All-you-can-eat sushi restaurants should not exist. Why do they?

All-you-can-eat restaurants should not exist.

People with large appetites crowd into all-you-can-eat establishments. These greedy customers eat vast amounts, driving up the restaurants' costs. Restaurants have no choice but to increase prices, but this turns off people with small appetites. Eventually the only people who eat at the restaurant are hulking athletes, and the restaurant fails - a victim of "adverse selection".

All-you-can-eat restaurants also suffer from moral hazard. Patrons can fill their plates for free, so eat until the marginal benefit of piling on additional food is zero.  It is trivial to show diagrammatically that all-you-can-eat pricing is inferior to marginal cost pricing:

 

Clearly, all-you-can-eat sushi restaurants should not exist. So why do they?

First, restaurants have fixed costs, like rent. They generally do not set prices equal to their marginal production costs, because if they did, they would never generate enough revenue to cover their fixed costs. In the real world, restaurants cover their fixed costs by pricing their products at the average cost of production - a state of affairs called "monopolistic competition". 

 

Both average cost pricing and all-you-can-eat pricing are inefficient: the only issue is which one is more wasteful. The deadweight loss associated with over-eating is greatest when the marginal cost of food production is high - for food that is highly labour intensive to prepare, for example, or for expensive ingredients. The deadweight loss associated with average cost pricing is greatest when fixed costs are high, when restaurants have to charge a price far above marginal cost to cover their overhead.

The diagram above explains why all-you-can-eat restaurants exist, but the existence of all-you-can-eat sushi restaurants remains a puzzle. The analysis above suggests all-you-can-eat restaurants will feature food that is easy to prepare in bulk, like roast beef, or cheap food, like potatoes or scrambled eggs or pancakes. Sushi is laboursome to prepare, and some of the key ingredients, like sushi-grade tuna, are very expensive. 

One possibility is that the opportunity cost of sushi ingredients, once purchased, is low. If sushi-grade tuna is not used right away, it has to be thrown out. It is better to feed the greedy than to throw food away.

Another possibility is that all-you-can-eat sushi restaurants flourish because they have found ways to curve moral hazard and adverse selection. Indeed, there are a number of features of the all-you-can-eat sushi experience that work to curb hazardous over-eating. First, consumers are charged for food that they don't eat, so it is risky to over-order. Second, the food arrives gradually, and the more one orders, the greater the time between orders (or so I've been told). Third, some restaurants limit the number of expensive items one can order - all-you-can-eat California roll, yes, all-you-can-eat red dragon roll, no. Finally, all-you-can-eat sushi restaurants tend to feature relatively more of the cheap-but-filling Asian food items - squash tempura, miso soup, cucumber roll, sushi made with crispy tempura or mayonnaise.

Some customers will parse the list of sushi offerings with great expertise, and order the most costly items from the menu. Yet perhaps this is a feature of the system, not a bug: perhaps all-you-can-eat sushi restaurants are effectively price discriminating between the more knowledgeable and less knowledgeable customers, just like restaurants who charge the same price for every wine on their menu?

Like moral hazard, adverse selection is not an insurmountable problem. All-you-can-eat sushi restaurants will tend to attract people with greater-than-average appetites. So what? People with lower-than-average appetites will eat elsewhere. As long as the people with greater-than-average appetites form a relatively homogeneous group, the restaurant will set prices so that it makes money serving hungry patrons, and fill its tables with the young and the greedy. It's called a "separating equilibrium" and, under the right conditions, it can exist.

The point of this post: Economic reasoning can be used to "prove" things that are patently false, like the non-existence of all-you-can-eat sushi. And sometimes "inefficient" choices are actually reasoned responses to something missing from the economist's model. 

Note: AC curve corrected.

Comments

[Nick Rowe]

Cool! I never thought of monopolistic competition.

I'm trying to imagine a 3D diagram, with number of customers on one axis, and amount of sushi on the other. Because I think you (strictly) need heterogenous customers to get it to work.

[Nick Rowe]

No. Scrap that about heterogeneity.

[Squeeky Wheel]

I think you need heterogeneity to demonstrate the false paradox, but not to show that all-you-can-eat-sushi exists.

People generally go to restaurants in groups. The individuals in the group have different eating habits. While a few will eat enough to cause a loss to the restaurant, the rest of the group will make up for it. And the first few are the reason the group selected all-you-can-eat instead of the sandwiches next door.

I think of the time some years ago when I went for all-you-can-eat-sushi with some students. The big Indian guy and the tiny Vietnamese guy ate 15-20 plates each. The American guy (me), the Chinese girl, the Myanmarese girl, and the Indonesian girl all had about 3-4 plates each. I also think of the hotel buffets in Singapore which cost a bomb (Singlish for very expensive).

[Avon Barksdale]

This is a classic Newsvendor problem (possibly multi-period). The critical fractile will tell you if going to an all-you-can-eat model makes sense. If the fractile is high enough, the optimal policy will have you, on average, throwing out a lot of inventory every period. You can build up goodwill with the customers if you use them as your trash can - provided that you understand how the critical fractile changes under the all-you-can-eat policy. If it stays high enough, that's the way to go.

See, "Optimal Inventory Policy", K.J. Arrow, T. Harris, and J. Marschak, Econometrica, Vol. 19, No. 3 (Jul., 1951), pp. 250-272

[Sven_R]

I don't think it is at all clear that restaurants are an example of monopolistic competition.
The requirement for monopolistic competition is that the demand curve slopes downwards within the range from a quantity of zero to the optimal production quantity.
I don't think it does, because at least for some kind of restaurants (lets say: pizza restaurants) customers seem to be very price sensitive, so the demand curve doesn't seem to slope down very much.

I think the reason for the confusion here lies in the separation of fixed and variable costs, a concept that isn't at all compatible with neoclassical analysis of the production function. Why? Because fixed costs can as well be seen as a part of marginal costs. Only the analysis of total, average and marginal costs is necessary for understanding production functions and competition.

I'll give an example: Suppose the pizza restaurant produces 100 pizzas a day and uses all its capacities in doing so. The fixed cost in this scenario might be something like 200$ and the variable costs for each pizza might be 1$. The price for each pizza might be 3$, so that there is no profit left (yes I know, very simplified example).
Now what is the cost of producing one additional pizza? Obviously not 1$, because the restaurant already works at full capacity. So what is needed for one additional pizza is more room/employees/etc...
So the marginal cost will include those additional "fixed costs" and so it might turn out that the marginal cost really is about 3$. Since that implies that marginal cost and average cost is about equal, there is no monopolistic competition but full competition.

Is there anything wrong with my above analysis?

Of course this post has nothing useful to say about all-you-can-eat restaurants.

[Gobanian]

No one who really wants to scoff a huge amount of food likes sushi in the first place. So not a problem.

[Enonymous]

I think you have a nice analysis but miss an important piece of disutility: it is painful for many people to do the cost/benefit analysis when ordering food. If you are a value conscious person you will subconsciously feel guilty for ordering the more expensive food or feel compelled to optimize your food choices based on cost. This detracts from the eating experience.

I personally would be willing to pay a small premium in order to simply order the food I wanted to eat without having to worry about cost/benefit. Is this irrational? Maybe, but we are wired this way (for example see articles on ego depletion about how exerting willpower now makes it harder to do later).

Curious to hear your comments on this way of looking at all-you-can-eat.

[Frances Woolley]

Enonymous: "I think you have a nice analysis but miss an important piece of disutility: it is painful for many people to do the cost/benefit analysis when ordering food."

Yes, this is definitely part of the story. When I go to Sushi 88 (my preferred non-all-you-can-eat sushi restaurant) there's always that little worry at the back of my mind "how much is it going to cost to buy enough sushi so that I'm not hungry when I walk out of here?" Also, for people who are unfamiliar with sushi there's the worry "how do I know I'm going to like this strange item enough to justify the $10 price tag"? This would suggest all-you-can-eat sushi restaurants would be more common in places where people had a slightly lower degree of comfort with sushi - enough comfort to like it, not enough to feel really expert at ordering. So Ottawa, as opposed to Toronto or Vancouver (not that all-you-can-eat places don't exist in those two cities also).

Sven_R "I don't think it does, because at least for some kind of restaurants (lets say: pizza restaurants) customers seem to be very price sensitive, so the demand curve doesn't seem to slope down very much."

The demand curve doesn't have to slope down very much - the point is that it slopes down enough to allow Colonnade pizza to charge a higher price than EzPzPizza. And different pizza companies are able to charge different prices, because they produce slightly different products. This is another aspect of monopolistic competition - no one firm can supply the entire market, because each firm is producing a slightly different product, and consumers like slightly different products. That's, I think, what Nick was thinking earlier when he talked about heterogeneous consumers.

"I think the reason for the confusion here lies in the separation of fixed and variable costs, a concept that isn't at all compatible with neoclassical analysis of the production function." I guess all of those intermediate micro textbooks that go on and on about fixed and variable costs just have it entirely wrong, then?

[Joshgans]

At SpringRolls, if you do the all you can eat option, then if you don't eat an order you have to pay for it. So the marginal cost curve is not how you have drawn it here.

[Frances Woolley]

Joshgans - the marginal cost curve here is the marginal cost TO THE PRODUCER (capital letters because this is something that really confuses students of undergrad micro). The price paid by consumers is not actually clearly labelled in the diagram, but paying for food not eaten would cause kinks in the price line, and actually be hard to show because it's hard to know a priori which food one will be unable to eat.

as an aside: at my latest all-you-can-eat sushi experience, we inadvertently ordered a "pizza sushi" - sushi with the rice base battered and then deep fried (it was an electronic ordering system, and we didn't check carefully enough). This was a dilemma - eat vile food, or pay for the privilege of not eating vile food?

[Frances Woolley]

From CH, via email:

Here in Vancouver, where corner sushi restaurants are ubiquitous and you can get a perfectly acceptable (but not gourmet) sushi meal (miso soup, 3 rolls-18 pieces) for $6-8, I have noticed an interesting pricing strategy among the all-you-can-eat sushi establishments. Typically, you are offered a choice of 1) ordering off the menu; or 2) the entire table orders the all-you-can-eat offering.

For someone with an “above average” appetite, I find that I am satisfy myself with an offering from 1), but if I want 2), the pricing is typically at a 70-100% premium to 1). Thus, if everyone at the table is not a total pig, the payback for those who order off the all-you-can-eat menu is set at a very high level. From personal experience, I have typically observed couples who partake in option 2), with the woman eating a normal amount and the man eating an above average amount. Net-net, I am willing to bet that the restaurant’s margin on the all-you-can-eat menu is higher than the standard menu.

[Frances Woolley]

Squeeky Wheel, CH:

The classic solution to the problem of adverse selection is to force people into pools - this is why insurance is so often sold on a group (all employees at Company X) rather than an individual basis.

CH's example of Vancouver sushi restaurants that will only serve the all-you-can-eat option if everyone at the table buys it is a really good example of a way of using pooling to minimize adverse selection problems.

[Nick Rowe]

I'm still thinking about this.

Suppose the fixed cost is a cost per customer, and the variable cost is a cost per food. In principle, 2-part pricing should work better. $5 per person, plus $1 per food item.

[Frances Woolley]

Nick - on heterogeneity - there has to be some amount of product differentiation for the restaurant market to be monopolistically competitive, I think, which may or may not require heterogeneity. It could work with a taste for variety, couldn't it?

[Frances Woolley]

Nick, but, interestingly enough, one almost never sees 2 part pricing in restaurants - though one sees all sorts of other pricing schemes. Why is that?

[Nick Rowe]

Frances: Yes. Either heterogeneity or taste for variety is sufficient. I always use the Ottawa (it wouldn't work in a very small town with one restaurant) restaurant market as my example of monopolistic competition.

I vaguely remember reading about 2-part pricing in crowded busy Hong Kong restaurants. And why don't those (horrible trendy) coffee places use it too, rather than charge outrageous money for a latte and let you hang out for free.

Moral hazard for slow service? Transactions costs? Dunno.

[Sven_R]

@Frances Woolley:

"The demand curve doesn't have to slope down very much - the point is that it slopes down enough to allow Colonnade pizza to charge a higher price than EzPzPizza. [...]"
Yes sure, but at least here in germany it is the case that you have tons of small pizza or doner kebap restaurants which do not belong to a chain and don't have any known brand. Their products are really interchangeable and so is their price!
I would suggest that a reasonable economic analysis of pricing behaviour should start at those restaurants facing full competition and only afterward go on to those restaurants who can charge a premium.

"I guess all of those intermediate micro textbooks that go on and on about fixed and variable costs just have it entirely wrong, then?"
I'm not sure which textbook you are talking about. I just looked up "fixed cost" in Mankiw's textbook and couldn't find anything. And that's not surprising: You only need the total cost curve and the thereof derived average and marginal cost curve to understand economics.
It seems to me that the whole concept of fixed and variable costs gets very often confused with the way it is used in accounting or business studies, where it is assumed that the level of fixed costs for your business is... well, fixed, and you just need to get as much out of that given production base as possible.
This is of course not the kind of analysis you should do when analysing general characteristics of abstract production functions in economics, because there you can assume that nothing is given. Instead, you only have to ask for every possible output quantity how much total costs you will. Everything else, including the optimal quantity of production will derive from that (again: assuming that the demand curve isn't sloping downward).

Of course there are actually cases when the separation in fixed costs and variable costs is fully compatible with the general economic analysis (like the production of software/movies/music... Here it is clear that there are virtually no variable costs, only fixed costs. The crux here is of course that the fixed costs are completely independent from quantity. The same is obviously not true for restaurants).

[Nick Rowe]

Sven: I have the 5th Canadian edition of Mankiw's Principles of Micro right here. Chapter 13 "The Costs of production". See the section on "Fixed and Variable Costs". "Fixed cost" is also in the glossary.

[Sven_R]

@Nick Rowe:
Thank you. I only have the german translated version of the 4th edition here. They left it out in the glossary.
Now I found it.
Anyway, please note that while he explains the difference between fixed and variable costs in this subsection and also shows them in the following diagrams, he doesn't seem to use them for his further reasoning. And he leaves them out completely in the next chapter (14) about prices under competition.

Additionally, I think his explanation of fixed costs in the subsection you cited is just not correct. In my german edition, he gives an example for a lemonade factory and he states, that the rent and the costs for the book-keeper are fixed because they don't depend on the produced quantity. I don't see any way how this can be true in general. He just seem to make the error I described in my last post, confusing business accounting practices with economic reasoning.

What do you think?

[Frances Woolley]

Nick: "And why don't those (horrible trendy) coffee places use it too, rather than charge outrageous money for a latte and let you hang out for free."

There has to be some kind of social/psychological explanation. Because nightclubs have cover charges, people will pay a cover charge when there's a band playing - perhaps our brains can cope better with the idea of exchanging tangible things, e.g. dollars for coffee, than they can with the idea of exchanging intangibles, e.g. dollars for space. Or perhaps this is one of these "moral limits of markets" things, i.e. there are some things that as a society we figure it is morally wrong to charge for.

[Robillard]

In the Vancouver market, there is often a big difference between all-you-can-eat sushi restaurants and regular ones. All-you-can-eat sushi restaurants typically use cheaper, lower quality ingredients. And the most expensive sushi items, namely sashimi, are typically not on the all-you-can-eat menu. This means that a person eating off the all-you-can-eat menu will consume less fish and more rice than they would consume otherwise.

In Japan, I don't think all-you-can-eat really exists as a restaurant concept, and certainly not for sushi restaurants. With the exception of some conveyor boat sushi restaurants, which are relatively inexpensive, sushi in Japan is considered to be a relative luxury. The quality of sushi restaurants in Japan is generally much higher than can be found in North America. On a related note, Japan does seem to have the all-you-can-drink concept though.

[Frances Woolley]

Robillard - "On a related note, Japan does seem to have the all-you-can-drink concept though." - Which I've only ever found in places like airplanes and all-inclusive holidays e.g. safaris. Where sedating people is easier than entertaining them or keeping them happy another way!

[Wonks Anonymous]

I didn't even know all-you-can-eat sushi restaurants existed. I might eat more sushi if there were some nearby.

[Hasdrubal]

Two part pricing: Don't we see that all the time, actually, with tipping? Restaurants charge for the food and preparation, but service is paid for at a customary rate with some wiggle room for what the customer feels is appropriate. The restaurant pays the servers as little as legally possible, tips often make up the majority of their income.

All you can eat in Japan: It's there, it's called "Viking" style, it's just not very common. The place where I saw it might actually be Japan's equivalent to North American all you can eat sushi. You went to the buffet and got slices of meat (like you would at a Mongolian buffet in the states) then took it back to your table and cooked it on a charcoal fired hibachi. Relatively expensive ingredient that the majority of the population doesn't eat a lot of with high inventory risk. Beef in Japan, sushi in the States, fills pretty much the same role.

[Robillard]

"Which I've only ever found in places like airplanes and all-inclusive holidays e.g. safaris. Where sedating people is easier than entertaining them or keeping them happy another way!"
It's my understanding that many Japanese, like many Asians, suffer from the "alcohol flush reaction" (http://en.wikipedia.org/wiki/Alcohol_flush_reaction), seemingly causing them to get buzzed very quickly off a relatively small amount of alcohol. In pop culture, Asians have a reputation for being less heavy drinkers than people of European descent. But this also seems odd given the reputation of Japanese salarymen for boozing with their colleagues after a long day at the office.

[Binky Bear]

Producer's responses for cost containment that I've seen include increased automation of sushi assembly to reduce labor cost per unit, labor timing to maximize production prior to peak dining times, and management of ingredient costs per time unit.
Several sushi places locally have assembly lines with machines that plop out preseasoned rice units onto standarized sheets of nigiri, then down the line for the addition of mechanically prepared vegetable ingredients, then fish/egg/other signature ingredient, then finishing.
Prior to rushes the assembly line has extra laborers who assemble nigiri based sushi and stock the ingredient bins; these sometimes become bussers/wait staff when the rushes come.
Managing ingredient costs per time unit or per customer average is a strategy of providing greater numbers of lower cost rolls with fewer "headline" items with expensive ingredients per time unit or per table or per customer group. This usually requires the headline producer to keep track of whichever determinant veriable drives the cost (time unit, customers, tables) and usually use a table or a subroutine in the resman computer to produce some combination of headline items that are both sufficient to satisfy customers and maintain cost ratios, thereby sustaining profitability.
The fact that in the US most headline ingredients for sashimi must be frozen helps manage losses from spoilage. The popularity of surimi and the California style roll is another cost managing aid. The greatest ingredient based cost management tool is 'fusion' style sushi which allows the inclusion of many low cost fillers which can be visually satisfying while lowering unit costs per roll, such as deep fried breaded items (ebi, asparagus, softshell crab) or 'salad' items which can include cheap vegetable, surimi, or shredded fish components with inexpensive vegetable and sauce fillers.
It's a making widgets kind of problem that is simple and kind of fun, to the extent that there are computer games based on this problem set in particular.

[Adrian Meli]

Interesting post-hadn't thought of the economics of all you can east sushi vs. a typical restaurant before. I think you hit on a lot of the reasons why comparing an all you can east sushi restaurant to an all you can eat pizza place is not an apples to apples comparison. I don't think sushi restaurants offer an equivalent dining experience to just ordering a la carte off the menu. I am going to pay more attention though the next time I see one!

[Redwood Rhiadra]

I will just note the classic Onion article "Continued Existence of Edible Arrangments Disproves Central Tenets of Capitalism" :-)

http://www.theonion.com/articles/continued-existence-of-edible-arrangements-disprov,19856/

[Mike Freimuth]

This is actually right up my alley and a nice break from macro. I think you have all the essential elements here but let me try to put them together.

First, the most efficient method of pricing would be to charge a fixed price for using the space at the table, the roof over your head, the health inspectors, etc. and then a variable (probably the marginal cost) price for the food. If it is monopolistic competition, and people are heterogeneous, it may be optimal to charge somewhat more than MC but two-part pricing would still be ideal. The reason restaurants don't do this is a mystery to me but let's put that aside and just assume they can't for some reason.

Now, you have the situation you laid out in the main post where there is some DWL from people eating too little under let's call it "standard" pricing and some DWL from them eating too much under all-you-can-eat pricing. But if you add heterogeneity of customers into it, you will see that under standard pricing, you would rather have the heavy eaters because the additional food that they eat will more than pay for itself and this will contribute more to the bottom line than the light eaters who take up just as much table space and other fixed costs.

This means that if you can attract only they heavy eaters and not the light eaters, you can charge them less than what it would cost them to eat under the optimal standard pricing scheme and still make more profit. But you have to do it in a way that doesn't attract the light eaters and allow them to eat less and pay less which would happen if you just lowered your prices under a standard pricing scheme. All you can eat allows you to do this.

[Kaleberg]

You run into a similar problem with salad bars. Why doesn't every person simply load their plate with the single most expensive ingredient? Maybe they aren't all economists? Maybe they all agreed to go to a place with a salad bar because that meant each person could get what they wanted at a reasonable average price and not have to fuss about the price of ingredients or who ate more of what? Maybe they weren't exactly sure of what they wanted and figured a salad bar would let them look at the ingredients and then decide?

Utility and nutrients are two different things. If you are only concerned about efficiency in acquiring nutrients, then you have to wonder why we all aren't eating Soylent Green.

Restaurants are extremely efficient operations. Their margins are minimal, even at the high end. In some ways, however, sushi actually has certain advantages in an all you can eat format. It is made from frozen fish, not fresh fish as fresh fish may contain parasites that are killed by freezing. This helps control inventory as the most expensive component can be purchased in bulk and defrosted in less than an hour as needed. Odds are that all you can eat sushi restaurants use farmed fish, not fresh fish, as most people can't tell the difference.

There is also a certain efficiency in production as many sushi are prepared as a long single roll which is then cut into a plate full of disks. For rolls you can do a lot of dry setups and premix the wet ingredients, so that filling an order is almost a binary operation (plus the plating). A lot of the sushi can be completely assembled in advance. Check out the sushi in a supermarket and decide how it compares to the sushi at an all you can restaurant. It might be just a grade or two better.

If you know Japanese food well, you know that the primary ingredient of sushi is rice. Rice is actually the focus of the dish in Japan, not fish. There are a lot fewer all you can eat sashimi, raw fish, restaurants.

Most all you can eat sushi restaurants use ingredients like avocado and mayonnaise which are not traditional in Japanese cooking and provide a lot of filling oils at relatively low cost. While people can consume huge quantities of fat at a sitting, fat does induce satiety sooner than simple protein. On a similar note, I'd be shocked if you found an all you can eat sushi restaurant that didn't have tempura and possibly other deep fried items on the menu.

Just as the economics of choosing a restaurant can seem in conflict with economic theory, the economics of operating a restaurant are often not what they seem on the surface.

[Avon Barksdale]

Fixed costs with pricing on the average cost curve does not imply inefficiency. Recall that the marginal cost curve intersects the average cost curve at its minimum. So, if the producer minimizes average costs, the equilibrium will be on the marginal cost curve. Zero profits attain – average costs equal marginal costs – there are no economic rents or externalities and thus no deadweight loss. This all results from the simple fact that the derivative of the total costs as a function of production is unaffected by the constant fixed price shift. Now, if the producer has some market power in that there are no perfect substitutes for her restaurant (monopolistic competition) then the producer can sell above average costs. The usual profit rectangle results which generates the deadweight loss. Monopolistic competition is not the same thing as fixed costs in production and fixed costs do not imply inefficiency. Perhaps you didn't intend this implication in your post.

Average cost considerations create an inefficiency in cases like the tragedy of the commons. In that case, the herders graze until average benefits equal the price of an animal. That is inefficient – the efficient number of grazers is attained when the marginal benefit equals the price of the animal, not the average. Here we have mutually inflicted externalities from the decision of each herder to graze – the fixed costs (scarcity) of the land are not internalized. Ownership with excludability solves the problem, but this is not the same thing as monopolistic competition.

The all-you-can-eat policy is almost certainly the result of optimal inventory considerations with perishability.

[Frances Woolley]

Thanks for all of the great comments, especially Binky Bear's and Kaleberg's insights into the workings of sushi restaurants, and Redwood's link to my favourite news source. Will reply sometime tomorrow.

[Mike Freimuth]

Avon,

I think you are missing the thrust of the average-cost pricing issue. It is not about the scale at which the restaurant is operating, it is about the scale at which each customer is eating. This sort of opens a can of worms but basically, there can be more than one "margin." It could be that the marginal cost of increasing the scale of the operation is equal to the average cost and that is equal to the price but that price could still be more than the marginal cost of providing an additional piece of sushi to a customer who is already in there eating but you can't lower the price of this additional piece without lowering the price of all the previous pieces. This would be solved by two-part pricing, but if that is impossible, then it may be beneficial to offer a lower average price to customers who eat more in a single sitting even if the restaurant is operating at the efficient scale in a larger sense.

[Mike Freimuth]

This should explain it thoroughly.

http://realfreeradical.com/2014/06/20/a-model-of-all-you-can-eat/

[Ben Kloester]

Sorry to jump in so late in the comments but

Frances: I think we do see 2-part pricing in restaurants quite a bit (especially in Japan!) but it is 'hidden'. It is pretty common in many places to charge a 'cover' which is ostensibly for some simple dish served on seating (in Japan it is often eda-mame and/or tsukemono, in Brazil it is usually bread and some crappy approximation of antipasto). This would help cover the fixed costs associated with customers.

Sven_R: I think proposing that pizza joints or chippies are not competitive monopolistic is defensible, but as soon as you move to more complex fare it seems like a reasonable proposition. I think sushi restaurants definitely are - there is little worse than BAD sushi.

Robillard: All-you-can eat is not the norm but still common enough in Japan but as binky bear said it is mostly yaki-niku (korean bbq), but also shabu shabu and sukiyaki (hot pots, the former also with lots of meat!) are common as all-you-can eat.

All-you-can drink is everywhere but almost always tied to either karaoke (which has relatively high per-hour cost) or a meal (often all-you-can-eat!). The Japanese, despite being enzymatically disadvantaged, drink an unbelievable amount so its surprising how common it is.

I've never seen all-you-can eat sushi in Japan but it is very common in Sao Paulo and the quality is very nearly equal to Japan!

[Avon Barksdale]

Mike,

I am not talking about the issue of all-you-can-eat vs average cost pricing. I am saying that Frances' statement:

"First, restaurants have fixed costs, like rent. They generally do not set prices equal to their marginal production costs, because if they did, they would never generate enough revenue to cover their fixed costs. In the real world, restaurants cover their fixed costs by pricing their products at the average cost of production."

is factually incorrect. The average cost equals the marginal PRODUCTION cost at the competitive market equilibrium in the presence of fixed costs.

Here is the logic:

AC(y) = F/y + c(y)/y,

AC is average cost, y is production, F is the fixed cost, c(y) is the production cost. Minimize AC(y):

(F+c(y*))/y* = c'(y*),

which in words is: Average cost = Marginal costs. Profits are zero.

I suspect that Frances called c(y)/y the marginal production cost. It is not. Only in the limit that y goes to zero is it the marginal cost.

[Frances Woolley]

Avon, your argument only works if firms are operating in the minimum point on their average cost curve. My argument is that something is preventing them from getting to that point e.g. product differentiation + heterogeneous consumers or a taste for variety.

Also, as others have said, there are many relevant margins. Marginal cost of a table v. marginal cost of food, for example.

[Avon Barksdale]

Frances,

"My argument is that something is preventing them from getting to that point e.g. product differentiation + heterogeneous consumers or a taste for variety."

No, that was not your statement. You claimed that fixed costs, like rent, prevented restaurants from pricing at marginal cost. This is not true. Furthermore, when the restaurants have market power they sell above average cost, not at it. It is misleading to suggest that it is monopolistic competition that allows the restaurant to use the average cost price, creating a deadweight loss. It's the opposite: The competitive restaurant sets the price at the average cost which equals the marginal cost. In the presence of a market power, the restaurant will price above average costs.

[Nick Rowe]

Avon: "Furthermore, when the restaurants have market power they sell above average cost, not at it."

Monopolistically competitive firms have market power, in the sense of downward-sloping demand curves. But in long run equilibrium (free entry and exit) they price at average cost, and earn zero profits. But the price is above marginal cost, because profit-maximisation implies marginal cost equals marginal revenue, and downward-sloping demand curve implies marginal revenue is less than price.

Profit-maximisation plus zero profits together imply that a gap between price and marginal cost is equal to the gap between average costs and marginal costs. You can say that average cost being above marginal cost implies a downward-sloping demand curve in equilibrium. Or you can say that a downward-sloping demand curve implies average cost is above marginal cost in equilibrium. Same thing either way.

[Robillard]

Thanks Ben Kloester. I should have limited my comments to sushi.

I went to a yakiniku restaurant once with family in Japan, but I can't recall if it offered all-you-can-eat or not. We definitely paid by the number and size of meat platters we ate. I really can't make a judgment from a single observation though.

[Avon Barksdale]

“Monopolistically competitive firms have market power, in the sense of downward-sloping demand curves. But in long run equilibrium (free entry and exit) they price at average cost, and earn zero profits.”

Nick, that is correct. Rereading my post, I mis-spoke. The competitive monopolistic firm sits above the minimum of the average cost curve, but still on it, which is what I meant, but not what I typed, which was wrong. In the long run, as more and more firms enter, the competitive monopolistic firm is driven to zero profits, but at the point where the demand curve touches at a tangent to the average cost curve, which the firm’s market power forces away from the minimum, and thus above marginal cost. My early post should have pointed that out, too. My point is, this has NOTHING to do with fixed costs.

[Majromax]

Isn't there also an insurance factor in "all you can eat" offerings?

If I sit down at a restaurant, I know that I am hungry, but I'm not sure in advance exactly how much I want to eat. With an a la carte offering, my food options come in significant chunks: appetizer, main course, dessert. Since I can only estimate my hunger at the time of order, I run the risk of a mismatch: I can be incorrect by up to half a course each way.

In the case of under-ordering food, I may be left in the unfortunate situation of still being hungry, but not having a good, available meal offering -- especially when constrained by social cues. If I am not particularly interested in dessert, it would be strange to go back and order something off of the appetizer menu even if I remain hungry.

A lesser failure is over-ordering food, where some is left at the table uneaten. That carries no additional cost once discovered, but can be in poor social form.

With an all-you-can-eat offering -- even of sushi -- there is no such potential for error, either way. From the customer's perspective, it feels as if just the right amount of food was delivered, whether the customer was indeed particularly hungry or whether their eyes were bigger than their stomachs. By paying a small premium over a la carte pricing, I'm guaranteed an economically and socially certain outcome.

[Frances Woolley]

Mike: "This means that if you can attract only they heavy eaters and not the light eaters, you can charge them less than what it would cost them to eat under the optimal standard pricing scheme and still make more profit. " -

That's a fascinating variant on the adverse selection story - but here the undesirables are the people who order a glass of water and a small side salad and call this dinner. Also if the people who are heavy eaters are also heavy drinkers and big tippers, this will make catering to this segment of the market even more profitable.

Majromax: "Isn't there also an insurance factor in "all you can eat" offerings?....I may be left in the unfortunate situation of still being hungry"

This seems to be less of a risk and more of a certainty, especially at high end restaurants, where the price seems to be inversely proportional to the amount of food on offer. And I especially don't get the tiny proportions of vegetables: three minuscule fingerling potatoes, 4 green beans, and a tablespoon or two of elegantly prepared what-ever-the-fancy-name is is *not* sufficient veggies for someone who's physically active! Sure it's possible to order vast quantities of bitter tasting salad greens, but I don't really like bitter tasting salad greens very much.

That's something I don't have a good economic explanation for - yet!

[Jacques René Giguère]

"especially at high end restaurants, where the price seems to be inversely proportional to the amount of food on offer": You go there to show that you're so rich and so not physically active (except at the gym) that you don't need to eat...
Unlike until recently when gorging and being fat was for the 1%...

http://lgsquirrel.wordpress.com/2010/06/23/beauty-according-to-art/

[Determinant]

People generally go to restaurants in groups. The individuals in the group have different eating habits. While a few will eat enough to cause a loss to the restaurant, the rest of the group will make up for it. And the first few are the reason the group selected all-you-can-eat instead of the sandwiches next door.

Ah, the principle of insurance! The amount of food eaten by one person is highly variable; that eaten by a sitting in the restaurant over an evening is quite regular. This is how insurance companies make money.

And people will pay for certainty; see all-inclusive vacations where you can drink what you want.

[Jacques René Giguère]

Determinant: I always wondered why you ended up as an engineer instead of an actuary...

[Determinant]

I sold insurance for a while. But insurers have a nasty side: if they find you too costly as an insured, they'll renege on the policy and litigate. And I can't stomach that part. It happened in my family and if I ever worked for an insurance company, I'd pay for it dearly. Some things are just better left as interests.

I bang on about insurance because Frances said insurance didn't make sense from an strictly micro view and it doesn't, but once you aggregate it like an insurer does it makes plenty of sense. It's one of those things with a third dimension that is key to understanding that's outside a strictly micro analysis.

And speaking of careers, I have an interview with the Public Service of Canada this Wednesday. The first in a series, but nice none the less.

The last one I had with the Feds was in Montreal and didn't go so well; the panel chair made an unwelcome joke about how there were no French people in Ontario. You can choose to work in English with the Federal Government in Montreal and eight people in the interview pool chose that option. It didn't go over so well.

I love Quebec and dearly wanted and still want to move there, but somehow Quebec just can't seem to love me.

[Jacques René Giguère]

Or maybe just some people on a Fed jury. Have you ever thought about Cegep teaching?

[kevin quinn]

Frances: This point may have been made - I'm rushing to class and haven't time to read all the comments, but surely an all-you-can eat place DOES use two-part pricing? - they charge a fee at the door. So why aren't they charging MC for the food and covering the fixed costs through the Fee?

[Determinant]

Or maybe just some people on a Fed jury. Have you ever thought about Cegep teaching?

Oh, those Fed employees were loons. The interview notes I received later showed they ordered sandwiches for lunch in a marginal note in the interview notes. They'd checked out mentally before I had finished speaking.

You can choose to work in English in the Federal Public Service in Montreal. It's just you have to have BBB French too (likewise French speakers have to have BBB English in Montreal). When this particular Board found I had BBB level French they got nervous (right in front of me too) as the preferred method to get rid of unwanted candidates wasn't available to them: to fail them out on second language testing.

No matter, I applied to the same job in Ontario and my French results make me a preferred fit for Ottawa.

I had another problem like that at another Fed Montreal job: they gave a horrible translation in a definition that didn't have the same meaning in English and French. You can work in English in Montreal in the Public Service of Canada in theory but.... It's been a pattern at more than one place, I am sorry to say.

CEGEP? No. But my French isn't good enough to teach; only my English is that good. I only have BBB level French, which is enough to read a Las Presse and carry on a simple conversation. That's a bit of a problem if I want to work at anything other than the six English CEGEPs and I don't have enough qualifications for those. And it's hard to improve beyond that because I like in a very, very English town in Ontario. You try learning English in Saguenay.

Perhaps I can swing Ottawa, which is a close second-best. The ski hills are a little poorer but at least I get to take my French out for regular use.

[kevin quinn]

Did the mystery ever get solved here? Nick: I don't see how heterogeneity can explain a marginal price BELOW marginal cost in a 2-part pricing scheme. Take a 2-type case. Think of two linear demand curves, same slope but one - the high-value type- with bigger intercept, and constant costs. If I must charge everyone the same fee and marginal price, and it is optimal to sell to both, the highest fee I can charge is limited to the economic surplus created when the low-value type is charged marginal cost. That leaves a lot of unextracted surplus form the high-value type. Raisng the marginal price above MC slightly, I must lower the fee. I lose a little triangle of surplus from the low-value type (I get most of the fee reduction back via the higher marginal price) On the high-value type I get all of the lower fee and then some back on the higher per-unit charge, since I'm extracting some of the surplus that had gone begging before. At the margin, the loss of profits from the low-value type is 2nd order, while the gain in profit from the high value type is first-order. So we want raise the marginal price above marginal cost to some extent. But why would heterogeneity ever see us lowering the marginal price below marginal cost. (An old joke comes to mind: your prices are so low, you're losing money on every item you sell! Yeah, but I make it up on the volume!) And I know he solution to the mystery cannot be that the restaurant has negative marginla cost!

[Nathanael]

"First, the most efficient method of pricing would be to charge a fixed price for using the space at the table, the roof over your head, the health inspectors, etc. and then a variable (probably the marginal cost) price for the food. If it is monopolistic competition, and people are heterogeneous, it may be optimal to charge somewhat more than MC but two-part pricing would still be ideal. The reason restaurants don't do this is a mystery to me but let's put that aside and just assume they can't for some reason."

Reason number one: ability to walk out on scams. No *new* customer likes to pay a cover charge because they're not sure what they're going to get: if they go in, spend a little time, and then send back the food because it's inedible, and walk out, they don't want to pay anything.

Reason number two: a variant of the above: *promotional pricing* -- if you're curious about the restaurant, you can walk in and buy the cheapest thing just to try it out, and if you like it, you may come back and buy more in the future.

Reason number three: simplicity of pricing making transactions more comprehensible to customers, which is appreciated.

Reason number four: having people visibly sitting in your restaurant serves as marketing. The marginal cost of seating someone is nothing unless the restaurant is already filled. However, the marginal benefit is large because it makes the restaurant look more "happening" and attracts more customers.

Important additional fact: some places DO have cover or "walk in the door" charges -- these are usually places which are *full*, or at least places where you can't tell from outside whether they're full. So it's clear that the lack of cover charges is related to the desirability of filling your restaurant even if you fill it with "unprofitable" customers.

Marketing. THE most important part of microeconomics, and yet not covered in most intro classes.

[orly]

thanks!!!

[Jacques René Giguère]

"having people visibly sitting in your restaurant serves as marketing. The marginal cost of seating someone is nothing unless the restaurant is already filled. However, the marginal benefit is large because it makes the restaurant look more "happening" and attracts more customers."
Or, as Yogi Berra said: "Nobody goes there anymore. It's too crowded!"

[Perin Menendez]

Sushi is one of the most adored foods in our area. Restaurants do exist in the present. Why questioning sushi restaurants' existence?