurants. This gives restaurants little incentive to work on cleanliness in the kitchen beyond the minimum required to keep the restaurant open. Personally, I'd prefer a higher level of hygiene than this minimum. What can we do to improve kitchen hygiene beyond this low level?

Jin and Leslie look at a change in policy to tackle this problem in Los Angeles in 1998. Before then, restaurants were rated (1 to 100) on their cleanliness but no one knew what those ratings were. After that, grades of A, B, or C (think letter grades from school based on these ratings) had to be posted by the restaurant. So what happened when they made the change? According to Jin and Leslie:
1. Hygiene ratings improved. It makes sense that restaurants will try harder to improve hygiene when customers know about it.
2. There were fewer food-borne illnesses. This follows obviously from #1, I think.
3. Consumers started to take hygiene ratings into account. Restaurants with better hygiene got larger increases in business than those with worse ratings.

It seems clear this change is good for consumers. First, published ratings give consumers more information that they can use to make more informed choices, so they can now go to the cleaner restaurants if they prefer. Second, average restaurant hygiene improved so that any given restaurant will become cleaner on average.

So why don't all cities do this? There has been substantial resistance from restaurants (particularly the dirty ones, you might think), who are concerned that people will not eat out as often once they know how un-hygienic their favorite restaurant is. We know that cleaner restaurants gain from this law, but what about dirtier ones? Ginger Jin has told me that restaurant revenues went up even for the dirtier restaurants (perhaps consumers thought they were even dirtier than they actually were), and that overall restaurant revenues went up. This concern by restaurants is therefore unfounded.

Once rankings are published, formerly dirty restaurants now have an incentive to get clean. As a result, consumers should choose to go to restaurants more, both because average quality has improved but also because people no longer face the uncertainty about whether their restaurant is unclean.

If you want to eat out with confidence, write, call, or email your city council-person and tell them you want the local health department's rating posted in every restaurant.

(Thanks to Baltimore Snacker, whose post on hygiene ratings reminded me to write about this.)

The Price-Quality Frontier

If you are an economist (which I am), it is natural to draw graphs that tell you useful things about restaurants. The x-axis indicates price (how much the restaurant costs) and the y-axis indicates quality (how much I liked the restaurant). Any restaurant can then be described by a point. This neglects the possibility that I might like a restaurant in some moods or for some purposes but not others, but it simplifies things considerably. Naturally, I prefer restaurants which are high up (good) and far to the left (cheap). Generally, you get what you pay for, so that more expensive places are better; most restaurants fall roughly from lower-left to upper-right. Absent a desire for variety, one would never want to go to a restaurant if there was another which was above it (better) and to the left (cheaper). The price quality frontier is the line drawn to connect all the restaurants which can't be improved upon without spending more. A restaurant is within or inside the price quality frontier if there are restaurants which are both better and cheaper. A restaurant is on the price quality frontier if there are no restaurant which are better without being cheaper. A restaurant extends the price quality frontier if it is on the frontier and the frontier would be lower absent this restaurant.