# Elasticity and the Law of Demand

JDN 2457289 EDT 21:04

This will be the second post in my new bite-size format, the first one that’s in the middle of the week.

I’ve alluded previously to the subject of demand elasticity, but I think it’s worth explaining in a little more detail. The basic concept is fairly straightforward: Demand is more elastic when the amount that people want to buy changes a large amount for a small change in price. The opposite is inelastic.

Apples are a relatively elastic good. If the price of apples goes up, people buy fewer apples. Maybe they buy other fruit instead, such as oranges or bananas; or maybe they give up on fruit and eat something else, like rice.

Salt is an extremely inelastic good. No matter what the price of salt is, at least within the range it has been for the last few centuries, people are going to continue to buy pretty much the same amount of salt. (In ancient times salt was actually expensive enough that people couldn’t afford enough of it, which was particularly harmful in desert regions. Mark Kulansky’s book Salt on this subject is surprisingly compelling, given the topic.)
Specifically, the elasticity is equal to the proportional change in quantity demanded, divided by the proportional change in price.

For example, if the price of gas rises from \$2 per gallon to \$3 per gallon, that’s a 50% increase. If the quantity of gas purchase then falls from 100 billion gallons to 90 billion gallons, that’s a 10% decrease. If increasing the price by 50% decreased the quantity demanded by 10%, that would be a demand elasticity of -10%/50% = -1/5 = -0.2

In practice, measuring elasticity is more complicated than that, because supply and demand are both changing at the same time; so when we see a price change and a quantity change, it isn’t always clear how much of each change is due to supply and how much is due to demand. Sophisticated econometric techniques have been developed to try to separate these two effects (in future posts I plan to explain the basics of some of these techniques), but it’s difficult and not always successful.

In general, markets function better when supply and demand are more elastic. When shifts in price trigger large shifts in quantity, this creates pressure on the price to remain at a fixed level rather than jumping up and down. This in turn means that the market will generally be predictable and stable.

It’s also much harder to make monopoly profits in a market with elastic demand; even if you do have a monopoly, if demand is highly elastic then raising the price won’t make you any money, because whatever you gain in selling each gizmo for more, you’ll lose in selling fewer gizmos. In fact, the profit margin for a monopoly is inversely proportional to the elasticity of demand.

Markets do not function well when supply and demand are highly inelastic. Monopolies can become very powerful and result in very large losses of human welfare. A particularly vivid example of this was in the news recently, when a company named Turing purchased the rights to a drug called Daraprim used primarily by AIDS patients, then hiked the price from \$13.50 to \$750. This made enough people mad that the CEO has since promised to bring it back down, though he hasn’t said how far.

That price change was only possible because Daraprim has highly inelastic demand—if you’ve got AIDS, you’re going to take AIDS medicine, as much as prescribed, provided only that it doesn’t drive you completely bankrupt. (Not an unreasonable fear, as medical costs are the leading cause of bankruptcy in the United States.) This raised price probably would bankrupt a few people, but for the most part it wouldn’t affect the amount of drug sold; it would just funnel a huge amount of money from AIDS patients to the company. This is probably part of why it made people so mad; that and there would probably be a few people who died because they couldn’t afford this new expensive medication.

Imagine if a company had tried to pull the same stunt for a more elastic good, like apples. “CEO buys up all apple farms, raises price of apples from \$2 per pound to \$100 per pound.” What’s going to happen then? People are not going to buy any apples. Perhaps a handful of the most die-hard apple lovers still would, but the rest of us are going to meet our fruit needs elsewhere.

For most goods most of the time, elasticity of demand is negative, meaning that as price increases, quantity demanded decreases. This is in fact called the Law of Demand; but as I’ve said, “laws” in economics are like the Pirate Code: They’re really more what you’d call “guidelines”.
There are three major exceptions to the Law of Demand. The first one is the one most economists talk about, and it almost never happens. The second one is talked about occasionally, and it’s quite common. The third one is almost never talked about, and yet it is by far the most common and one of the central driving forces in modern capitalism.
The exception that we usually talk about in economics is called the Giffen Effect. A Giffen good is a good that’s so cheap and such a bare necessity that when it becomes more expensive, you won’t be able to buy less of it; instead you’ll buy more of it, and buy less of other things with your reduced income.

It’s very hard to come up with empirical examples of Giffen goods, but it’s an easy theoretical argument to make. Suppose you’re buying grapes for a party, and you know you need 4 bags of grapes. You have \$10 to spend. Suppose there are green grapes selling for \$1 per bag and red grapes selling for \$4 per bag, and suppose you like red grapes better. With your \$10, you can buy 2 bags of green grapes and 2 bags of red grapes, and that’s the 4 bags you need. But now suppose that the price of green grapes rises to \$2 per bag. In order to afford 4 bags of grapes, you now need to buy 3 bags of green grapes and only 1 bag of red grapes. Even though it was the price of green grapes that rose, you ended up buying more green grapes. In this scenario, green grapes are a Giffen good.

The exception that is talked about occasionally and occurs a lot in real life is the Veblen Effect. Whereas a Giffen good is a very cheap bare necessity, a Veblen good is a very expensive pure luxury.

The whole point of buying a Veblen good is to prove that you can. You don’t buy a Ferrari because a Ferrari is a particularly nice automobile (a Prius is probably better, and a Tesla certainly is); you buy a Ferrari to show off that you’re so rich you can buy a Ferrari.

On my previous post, jenszorn asked: “Much of consumer behavior is irrational by your standards. But people often like to spend money just for the sake of spending and for showing off. Why else does a Rolex carry a price tag for \$10,000 for a Rolex watch when a \$100 Seiko keeps better time and requires far less maintenance?” Veblen goods! It’s not strictly true that Veblen goods are irrational; it can be in any particular individual’s best interest is served by buying Veblen goods in order to signal their status and reap the benefits of that higher status. However, it’s definitely true that Veblen goods are inefficient; because ostentatious displays of wealth are a zero-sum game (it’s not about what you have, it’s about what you have that others don’t), any resources spent on rich people proving how rich they are are resources that society could otherwise have used, say, feeding the poor, curing diseases, building infrastructure, or colonizing other planets.

Veblen goods can also result in a violation of the Law of Demand, because raising the price of a Veblen good like Ferraris or Rolexes can make them even better at showing off how rich you are, and therefore more appealing to the kind of person who buys them. Conversely, lowering the price might not result in any more being purchased, because they wouldn’t seem as impressive anymore. Currently a Ferrari costs about \$250,000; if they reduced that figure to \$100,000, there aren’t a lot of people who would suddenly find it affordable, but many people who currently buy Ferraris might switch to Bugattis or Lamborghinis instead. There are limits to this, of course: If the price of a Ferrari dropped to \$2,000, people wouldn’t buy them to show off anymore; but the far larger effect would be the millions of people buying them because you can now get a perfectly good car for \$2,000. Yes, I would sell my dear little Smart if it meant I could buy a Ferrari instead and save \$8,000 at the same time.

But the third major exception to the Law of Demand is actually the most important one, yet it’s the one that economists hardly ever talk about: Speculation.

The most common reason why people would buy more of something that has gotten more expensive is that they expect it to continue getting more expensive, and then they will be able to sell what they bought at an even higher price and make a profit.

When the price of Apple stock goes up, do people stop buying Apple stock? On the contrary, they almost certainly start buying more—and then the price goes up even further still. If rising prices get self-fulfilling enough, you get an asset bubble; it grows and grows until one day it can’t, and then the bubble bursts and prices collapse again. This has happened hundreds of times in history, from the Tulip Mania to the Beanie Baby Bubble to the Dotcom Boom to the US Housing Crisis.

It isn’t necessarily irrational to participate in a bubble; some people must be irrational, but most people can buy above what they would be willing to pay by accurately predicting that they’ll find someone else who is willing to pay an even higher price later. It’s called Greater Fool Theory: The price I paid may be foolish, but I’ll find someone who is even more foolish to take it off my hands. But like Veblen goods, speculation goods are most definitely inefficient; nothing good comes from prices that rise and fall wildly out of sync with the real value of goods.

Speculation goods are all around us, from stocks to gold to real estate. Most speculation goods also serve some other function (though some, like gold, are really mostly just Veblen goods otherwise; actual useful applications of gold are extremely rare), but their speculative function often controls their price in a way that dominates all other considerations. There’s no real limit to how high or low the price can go for a speculation good; no longer tied to the real value of the good, it simply becomes a question of how much people decide to pay.

Indeed, speculation bubbles are one of the fundamental problems with capitalism as we know it; they are one of the chief causes of the boom-and-bust business cycle that has cost the world trillions of dollars and thousands of lives. Most of our financial industry is now dedicated to the trading of speculation goods, and finance is taking over a larger and larger section of our economy all the time. Many of the world’s best and brightest are being funneled into finance instead of genuinely productive industries; 15% of Harvard grads take a job in finance, and almost half did just before the crash. The vast majority of what goes on in our financial system is simply elaborations on speculation; very little real productivity ever enters into the equation.

In fact, as a general rule I think when we see a violation of the Law of Demand, we know that something is wrong in the economy. If there are Giffen goods, some people are too poor to buy what they really need. If there are Veblen goods, inequality is too large and people are wasting resources competing for status. And since there are always speculation goods, the history of capitalism has been a history of market instability.

Fortunately, elasticity of demand is usually negative: As the price goes up, people want to buy less. How much less is the elasticity.

# How following the crowd can doom us all

JDN 2457110 EDT 21:30

Humans are nothing if not social animals. We like to follow the crowd, do what everyone else is doing—and many of us will continue to do so even if our own behavior doesn’t make sense to us. There is a very famous experiment in cognitive science that demonstrates this vividly.

People are given a very simple task to perform several times: We show you line X and lines A, B, and C. Now tell us which of A, B or C is the same length as X. Couldn’t be easier, right? But there’s a trick: seven other people are in the same room performing the same experiment, and they all say that B is the same length as X, even though you can clearly see that A is the correct answer. Do you stick with what you know, or say what everyone else is saying? Typically, you say what everyone else is saying. Over 18 trials, 75% of people followed the crowd at least once, and some people followed the crowd every single time. Some people even began to doubt their own perception, wondering if B really was the right answer—there are four lights, anyone?

Given that our behavior can be distorted by others in such simple and obvious tasks, it should be no surprise that it can be distorted even more in complex and ambiguous tasks—like those involved in finance. If everyone is buying up Beanie Babies or Tweeter stock, maybe you should too, right? Can all those people be wrong?

In fact, matters are even worse with the stock market, because it is in a sense rational to buy into a bubble if you know that other people will as well. As long as you aren’t the last to buy in, you can make a lot of money that way. In speculation, you try to predict the way that other people will cause prices to move and base your decisions around that—but then everyone else is doing the same thing. By Keynes called it a “beauty contest”; apparently in his day it was common to have contests for picking the most beautiful photo—but how is beauty assessed? By how many people pick it! So you actually don’t want to choose the one you think is most beautiful, you want to choose the one you think most people will think is the most beautiful—or the one you think most people will think most people will think….

Our herd behavior probably made a lot more sense when we evolved it millennia ago; when most of your threats are external and human beings don’t have that much influence over our environment, the majority opinion is quite likely to be right, and can often given you an answer much faster than you could figure it out on your own. (If everyone else thinks a lion is hiding in the bushes, there’s probably a lion hiding in the bushes—and if there is, the last thing you want is to be the only one who didn’t run.) The problem arises when this tendency to follow the ground feeds back on itself, and our behavior becomes driven not by the external reality but by an attempt to predict each other’s predictions of each other’s predictions. Yet this is exactly how financial markets are structured.

With this in mind, the surprise is not why markets are unstable—the surprise is why markets are ever stable. I think the main reason markets ever manage price stability is actually something most economists think of as a failure of markets: Price rigidity and so-called “menu costs“. If it’s costly to change your price, you won’t be constantly trying to adjust it to the mood of the hour—or the minute, or the microsecondbut instead trying to tie it to the fundamental value of what you’re selling so that the price will continue to be close for a long time ahead. You may get shortages in times of high demand and gluts in times of low demand, but as long as those two things roughly balance out you’ll leave the price where it is. But if you can instantly and costlessly change the price however you want, you can raise it when people seem particularly interested in buying and lower it when they don’t, and then people can start trying to buy when your price is low and sell when it is high. If people were completely rational and had perfect information, this arbitrage would stabilize prices—but since they’re not, arbitrage attempts can over- or under-compensate, and thus result in cyclical or even chaotic changes in prices.

Our herd behavior then makes this worse, as more people buying leads to, well, more people buying, and more people selling leads to more people selling. If there were no other causes of behavior, the result would be prices that explode outward exponentially; but even with other forces trying to counteract them, prices can move suddenly and unpredictably.

If most traders are irrational or under-informed while a handful are rational and well-informed, the latter can exploit the former for enormous amounts of money; this fact is often used to argue that irrational or under-informed traders will simply drop out, but it should only take you a few moments of thought to see why that isn’t necessarily true. The incentives isn’t just to be well-informed but also to keep others from being well-informed. If everyone were rational and had perfect information, stock trading would be the most boring job in the world, because the prices would never change except perhaps to grow with the growth rate of the overall economy. Wall Street therefore has every incentive in the world not to let that happen. And now perhaps you can see why they are so opposed to regulations that would require them to improve transparency or slow down market changes. Without the ability to deceive people about the real value of assets or trigger irrational bouts of mass buying or selling, Wall Street would make little or no money at all. Not only are markets inherently unstable by themselves, in addition we have extremely powerful individuals and institutions who are driven to ensure that this instability is never corrected.

This is why as our markets have become ever more streamlined and interconnected, instead of becoming more efficient as expected, they have actually become more unstable. They were never stable—and the gold standard made that instability worse—but despite monetary policy that has provided us with very stable inflation in the prices of real goods, the prices of assets such as stocks and real estate have continued to fluctuate wildly. Real estate isn’t as bad as stocks, again because of price rigidity—houses rarely have their values re-assessed multiple times per year, let alone multiple times per second. But real estate markets are still unstable, because of so many people trying to speculate on them. We think of real estate as a good way to make money fast—and if you’re lucky, it can be. But in a rational and efficient market, real estate would be almost as boring as stock trading; your profits would be driven entirely by population growth (increasing the demand for land without changing the supply) and the value added in construction of buildings. In fact, the population growth effect should be sapped by a land tax, and then you should only make a profit if you actually build things. Simply owning land shouldn’t be a way of making money—and the reason for this should be obvious: You’re not actually doing anything. I don’t like patent rents very much, but at least inventing new technologies is actually beneficial for society. Owning land contributes absolutely nothing, and yet it has been one of the primary means of amassing wealth for centuries and continues to be today.

But (so-called) investors and the banks and hedge funds they control have little reason to change their ways, as long as the system is set up so that they can keep profiting from the instability that they foster. Particularly when we let them keep the profits when things go well, but immediately rush to bail them out when things go badly, they have basically no incentive at all not to take maximum risk and seek maximum instability. We need a fundamentally different outlook on the proper role and structure of finance in our economy.

Fortunately one is emerging, summarized in a slogan among economically-savvy liberals: Banking should be boring. (Elizabeth Warren has said this, as have Joseph Stiglitz and Paul Krugman.) And indeed it should, for all banks are supposed to be doing is lending money from people who have it and don’t need it to people who need it but don’t have it. They aren’t supposed to be making large profits of their own, because they aren’t the ones actually adding value to the economy. Indeed it was never quite clear to me why banks should be privatized in the first place, though I guess it makes more sense than, oh, say, prisons.

Unfortunately, the majority opinion right now, at least among those who make policy, seems to be that banks don’t need to be restructured or even placed on a tighter leash; no, they need to be set free so they can work their magic again. Even otherwise reasonable, intelligent people quickly become unshakeable ideologues when it comes to the idea of raising taxes or tightening regulations. And as much as I’d like to think that it’s just a small but powerful minority of people who thinks this way, I know full well that a large proportion of Americans believe in these views and intentionally elect politicians who will act upon them.

All the more reason to break from the crowd, don’t you think?

# No, capital taxes should not be zero

JDN 2456998 PST 11:38.

It’s an astonishingly common notion among neoclassical economists that we should never tax capital gains, and all taxes should fall upon labor income. Here Scott Sumner writing for The Economist has the audacity to declare this a ‘basic principle of economics’. Many of the arguments are based on rather esoteric theorems like the Atkinson-Stiglitz Theorem (I thought you were better than that, Stiglitz!) and the Chamley-Judd Theorem.

All of these theorems rest upon two very important assumptions, which many economists take for granted—yet which are utterly and totally untrue. For once it’s not assumed that we are infinite identical psychopaths; actually psychopaths might not give wealth to their children in inheritance, which would undermine the argument in a different way, by making each individual have a finite time horizon. No, the assumptions are that saving is the source of investment, and investment is the source of capital income.

Investment is the source of capital, that’s definitely true—the total amount of wealth in society is determined by investment. You do have to account for the fact that real investment isn’t just factories and machines, it’s also education, healthcare, infrastructure. With that in mind, yes, absolutely, the total amount of wealth is a function of the investment rate.

But that doesn’t mean that investment is the source of capital income—because in our present system the distribution of capital income is in no way determined by real investment or the actual production of goods. Virtually all capital income comes from financial markets, which are rife with corruption—they are indeed the main source of corruption that remains in First World nations—and driven primarily by arbitrage and speculation, not real investment. Contrary to popular belief and economic theory, the stock market does not fund corporations; corporations fund the stock market. It’s this bizarre game our society plays, in which a certain portion of the real output of our productive industries is siphoned off so that people who are already rich can gamble over it. Any theory of capital income which fails to take these facts into account is going to be fundamentally distorted.

The other assumption is that investment is savings, that the way capital increases is by labor income that isn’t spent on consumption. This isn’t even close to true, and I never understood why so many economists think it is. The notion seems to be that there is a certain amount of money in the world, and what you don’t spend on consumption goods you can instead spend on investment. But this is just flatly not true; the money supply is dynamically flexible, and the primary means by which money is created is through banks creating loans for the purpose of investment. It’s that I term I talked about in my post on the deficit; it seems to come out of nowhere, because that’s literally what happens.

On the reasoning that savings is just labor income that you don’t spend on consumption, then if you compute the figure W – C , wages and salaries minus consumption, that figure should be savings, and it should be equal to investment. Well, that figure is negative—for reasons I gave in that post. Total employee compensation in the US in 2014 is \$9.2 trillion, while total personal consumption expenditure is \$11.4 trillion. The reason we are able to save at all is because of government transfers, which account for \$2.5 trillion. To fill up our GDP to its total of \$16.8 trillion, you need to add capital income: proprietor income (\$1.4 trillion) and receipts on assets (\$2.1 trillion); then you need to add in the part of government spending that isn’t transfers (\$1.4 trillion).

If you start with the fanciful assumption that the way capital increases is by people being “thrifty” and choosing to save a larger proportion of their income, then it makes some sense not to tax capital income. (Scott Sumner makes exactly that argument, having us compare two brothers with equal income, one of whom chooses to save more.) But this is so fundamentally removed from how capital—and for that matter capitalism—actually operates that I have difficulty understanding why anyone could think that it is true.

The best I can come up with is something like this: They model the world by imagining that there is only one good, peanuts, and everyone starts with the same number of peanuts, and everyone has a choice to either eat their peanuts or save and replant them. Then, the total production of peanuts in the future will be due to the proportion of peanuts that were replanted today, and the amount of peanuts each person has will be due to their past decisions to save rather than consume. Therefore savings will be equal to investment and investment will be the source of capital income.

I bet you can already see the problem even in this simple model, if we just relax the assumption of equal wealth endowments: Some people have a lot more peanuts than others. Why do some people eat all their peanuts? Well it probably has something to do with the fact they’d starve if they didn’t. Reducing your consumption below the level at which you can survive isn’t “thrifty”, it’s suicidal. (And if you think this is a strawman, the IMF has literally told Third World countries that their problem is they need to save more. Here they are arguing that in Ghana.) In fact, economic growth leads to saving, not the other way around. Most Americans aren’t starving, and could probably stand to save more than we do, but honestly it might not be good if we did—everyone trying to save more can lead to the Paradox of Thrift and cause a recession.

Even worse, in that model world, there is only capital income. There is no such thing as labor income, only the number of peanuts you grow from last year’s planting. If we now add in labor income, what happens? Well, peanuts don’t work anymore… let’s try robots. You have a certain number of robots, and you can either use the robots to do things you need (including somehow feeding you, I guess), or you can use them to build more robots to use later. You can also build more robots yourself. Then the “zero capital tax” argument amounts to saying that the government should take some of your robots for public use if you made them yourself, but not if they were made by other robots you already had.

In order for that argument to carry through, you need to say that there was no such thing as an initial capital endowment; all robots that exist were either made by their owners or saved from previous construction. If there is anyone who simply happened to be born with more robots, or has more because they stole them from someone else (or, more likely, both, they inherited from someone who stole), the argument falls apart.

And even then you need to think about the incentives: If capital income is really all from savings, then taxing capital income provides an incentive to spend. Is that a bad thing? I feel like it isn’t; the economy needs spending. In the robot toy model, we’re giving people a reason to use their robots to do actual stuff, instead of just leaving them to make more robots. That actually seems like it might be a good thing, doesn’t it? More stuff gets done that helps people, instead of just having vast warehouses full of robots building other robots in the hopes that someday we can finally use them for something. Whereas, taxing labor income may give people an incentive not to work, which is definitely going to reduce economic output. More precisely, higher taxes on labor would give low-wage workers an incentive to work less, and give high-wage workers an incentive to work more, which is a major part of the justification of progressive income taxes. A lot of the models intended to illustrate the Chamley-Judd Theorem assume that taxes have an effect on capital but no effect on labor, which is kind of begging the question.

Another thought that occurred to me is: What if the robots in the warehouse are all destroyed by a war or an earthquake? And indeed the possibility of sudden capital destruction would be a good reason not to put everything into investment. This is generally modeled as “uninsurable depreciation risk”, but come on; of course it’s uninsurable. All real risk is uninsurable in the aggregate. Insurance redistributes resources from those who have them but don’t need them to those who suddenly find they need them but don’t have them. This actually does reduce the real risk in utility, but it certainly doesn’t reduce the real risk in terms of goods. Stephen Colbert made this point very well: “Obamacare needs the premiums of healthier people to cover the costs of sicker people. It’s a devious con that can only be described as—insurance.” (This suggests that Stephen Colbert understands insurance better than many economists.) Someone has to make that new car that you bought using your insurance when you totaled the last one. Insurance companies cannot create cars or houses—or robots—out of thin air. And as Piketty and Saez point out, uninsurable risk undermines the Chamley-Judd Theorem. Unlike all these other economists, Piketty and Saez actually understand capital and inequality.
Sumner hand-waves that point away by saying we should just institute a one-time transfer of wealth to equalized the initial distribution, as though this were somehow a practically (not to mention politically) feasible alternative. Ultimately, yes, I’d like to see something like that happen; restore the balance and then begin anew with a just system. But that’s exceedingly difficult to do, while raising the tax rate on capital gains is very easy—and furthermore if we leave the current stock market and derivatives market in place, we will not have a just system by any stretch of the imagination. Perhaps if we can actually create a system where new wealth is really due to your own efforts, where there is no such thing as inheritance of riches (say a 100% estate tax above \$1 million), no such thing as poverty (a basic income), no speculation or arbitrage, and financial markets that actually have a single real interest rate and offer all the credit that everyone needs, maybe then you can say that we should not tax capital income.

Until then, we should tax capital income, probably at least as much as we tax labor income.