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.