This post is about utility theory based on the doctrine of revealed preference. I hope the reader will discern, despite my sweeping and dismissive critiques, that I am actually an admirer of utility theory. It’s brilliant as a logical exercise. I think it’s even rather useful, as a way to dodge modern relativism, and provide a rational basis for making policy decisions. But in the end, it can’t withstand philosophical scrutiny.
Why does utility theory need to “withstand philosophical scrutiny?” What does philosophy have to do with it? To the extent that utility theory merely as a technical tool for deriving theoretical demand curves, which can then be studied empirically, maybe it doesn’t. But economists use utility theory to define efficiency and to optimize policy. ‘Optimal’ means ‘best,’ the superlative of ‘good.’ The question of what is good is a philosophical question, to which utility theory is a kind of elaborate non-answer answer.
“What is good? Let the consumer decide!” says the economist. And then, when the consumer has decided, the economist says, “Behold the consumer’s decision. That is good.” From this seemingly vacuous starting point, called the doctrine of revealed preference, utility theory begins an inquiry which turns out to generate surprising rich and elaborate, if defeasible, conclusions.
To dramatize how this is accomplished, I'll introduce a bit of fantasy which I'll call the Time Warp Fable. Suppose that, for a research project in your economics class, you invent a time warp machine, which can freeze time, for everyone else but not yourself, and which also allows you to “wake up” individual people by tapping them, so that you can ask them questions. The people you tap have no memories of anything that happens in the time warp, except the very short-term memory needed to interact with you. So, if you ask them, “would you prefer x apples or y oranges?” substituting a thousand different values for x and y, they won't find the interview tedious, because they won't remember the previous questions in the series. You ask everyone in your economics class a vast series of questions, until you can exhaustively describe people's preferences in a manner that can be adumbrated by a graphical representation such as that shown in Figure 1:
Figure 1. Indifference Curves and Consumer Choice
Here’s a quick review of what all economists, and even good undergraduates, know about the above chart. (Feel free to skim or skip.) Every point in the chart represents some consumption bundle. Consumers are assumed to have preferences that satisfy the assumptions of completeness, transitivity, and non-satiation. Bundles that are equally preferred are joined in “indifference curves.” Non-satiation implies that indifference curves slope down; transitivity, that they do not cross one another. Non-satiation also implies that any point on a “higher” indifference curve (further from the origin) is preferred to any point on a “lower” indifference curve (nearer the origin). Consumers have budget constraints, such as B, consisting in all the ways they can spend their full income. The consumer’s optimum consumption bundle is located where the budget constraint is tangent to an indifference curve, such as (G*, S*) in Figure 1. This optimum is on the highest feasible indifference curve, I2 in this case, which is preferred to I1 and all other lower indifference curves, whereas I3 would be preferred, but is not feasible. Changes in the budget constraint, due to changes in income or relative prices, will interact with the utility function (represented by the indifference curve map) to determine the consumer’s response. (End review.)
It is an ingenious construct.
I said that Figure 1 only “adumbrates” the utility-theoretic notion of people's preferences, because it has only two axes, “goods” and “services.” Consumables would need to be broken down much more than that, to achieve a decent description of preferences. Sometimes economists label the axes with more adequately differentiated categories, such as “pizza” and “beer,” but that is just as incomplete, though in a different way. People spend their money on far more things than pizza and beer. Figure 1 must be understood as a kind of placeholder or symbol for the real utility function, which has a dimension for every kind of good or service you consume. This n-dimensional utility function can’t be drawn, so the 2-dimensional utility function is used as an example, simplified to the point of silliness, to suggest to the mind the, so to speak, real utility function, which can only be expressed in mathematical equations such as U=f(c1,c2,c3,...cn), where n is the total number of relevantly different consumables available.
I just used the word “real” to contrast the n-dimensional goods space in which real consumers make decisions, with the silly 2-dimensional goods space used to illustrate concepts. But in what sense, if any, is any utility function real?
In the Time Warp Fable, the utility function described people’s answers to a very, very long interview. Call it the Utility Function Interview. But the Utility Function Interview could never actually be conducted. No one would ever have the patience to submit to it. To the old riddle that asks, “if a tree falls in the forest, does it make a sound?” the answer is surely yes, for sound is a physical reality. But if a consumer preference is never reported or exercised, does it exist? It seems doubtful. If it does, it must exist as some sort of predisposition in the mind to choose X over Y, even if circumstances never present the individual with this choice. But do such predispositions always exist at all? Or are consumer choices as likely as not to be made ex nihilo, on the spur of the moment, by free will, so that the preference didn't exist before the decision? And what does it matter anyway? Metaphysics aside, what’s the use of the concept of a utility function, if we can never actually observe people’s utility?
Utility theory would be a mere silly escapade into far-fetched hypotheticals, but for one thing: money. Money, as it were, conducts the great Utility Function Interview for us. It’s infeasible to conduct the comprehensive consumer surveys I imagined in the Time Warp Fable, yet every time a consumer walks into a supermarket, something like this interview is conducted. From every shelf, hundreds of price tags stare the consumer in the face, and ask, “Would you like to buy this product for this price?” The popcorn and the apples conspire to ask, “Would you prefer five pounds of apples to five cups of popcorn?” The chicken asks, “How much more chicken will you buy this week, for $0.88/pound, than you did last week, for $1.49/pound?” So vast is the quantity of data generated by people’s everyday transactions, that to generate a rough data-driven description of the typical person’s utility function, at least over some large range of consumption bundles, might not be a completely infeasible project. I’m not aware that anyone has attempted it, but the fact that such an attempt might be possible gives some legitimacy to utility as a theoretical construct.
Now stop for a moment to contemplate the sheer ambition of utility theory. The axes of an indifference curve map can be anything. The Utility Function Interviewer needn’t limit himself to asking “Would you prefer five apples or four oranges?” He can ask, “Would you prefer to have a mansion, or a man in love with you?” Or “would you prefer to have a Porsche, or a talent for poetry?” Or “would you prefer to be president, or to fully understand particle physics?” Economists don’t always realize the scope of utility theory, and if they do, would be as likely to evade or apologize for it, as to be proud of it. But once utility theory has gotten started, you can’t set bounds to it.
Now, in recent decades, behavioral economists have made a powerful attack on utility theory for assuming that people are perfectly rational and selfish, when in reality they are somewhat fallible and generous. But we should have known that all along, and maybe everyone did, it’s hard to tell. I won’t stop here to assess whether the behavioral economists have provided valuable caveats and clarifications, or attacked straw men, or dispelled a real naivete and credulity about the adequacy of utility theory as a description of human motivation and action. My critique of utility theory is quite different in character.
Let me start with the following two observations:
- Most human enjoyment is social; and
- Money can buy only inputs to most enjoyable activities.
How devastating these two objections are for the claims of utility theory may be illustrated with what I'll call the Playing Card Puzzle.
Supply and demand interact to set the price of a deck of cards. Capitalist productivity has made decks of cards very cheap, even for people who are quite poor. Let’s suppose, then, that rising productivity reduces the price of a deck of cards from $20 to $1. To keep things simple, assume that the same number of decks of cards are sold. An economist might value the benefits of this by saying that $19 of “consumer surplus” have been added to the economy for each deck of cards that would have been sold at $20.
But no one gets much pleasure from simply owning a deck of cards. They get pleasure from playing cards. And to play cards, having a deck isn’t enough. You need to have time to play. You need to know the rules of a card game. You need to have someone to play with.
It’s almost inevitable that an economist will treat the price paid for the deck of cards as the value of the deck of cards. What else can an economist do? The economist must focus on money transactions, because money transactions are the great searchlight that sheds light on the utility function. When people spend money, they provide a basis for making inferences about their preferences. The $1 pack of playing cards can be compared to the $1 apple and the $1 candy bar. And this is cooked into the way GDP is calculated, for GDP relies on money transactions to set a value on everything, to lump into the grand summary statistic that is used to measure the wealth and poverty of nations.
But it’s obvious common sense that mere ownership of a pack of cards typically contributes nothing to utility. What contributes to utility is the activity of playing cards. And that activity is only very loosely correlated with the ownership of playing cards. (Actually, if we want to make things still more complicated, cards might have option value, as insurance against a boring evening, and contribute to psychic welfare even if they're never used… but never mind.) Some who own no playing cards play them often, because they have friends who do. Many own playing cards, yet never play cards.
Standard utility theory and GDP calculations both treat playing cards as a “final good,” but they’re not. They’re an intermediate good, an input into the activity of playing cards. The purchase of a deck of cards is a kind of speculation, which pays off if and only if games of cards are subsequently organized.
And what goes for cards goes for much of what we buy. A life utterly destitute of companionship would be a horror to most people, regardless of what degree of luxury they could enjoy in terms of material possessions, yet companionship can't be bought directly, though many purchases are aimed at getting it. Cars and computers, for example, are used to connect with friends, though also for work and business, including personal bureaucracy. The $10 one pays for a cocktail in a bar is typically paid, not so much for alcohol, as for the hope of meeting a special someone there. Gym memberships, as often as not, are ways to improve one’s appearance and attract the opposite sex. The arts are inherently social, in that a poem, novel, or film links an artist with an audience. Also, most people prefer to watch movies with other people. Beds aren’t very interesting until they’re shared. Even food, the quintessential consumable, is often as much an input to social enjoyment as a means to merely sensory pleasure. Again and again, we find that the spending traditionally referred to as consumption is really connected to enjoyment only via social interactions that occur outside the monetary economy. The market turns out to offer mostly intermediate goods, inputs, often rather inessential and almost always insufficient in themselves, into the social production of enjoyment through various forms of non-monetary human interaction.
None of this refutes the doctrine of revealed preference per se. Again, you can put anything on the axes of the utility function. You can put card games as easily as decks of cards. But it’s decks of cards, not card games, that can be sold in a store. Money can shed light on decks of cards, not card games. Without money to probe people’s preferences for us, we could still derive a notion of a utility function from magical scenarios like the Time Warp Fable, but it loses its footing in the realm of practical, observable decision-making. Money conducts the Utility Function Interview, but it does so in a tendentious way. It is constantly comparing unlikes, e.g., setting a final good like a bag of candy beside a risky intermediate good like a pad of paper on which to write a love letter, and giving them the same value just because they have the same market price.
So far, utility theory isn’t doing very well. But in order to make this post less disappointing, I want to preview a conclusion, almost a hunch, that will take me a long time to establish, namely: utility theory is a bad description of individual welfare, but a reasonably good description of household welfare, at least in happy families.
Let me suggest that for a single individual, most solitary enjoyments are so unsatisfactory that money by itself is a very poor means to happiness. Over and above basic needs, which for most single people are fairly easily met, if they aren't addicted to luxuries, most spending is on speculative investments that might lead to some sort of social enjoyment. A young man spends $50 on dinner and a movie with a date, but the dinner and movie aren’t worth $50. The romance may be worth far more, if it happens; the evening might be worse than wasted if it doesn’t; but in any case, the $50 is only tenuously related to any real utility or pleasure enjoyed. In a rich society, the $50 may need to be spent as part of a signaling game. A walk by the river would send a different, less appealing signal, of poverty, indifference, being a cheapskate. But in a poorer society, where a walk by the river would not send that signal, it might serve the purpose just as well as dinner and a movie, or perhaps even better.
But now consider a household, consisting of a happily married couple with children. Their social needs are wonderfully well-met within the household. Conversation, love, sexual pleasure, reminiscence are all provided for. The beauty of nature can be enjoyed in a shared fashion. All sorts of cheap or free pleasures, such as singing, playing cards, going for a walk, and so forth, are readily available. But they need money. Childrearing demands privacy, and therefore living space. Houses are expensive. Child care is a constant need which makes it hard for the couple to hold two jobs, and to support several people on one job is difficult. There are more mouths to feed. Education is a pressing necessity for the sake of the children’s future. Where the single person’s happiness depends mostly on forms of social enjoyment that money can’t buy because they depend on success in complex multilateral games, the happy family has the social enjoyment problem solved. What it needs are precisely the sorts of things money can buy: food, clothing, education, housing. It knows what to do with them if it gets them.
If the subject whose utility indifference curves are supposed to elucidate is interpreted as being a single individual, utility theory is largely misleading and misguided, because money mostly buys speculative investments in rather inessential inputs to complex social games, with payoffs that depend on social dynamics that occur outside the monetary economy, so that monetary transactions fail to reveal people’s real preferences. But if indifference curves are interpreted as belonging to households, and in particular, to well-ordered happy families, utility theory is powerfully insightful, because such households stand mostly in need of consumables, and can convert them efficiently into enjoyment.
That’s an intriguing story, but how can I prove it, or even argue for it?
A general problem for intellectuals, is how to avoid falling into a bottomless pit of skepticism. The questions “Why?” and “How do you know?” are never far away, and are rarely easily answered. They can recur, and recur, and recur, in an infinite regress which is very difficult to terminate. Revealed preference, in essence, answers the question, “What is the good life for man?” by delegating it. It says, let people choose. This delegation can be interpreted as a belief that choice really is the only good, or that people infallibly know what is good for them, or-- more reasonably-- that people tend to know what’s good for them, and should usually be deferred to rather than dictated to. Whatever the justification may be for trusting people to know (more or less) their own good, if markets enable people to reveal their preferences and get more of what they want, we are entitled to interpret economic growth as betterment of the human condition, while remaining amazingly nonjudgmental about what the good life for man actually consists in. But the Playing Card Parable brings this whole delicate construct crashing down. Money doesn’t buy happiness; it buys inputs to complex social games; and so, no conclusions about human welfare are warranted from the abundance of consumer goods and calculations of consumer surplus. Revealed preference seemed to be a safety net, rescuing us from falling into the bottomless pit of skepticism. But it turned out to be a mere spider’s web, with no power to catch us, or to halt our descent.
Have we any other resource to avoid falling into the pit of complete relativism, skepticism, and abdication of value judgments?
Well, yes. One in particular is worth invoking here: SOCIOBIOLOGY. To that rich source of insight about human nature, we now turn.
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