In a buffet, we can eat any food provided that we want (and we can) within a time period. The question is: if the buffet is offered for free, would we eat less than if the buffet has to be paid by our own money? In fact, buffet is expensive and so often people take it only when it is funded by the company they work for. They personally do not need to pay in such a situation. So, the question asked by this post is not artificial. It is quite relevant in the real world.
I exactly encountered such a free buffet. During the buffet, I raised the question and said that I would eat more if I had to pay for it. That's my answer, which, I think, purely reflects my personal choice. There is nothing wrong or right about it.
But a colleague, an economist, did not think so and said that my choice was irrational. His point was that the cost of the buffet was a sunk cost, and sunk cost shouldn't affect one's decision (to eat more or less); otherwise, one is irrational.
As an economist too, I of course know what sunk cost is about (actually I have to teach this concept in class). The concept is that cost mentioned in economics is about opportunity cost, not accounting cost. Opportunity cost is the foregone value from the next best option. What does it mean? It means that when people choose, there must be some options that they can choose. When one chooses an option instead of all others, one forgoes all these other options. Among these forgone options, one of them is of highest value to the chooser. Its value is just next to the chosen option. The cost of choosing an option is the value foregone of the next best option as this is what one sacrifices in order to get the chosen option.
Economics considers that opportunity cost is what a decision-maker should be mindful. If what is next best is still less valuable than the chosen option, taking the chosen option lets the chooser get the highest value among all available options. If what is next best is more valuable than the chosen option, taking the chosen option is a mistake: taking it won't let the chooser get highest value.
The logic is in fact quite tautological once we figure out the meaning and the definition. But this self-explanatory principle will be violated by actual choosers (and so they need economists' reminder of the principle) especially because the term "cost" in the real world is often used to refer to something else (not opportunity cost). The daily usage of the term "cost" will confuse our decision-making and so we need economics to remind us. In particular, the term "cost" used in daily life is normally an accounting concept: whatever is spent is a cost item. Sunk cost is exactly a "cost" in accounting sense but not in economics sense (not opportunity cost).
Then, what is sunk cost? It is about certain expenditure that has been spent but the item purchased can only be used for one purpose (say, for running a business unit) and the money spent can't be recovered (say, by re-selling the item).
It seems that high-school economics often uses concert ticket as an example. If you have paid $200 for a ticket, the $200 is a sunk cost. You can't get it back (assuming that re-selling it is illegal). The ticket has no alternative use (can only be used as a permit to attend the concert). So, high-school economics tells you that you should ignore this $200 when making further decisions.
For example, after you has paid $200, you realize that there is another concert to be held in the same time. You have to decide to go to another concert or the original one. For this decision, the $200 should not matter. If you think that the new concert is valued at $300 while the original one is valued at $250, you should go to the new concert. If you think that going to the new concert, your cost is $200 (original concert ticket) and $260 (new concert ticket), which is higher than $300, and so you shouldn't go, you are wrong. You should ignore the sunk cost $200.
This example explains why sunk cost should be ignored. In fact, I don't like this example very much but it is frequently mentioned by my past students. I heard it from them. So, I think students are familiar with it, and therefore use it here. Why I don't like it? Let me mention this later.
Turning back to the buffet problem, is eating more irrational when I have to pay on my own? My colleague's point is that the buffet cost is sunk. Hence, it shouldn't affect one's decision to eat how much, or one is irrational. Is the buffet cost a sunk cost? Yes, it is. The money can't be recovered, once paid. It won't be that you can get back part of the money if you eat less. Thus, if one's decision is affected by whether a sunk cost has been made or not, one is irrational.
In fact, people often haven't made decision rationally. In particular, they make decisions differently depending on whether the sunk cost has been incurred or not. This is a well-documented phenomenon known as sunk cost fallacy. My colleague obviously thought that I had committed this fallacy.
But do I think I had made a mistake? Do I think I acted irrationally? I don't think so. Nonetheless, with a sudden attack from my colleague as such, I failed to respond immediately. In my view, my choice is very natural. A choice like this won't be right or wrong. I had expressed this view at that time. But obviously such a common-sense based argument couldn't convince an economist. You need an economics argument to refute an economics argument. But I couldn't thought of any at that time.
Somewhat knowing that I was embarrassed by the attack, my colleague thought of some escape routes for me. He said that it could be a taste change when one had to pay a bill. If bill-paying in itself could change my taste for food, eating more when I have to pay is of course rational. I am simply doing something (eating more) to satisfy my new taste (stronger desire for food).
But I don't think my taste has changed with or without paying the bill. Furthermore, I don't like the explanation via taste change. Taste change is too much an "everything works" explanation: whenever you can't explain something, you can always explain it by taste change. It always works as no one can demonstrate if there is a taste change or not. Nevertheless, I couldn't think of other ways to avoid the accusation of being irrational at that moment.
The buffet was over and I still couldn't think of a satisfactory defense. We left but I still kept this in my mind. I still think the choice is natural and nothing wrong. It is not about rationality or irrationality. But how can I explain away the sunk cost factor?
Afterward I had thought about several explanations but none very convincing (to me). Eventually I have an idea and wonder why I couldn't think of it earlier. The issue is extremely simple.
It is simply about income effect.
What is income effect? If we have more money, will we buy more of a good? If so, there is a positive income effect from this good. If we buy less, there is a negative income effect from the good. If we simply won't buy more or less, there is no income effect from the good.
The fallacy of accusing me to have committed sunk cost fallacy is that it assumes the income effect must be zero for any goods for any one.
As mentioned, buffet is expensive (perhaps some richer people may not think so but I do) and so there should be a significant income effect from it. Having paid the buffet cost, it is equivalent to a reduction in one's income. The payment won't be affected by eating more or less. So, it is basically about an income change. Yes, the money can't be recovered, once paid. But you can't say, therefore, no income effect exists. If one has to pay, one's income is lower. By eating more, this means income effect is negative (a lower income is associated with a higher consumption of a good). By eating less, this means income effect is positive. By eating the same with or without paying, this means income effect is zero.
The income effect of buffet food to me is negative. Having paid, I am poorer, and I will eat more. The case is just as simple as this. This is not about rationality or irrationality.
Of course, you may wonder why the income effect of buffet food is negative. Wouldn't we have more buffets if we are richer? However, food in one buffet and the number of time having buffets are different things. Richer people may more frequently go for buffets. But they may eat less in each buffet.
In fact, the negative income effect from buffet food is also an understandable pattern for a normal person (like me). Buffet is expensive. If I have to pay, I may choose to eat less before (and after) having it. I save the money for eating before (and after) having it. If I don't have to pay, I can also choose to save but there is no reason why a richer me and a poorer me choose to save the same. It is not about taste change. It is simply about the fact that income may have an effect on a person's choice, given the same taste.
[Being a little bit technical (hi,economics' readers can ignore this part), I mean the indifference map is the same (same taste) but at higher levels of the indifference curves (richer) and at lower levels of the curves (poorer), the same person may consume different quantities of the good.]
Hence, when one says sunk cost shouldn't induce people (like me) to choose differently, they are assuming no income effect. How can they make such an assumption in general? It may be true in some cases but not in all cases!
Well, there is an occasion where income effect can be validly assumed to be zero though normally high-school or even university microeconomics may not mentioned it.
In consumer theory, economics assumes that a person will choose to attain the highest feasible satisfaction (the technical term is "utility"). This satisfaction is not the same as money. It is not that economics assumes people's goal is to earn as much money as possible at all cost (caring only about money but not other things). This is a reasonable assumption (for example, people may choose to earn less so that they can enjoy more leisure time or they want to become an artist or musician instead of a banker). But perhaps few economists are now aware that this amounts to the assumption that income effect may not be zero. In fact, the opposite side is: if one assumes that money is a decision-maker's only goal, then there is no income effect.
This looks so surprising. Why does money-only implies no income effect?
First, we must bear in mind that normally a human being will not care only about money. He or she cares about what money can buy but not simply wants more money only. If we say a person cares only about money, it must involve stepwise decisions: one may set a target as getting the highest amount of money as a first step; achieving this first step, one will then wisely use the (highest) money amount in achieving the real life goal (eating, living, enjoying, etc).
Second, now if we can validly assume a person take money as the only goal (in the first step of the whole plan), this person is like running a business (either as one's personal money-making plan or working for a profit-maximizing company).
Third, if one is running a business, every buying and selling decision intends simply to maximize the money earned. Now, suppose that you have $1 million, and you think the best way to earn most is to buy materials worth $1000, which enables you to produce something worth $1500 for sale. In this situation, you will do it for earning the $500 as this is the profit-maximizing action.
Will your decision be affected if you don't have $1 million but $2 million, provided that the buy-$1000 and sell-$1500 is still the best way to earn? If you are rational, you won't change your decision. If you change your decision and you are rational, there must be something other than money you have to consider (say, you need to keep the $1000 to buy a present for your mother). If so, you are not purely concerned with money amount. If you are purely concerned with money amount, your decision won't change.
Now, you should understand why money-only implies no income effect. For a money-only decision maker, maximizing money is the only goal. Then, one should simply take the money-maximizing action. The decision-maker's income alone is not a factor that can change what is the money-maximizing action when all the actions are feasible under different income levels.
Well, sunk cost fallacy is exactly a valid accusation for a money-only decision maker. A restaurant owner finds that there will be too few clients if lunches are served. The revenue of $40,000 a month cannot cover the rent of $100,000 a month. In addition, salary and food cost amounts to $30,000 a month if lunches are served. Deciding to stop serving lunch, the restaurant owner commits a sunk cost fallacy as the rent should be ignored. Serving lunches can cover other costs at only $30,000 and is thus a profit-maximizing move (though the $100,000 is still not covered by serving lunches).
In such a case, the obvious advise that an economist can give is that lunches should be served if one aims at earning money. But don't forget that money is usually not the only goal for a decision maker. Income effect is present. Extending sunk cost fallacy to all other cases, such as non-business decisions, is like treating all decision makers as a firm or a business unit. When a consumer makes decision, we shouldn't advise as if the consumer must act like a business unit. Otherwise, we commit another fallacy. Nevertheless, I know not a few number of economists will do so. (One example is Ronald Coase, who is well known for ignoring income effect when formulating his famous theorem in his name; but I don't want discuss this in this blog post.) I almost also let myself do so (when thinking about the buffet decision).
Finally, let me say: I also observe that there is a habit or even a trend that economists forget about all these foundational issues like income effect. Sometimes economists simply ignore individual decision-makers have their own goals and money is not necessarily the only goal, and there are decisions other than business decisions. Not a few economists prefer using examples like concert tickets to illustrate sunk cost but that's exactly a case involving not a business decision but a consumer's decision and so income effect may be at work.
My observation is that this situation is particularly severe in elementary economics courses. Perhaps I am old-fashioned. I do not like this style of teaching: treating an individual as a firm, or an individual should learn the way a firm makes decisions. In fact, the textbook used in my microeconomics course, Pindyck and Rubinfeld, introduces sunk cost only when discussing a firm's decision, not in the theory of consumer (like some elementary economics textbooks do). When I handled this part in the past, I don't have any feeling. But now I think there is wisdom in such a treatment.
