2. Utility Theory and Revealed Preference

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:

1. Most human enjoyment is social; and
2. 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.

1. Supply and Demand

In this post, I'm going to do something rather audacious. I'm going to commit an act of iconoclasm, almost of lese-majeste. I'm going to attack the model of supply, demand, and market equilibrium, the centerpiece of economics, taught in every principles of economics class. I'm going to argue that, except in special cases, it's gratuitously inaccurate and deficient in insight. I'm going to offer two alternative charts, one for the short run, one for the long run, which I think ought to replace the classic supply-and-demand chart in many or most of the places where it occurs, starting with undergraduate textbooks. Maybe by the time I’m finished, the sky will have fallen.

The traditional representation of supply, demand, and market equilibrium is shown in Figure 1:

Figure 1

Let me quickly review what not only every economist, but every good undergraduate economics student, knows about this chart. (Feel free to skim or skip.) Reversing the usual mathematical convention, quantity, shown on the horizontal axis, is the dependent variable. Price, shown on the vertical axis, is the independent variable. Demand (D) and supply (S) are functions of price. If the price is high enough, suppliers will want to sell more than demanders are willing to buy, resulting in a surplus. If the price is low enough, demanders will want to buy more than suppliers are willing to sell, resulting in a shortage. But there exists an equilibrium price, P*, at which the quantity demanded and the quantity supplied are both equal to Q*. (End review.)

This graphical argument… but perhaps I should explain what I mean by graphical argument before I go on. If there is one skill that sets economists apart from everyone else, it may be their facility for graphical argument. Graphical argument is not the same as data visualization. It is a translation into a graphical medium not of numbers and facts but of assumptions and principles and intuitions and deductions and conclusions, or in short, of arguments. It can be casual, carefree, and sloppy in a way. Economists might draw the demand curve with a different slope every time. It's even typical not to draw the demand curve going all the way to the vertical axis, which would look neater, but would suggest that we tend to know how high the price will need to rise before there would be no buyers at all, which we typically do not know. “A picture is worth a thousand words,” the wise saying has it, but of course there's no exact ratio. Sometimes words do the job better, but there are times when a graph can convey an argument not only far more swiftly, but also somewhat more precisely, than any number of words could do, provided that the viewer of the graph has the knack for reading it. Economists learn a sort of graphical language as part of their training, and thereafter can argue to each other using graphs, in a way that no one in the world but economists, as far as I know, is able to do. If you want to learn economics, you need to take graphs seriously. However, some economists take their graphs too seriously, and are afraid to draw new ones because they have so much veneration for the old.

Anyway, this graphical argument is impressively general, inasmuch as the chart is used to describe the market for almost anything, from haircuts to broccoli to dentistry to Exxon shares to foreign currencies.

Now for my objections. First of all, the price-taking assumption.

In making demand and supply functions of price, economists assume that demanders and suppliers are “price takers,” who don’t set prices, but accept prices that are somehow set by “the market.” To people living in a modern capitalist economy, the price-taking assumption will seem quite reasonable for buyers. We’re all accustomed to walk into stores and see prices posted. Take it or leave it. No haggling.

Sellers, by contrast, do seem to set prices, but the price-taking assumption might still be warranted, if sellers operate under conditions approximating “perfect competition,” which can be defined most exactly with the help of another term and concept, “elasticity of selective demand.” Elasticity, in general, is the percentage change in a dependent variable divided by the percentage change in an independent variable. Elasticity of demand describes how responsive customers are to price changes. That’s as far as undergraduate economics textbooks usually go, but in the field of marketing, a further distinction is made between selective demand, the demand for a single branded product, and category demand, the demand for a type of product. Elasticity of selective demand is the percent change in quantity demanded over the percent change in price for a single branded product. Perfect competition refers to a case where the elasticity of selective demand for all sellers’ products is… (negative) infinity! If that were so, sellers would have no choice but to charge what the market would bear, not a penny more. The price-taking assumption would hold.

So, how well does the assumption of perfect competition, or in other words, infinite elasticity of selective demand, describe the situation that real firms find themselves in? We wouldn’t expect it to hold perfectly, of course, but is it a decent approximation of reality? A meta-analysis of studies of price sensitivity by Tellis (1988) draws on many other studies and concludes that the median value for price elasticity of selective demand is -1.76, and the mode is -1.50. Only a tiny fraction of studies found price elasticities of selective demand below -6. This isn’t even close to perfect competition. Conclusion: The price-taking assumption, on the supply side, doesn’t describe reality in most markets.

Where does that leave economic theory? Its most famous chart assumes that sellers are price-takers, when they’re not. Can it even get off the ground? It might help that economic theory offers not one but four models of market structure. In addition to perfect competition, there is monopoly, oligopoly, and finally “monopolistic competition,” which probably comes closest to being a realistic description of most real product markets. Unfortunately, conventional economic theory derives the supply curve from a model featuring perfect competition, so monopolistic competition does nothing to justify the classic demand-and-supply chart.

I had to teach undergraduates the concept of the supply curve as a function of price, when I was an economics professor. It was my duty to be a spokesman for the field, even at the expense of truth. I did it.

To discard the price-taking assumption, and come up with a new way of thinking about markets that does not rely on it, will be a difficult labor, requiring sustained development over many future blog posts. For the remainder of this post, I’ll leave the price-taking assumption unmolested, drawing charts in which the “law of one price” still holds. But I have registered my dissent, and replacing the price-taking assumption with something more acceptable is hereby placed on my long-term agenda.

My second objection to the classic supply-and-demand chart is that markets don't clear.

Figure 1 tells a story in which markets clear. Quantity demanded equals quantity supplied. All goods made, are sold. Economists tend to regard this result with satisfaction, yet in the short run at least, it’s brazenly counter-factual. In the real world, the quantities sellers offer for sale usually exceed the quantities that buyers purchase, which is why there are always unsold goods sitting on store shelves. Of course, this isn’t a bug, it’s a feature. It’s because there are so many unsold goods sitting on stores’ shelves that consumers in capitalist economies enjoy such a rich selection of things to buy, which used to amaze visitors from the Soviet Union. But the supply-and-demand chart would be truer, in the short run, if drawn as in Figure 2:

Figure 2

In Figure 2, there are demand (D) and supply (S) curves, which represent how much buyers are willing to buy, and sellers to sell, for any given price, as usual. But the A curve represents actual sales, as a function of price. It lies to the left of both demand and supply, since (a) for a sale to take place, both a buyer and a seller are needed, and (b) for buyers and sellers to find each other is a non-trivial problem, and it sometimes fails to occur.

Moreover, the matching problem becomes more severe when quantity demanded and quantity supplied are equal or nearly equal. To see why, suppose you’re shopping for lawn mowers. If there are lots of lawn mowers for sale, your search will be easy, and you’ll probably find one. If there’s only one lawn mower for sale in the county, you’ll end up driving from store to store, and being told “sold out” again and again, until maybe you give up. The lawn mower is there, but it’s too difficult to find, so the sale doesn’t happen. Consequently, A is “bowed inward” near the price where quantity demanded equals quantity supplied.

Like D and S, A is a function of price. For any given price, the difference between Qa and Qs represents unsold goods, or goods left in inventory, or simply “inventories.” The difference between Qa and Qd represents “frustrated demand,” that is, buyers who wanted to buy the good at the market price, but didn’t succeed in finding a seller. Pactual means the price that sellers charge, or the price that prevails in the market. It is a kind of equilibrium price, but I’m reluctant to use the word “equilibrium” to describe it, since conventional theory has reserved that term for the intersection of the demand and supply curves. When sellers charge Pactual, frustrated demand is rather small, since sellers have substantial inventories. At the price where D and S intersect, the search problem would become very difficult, many consumers would be frustrated, and suppliers would raise prices, to avoid running down inventories, and also because frustrated consumers wouldn't mind paying more to avoid a costly and perhaps fruitless search.

This version of the demand and supply chart has a couple of advantages over the conventional one.

1. It communicates the concept, and the function, of inventories in a capitalist economy. Inventories are a striking and important feature of capitalist economies, and it's nice to have them in the model, rather than supposing that “markets clear.”
2. It also provides a clue to how markets equilibrate, rather than leaving it all to the magical beneficence of the “invisible hand.” Suppliers desire to keep a certain amount of inventory on hand. If sales are more than they expected, inventories are depleted, and suppliers ramp up production, and maybe raise prices. If sales are less than they expected, inventories accumulate, and suppliers slow production down, and maybe cut prices.

I suspect many who are habituated to the classic demand-and-supply chart will feel that my critique of market clearing is a case of excessive cleverness turning into obtuseness. Of course, we always knew there were inventories! The classic chart leaves them out of account, in order to focus on something else. In any case, having goods on store shelves for a while before they're sold is just part of the process of supplying them. Markets clear (so the defense would go) if all goods are sold eventually.

It won't do. Quantity supplied is typically defined as the quantity of goods that suppliers are willing to sell at a given price. By that definition, quantity supplied for a given period must include both sales during that period, and inventories left over at the end of it, for those inventories were ready to be sold during the period in question.

However, as longer periods are considered, cumulative sales grow and inventories don't, so in the long run, market clearing becomes a defensible approximation. But as market clearing becomes more defensible, the upward-sloping supply curve becomes less so.

For my third objection to the classic supply-and-demand chart is that supply curves ought not, in general, to slope up.

In the short run, an upward-sloping supply curve makes some sense, because the quantity of the good available is limited and/or the capacity to produce it cost-effectively is limited. Indeed, if the time scale is short enough, a vertical supply curve might seem most appropriate. No more widgets can be got to the store shelves in the next hour. But in the long run, unless fundamental natural scarcities are a binding constraint at the margin-- more on that in a moment-- suppliers should be able to increase supply more by simply doing more of the same, without increasing costs. So the price should, at the worst, stay constant as the market expands.

And very likely, prices can actually fall as quantity increases. We’re all familiar with the bulk discount. In the supermarket, the five-pound bag of apples is cheaper per pound than the loose apples. The big box of cereal and the big bottle of olive oil are proportionally cheaper than the smaller ones. It’s almost an economic law of everyday experience that when you buy more, you get a better price. This is sometimes explained as “second-degree price discrimination,” but I think the more important reason is economies of scale, one of the most important principles in economics. If you do something on a larger scale, you can generally do it more efficiently, and unit costs fall.

It’s cheaper, per pound, for suppliers to sell you oil in big bottles than little bottles. First, it saves packaging because of the nature of space. Roughly, as the dimension of a container increases, its surface area, and therefore the cost of the materials, grows with the square of the dimension, while the volume, and therefore how much it can hold, grows with the cube of the dimension. Second, it saves labor on the part of the person or machine putting labels on the bottles, and of the supermarket checkout clerk ringing up your order. It’s cheaper, per box, for the supermarket to sell you three boxes of cereal than one, because the clerk can scan just one box and then type the number “3” in a machine.

More importantly and more generally, large-scale production allows for more specialization of workers, and warrants more investment in specialized capital equipment. Henry Ford, perhaps the greatest industrialist of all time, transformed the modern economy by mass producing automobiles. What had previously been done in workshops, he did on an assembly line, where conveyor belts brought products to workers who did the same task over and over again. This required a lot of capital, starting with the conveyor belts, and a lot of workers, to do all the narrowly specialized tasks. It worked wonders for productivity, allowing unskilled factory workers to out-perform skilled craftsmen, but only if it were done on a very large scale. The famous “pin factory” described in Adam Smith’s Wealth of Nations to illustrate the almighty power of the division of labor to raise productivity is another example. Indeed, while it’s become fashionable to see the Industrial Revolution as driven by advances in science and technology, few of the technological advances since, say, 1800, could be implemented economically on a small scale, and I suspect that the Industrial Revolution owes as much to institutional innovations that facilitate complex divisions of labor and large-scale industrial operations, as it does to the progress of science and technology.

Now, some scarcities are given by nature, and when markets are pushing the limits of those, supply curves do, legitimately, slope up. The supply curve for oil is the best example of this. Some deposits are near the surface and easy to get, while others need to be expensively drilled from sea beds or squeezed from oil shale. But most goods do not absorb a large enough share of the total supply of the resource inputs they need, to affect the prices of any of them. A few things at random-- say, baseball bats, wrenches, and teddy bears-- may serve to illustrate. All of them require some natural resources, e.g., wood, metal, and cotton. But very little of the world’s wood, metal, and cotton is used (respectively) for baseball bats, wrenches, and teddy bears. It’s hardly plausible that an increase in demand for baseball bats, wrenches, or teddy bears would raise the world prices of wood, metal, or cotton. Nor do these industries use significant fractions of society’s capital or labor. So if demand for baseball bats, wrenches, or teddy bears increases, suppliers should, in the long run, be able, in the worst case, to expand their operations by doing more of the same. Prices shouldn’t need to rise, and the supply curve should be flat, or, if economies of scale come into play, slope down.

It’s easy to incorporate economies of scale into our model, simply by drawing the supply curve as sloping down instead of up. (There are some hidden subtleties here, about how the supply curve needs to be redefined to permit it to slope down without absurdity, but never mind that for now.) Figure 3 shows the classic demand-and-supply chart, with the supply curve sloping down. (Note that I've relabeled the horizontal axis “ln Q,” or “natural logarithm of quantity,” because supply curves generally don't slope down very steeply, and the log scale horizontal axis makes the visible downward slope of the supply curve consistent with a much flatter slope, for high values of Q, were the same curve drawn in P/Q space.)

Figure 3

In Figure 3, “markets clear,” a defensible assumption for a long-run model. “Equilibria” are located at the intersections of a demand curve and a supply curve.

But Figure 3 contains a startling insight that is missing from Figure 1. As long as demand slopes down and supply slopes up, there is always exactly one intersection (which could involve a negative price, but never mind). But if the supply curve slopes down, there may be one intersection, or no intersections, or multiple intersections. The production and sale of the good only occurs if the market is large enough to support it.

Dvillage describes a small "village" market that is too small to sustain the industry in question. There is no scale of production at which suppliers will supply the good for a price that enough buyers are willing to pay.

Dtown describes a medium-sized "town" market where the existence and non-existence of the industry are both equilibria. If the industry does not exist, no one has an incentive, at the margin, to create it. A very small producer would fail, because his average costs would exceed buyers’ willingness to pay. The industry could emerge only if quantity jumps from 0 to Q1. Think of a visionary entrepreneur, raising venture capital to launch, on a viable scale, a company that would be impossible to bootstrap.

Finally, Dcity describes a large "city" market where the existence of the industry is the only equilibrium, because some buyers’ willingness-to-pay exceeds average production cost even at the smallest scale of operations.

Figure 3 contains an important lesson, namely, that increasing demand can trigger the emergence of new markets and the availability of new goods. That’s the main reason why most people live in towns and cities-- larger populations mean more shopping options and a wider variety of jobs-- instead of being spread out evenly over the land. It also deserves consideration as an explanatory factor in economic growth: growing demand motivates the introduction of new goods, which is perceived as “invention” by outsiders, but which may often be the implementation and commercialization of technical possibilities long perceived by insiders, but not economically viable until the market reached a certain scale. Figure 3 also elucidates why luxury consumption can have social value, since customers with high willingness-to-pay help to create markets that might not come into existence without them, but which, once they exist, can grow and gain economies of scale until their products become affordable to the middle classes or the poor.

Lest I overreach, let me stress that the classical supply-and-demand model is a good description of some markets, especially (a) most commodity markets, and (b) broad factor markets. In fact, Tyler Cowen and Alex Tabarrok, in their textbook Modern Principles of Economics, take advantage of this by turning their chapters on supply and demand into a case study of the oil industry, thus sidestepping the lack of realism of the upward-sloping supply curve in general, by focusing on one of the few prominent industries where it definitely does make good sense to draw the supply curve sloping upward. For that and other more important reasons, I liked to teach from their textbook, since I felt it enabled me to be more honest in the classroom. But the classic supply-and-demand model is a clumsy description of most markets for specific consumer products, intermediate inputs, and capital goods. These markets are generally better described by Figure 2, in the short run, and Figure 3, in the long run.

I don’t know if anyone will ever read this post. But it sure feels good to have written it! I spent a lot of time drawing demand-and-supply charts in the classroom, feigning conviction and enthusiasm, and concealing the special care I was using to select examples that would help build intuition for the charts I was drawing, when I knew that most examples would not build intuition for the the charts I was drawing, but instead, would point the way to different insights, which I was not allowed to teach, because it was my duty to be, not a lone freethinker, but a spokesman for the discipline of economics, and these other, truer models didn’t have the authority of the discipline behind them. It left me with a hunger to tell the truth about demand and supply, which the textbook conventions forbade me to do. Now I’ve done that, or at least, I’ve tried my best.

I think the reason why it's built into the design of universities that those who teach should do scholarship, is that when one teaches something, some bit of inherited knowledge or some doctrine or argument, one thinks about it a lot, and starts to understand its strengths and weaknesses, and if it's a little bit wrong, that becomes painful. One feels the need to push back, to try to correct or improve it, as a way to win the right to teach what you think is the truth by persuading one's peers of it first. Alas, overwhelming forces of groupthink have created an insurmountable resistance to changes of core doctrine, and while young scholars are commanded to innovate (publish or perish), they are driven to the margins of specialized fields to do their innovating without disturbing the great inherited doctrines, so that scholarship becomes unconnected with teaching, and the institutional purpose of combining these two functions in the professor’s job description is thwarted.

It may be clear by now one feature of the classic supply-and-demand model which I do not object to is the downward-sloping demand curve. It's good to lay some firm foundations on which knowledge can be built. So before moving on to criticize the more problematic parts of the model, we can take a closer look at the "microfoundations"-- an important word, which means underlying assumptions and arguments-- of the demand curve. And that brings us to UTILITY THEORY.