Law of Demand

Subsidies can’t make things unaffordable

pnrj public policy , , , , ,

May 12 2458616

In last week’s post I talked about a supposed benefit of subsidies that almost never materializes. In this week, I’m going to talk about a supposed harm of subsidies that is literally impossible.

The American Enterprise Institute (a libertarian think-tank) has been sending around a graph of price increases over the last 20 years by sector, showing what everyone already intuitively knows: healthcare and education have gotten wildly more expensive, while high-tech products have gotten extremely cheap. Actually I was a surprised how little they found housing prices had increased (enough to make me wonder what metric they are using for housing prices).

They argue that it is government intervention which has created these rising prices:

Blue lines = prices subject to free market forces. Red lines = prices subject to regulatory capture by government.

Along similar lines, Grey Gordon and Aaron Hedlund published a book chapter presenting evidence that student loans and federal subsidies are responsible for increases in college tuition. They are professional economists, so I feel like I ought to take their argument seriously… but it’s really hard to do, because it’s such a silly concept at the most basic level. I could nitpick their assumptions about elasticity of demand and monopoly power, but the whole argument just doesn’t pass the smell test.

Subsidies always make things more affordable for the person being subsidized.

It’s possible for subsidies to create other distortions, and make things more expensive for those who aren’t subsidized. But it’s literally impossible for subsidies to make something unaffordable to the person being subsidized.

That result is absolutely fundamental, and it comes directly from the Law of Supply and Law of Demand.

Subsidies

On this graph, the blue line is the demand curve. The red line is the supply curve. The thick green line is where they intersect, at the competitive equilibrium price. In this case, that equilibrium means we sell 6 units at a price of $3 each.

The thin green lines show what happen if we introduce a subsidy. Here the subsidy is $3. The sticker price can be read off of the supply curve: It will rise to $4. But the actual price paid by consumers is read off the demand curve: It will fall to $1. Total sales will rise to 8 units. The total cost to the government is then 8($3) = $24.

These exact numbers are of course specific to the example I chose. But the overall direction is not.

We can go ahead and draw this with all sorts of different supply and demand curves, and we’ll keep getting the same result.

Here’s one where I didn’t even make the curves linear:

Subsidies_2

In this case, a subsidy of $5.40 raises the sticker price from $6.10 to $11.20, only reducing the price for consumers to $5.80, while increasing the quantity sold from 3.5 to 4.8. The total cost of the subsidy is $25.92. The price effects are very different in magnitude from the previous example, and yet all the directions are exactly the same—and they will continue to be the same, however you draw the curves.

And here’s yet another example:

Subsidies_3

Here, a subsidy of $2.30 raises the sticker price from $4 to $5.30, lowers the cost to consumers to $3, increases the quantity sold from 4 to 7 units, and costs $16.10.

If you’re still not convinced, try drawing some more of the same diagrams yourself. As long as you make the supply curve slope upward and the demand curve slope downward, you’ll keep getting the same results.
A subsidy will always do four things:

  1. Increase the sticker price, benefiting sellers.
  2. Decrease the price that subsidized consumers actually pay, benefiting those consumers.
  3. Increase the quantity sold.
  4. Cost the government money.

The intuition here is quite simple: If I give you free money every time you buy a thing, you’ll buy more of that thing (3) because it costs you less to do so (2). Because you buy more of the thing, the price will go up (1), but not enough to cancel out the reduced cost to you (or else you’d stop). Since I’m giving you free money, that will cost me money (4). This intuition is fully general: It doesn’t matter what kind of product we are talking about, you’re never going to buy less or have to pay more for each one because I gave you free money.

The size of each effect depends upon elasticity of demand and supply, in basically the same way as tax incidence. The more inelastic side of the market is harmed less by the tax and also benefits less from the subsidy. For any given change in quantity, more inelastic markets raise more tax revenue and cost more subsidy spending.

If we allow elasticities of demand or supply to be zero or infinite (which is almost never the case in real life), then some of these effects might be zero. But they will never go the opposite direction, not as long as the supply curve slopes upward and the demand curve slopes downward.

I suspect that education has relatively inelastic demand and relatively elastic supply, which would mean that the subsidies are actually largely felt by the consumer, not the seller. But that’s actually a legitimate economic question: I might be overestimating the elasticity of supply.

There are other legitimate economic questions here as well, such as how much benefit we get out of a given subsidy versus other ways we might spend that money, and how subsidies may hurt others in the same market who aren’t subsidized.

What is not a legitimate question is the one that these libertarian think-tanks seem to be asking, which is “If you give people money, will they end up with less stuff?” No, they won’t. That’s not how any of this works.

And I’m pretty sure the people in these think-tanks are smart enough to know that. They might be blinded by their anti-government ideology, but I actually suspect it’s more sinister than that: They know that what they are saying isn’t true, but they consider it a “noble lie”: A falsehood told to the common folk in the service of a higher good.

They are clever enough to not simply state the lie outright, but instead imply it through misleading presentation of real facts. Yes, it’s true that subsidies will raise the sticker price—so they can say that this was all they were asserting. But not only is that obvious and trivial: It wouldn’t even support the argument they are obviously trying to make. Nobody cares about the sticker price. They care about what people actually pay. And a subsidy, by construction, as a law of economics, cannot possibly increase the amount paid by the buyer who is subsidized.

What they obviously want you to think is that the reason healthcare and education are so unaffordable is because the government has been subsidizing them. But this is basically the opposite of the truth: These things became unaffordable for various reasons, and the government stepped in to subsidize them in order to stop the bleeding. Is that a permanent solution? No, it’s not. But it does actually help keep them affordable for the time being—and it could not have done otherwise. There’s simply no way to give someone free money and make them poorer. (Of course, fully socialized healthcare and education might be permanent solutions, so if the libertarians aren’t careful what they wish for….)

Asymmetric nominal rigidity, or why everything is always “on sale”

pnrj critique of neoclassical economics, heuristics and biases, macroeconomics, market failure , , , , , , , , , , , , ,

July 9, JDN 2457579

The next time you’re watching television or shopping, I want you to count the number of items that are listed as “on sale” versus the number that aren’t. (Also, be careful to distinguish labels like “Low Price!” and “Great Value!” that are dressed up like “on sale” labels but actually indicate the usual price.) While “on sale” is presented as though it’s something rare and special, in reality anywhere from a third to half of all products are on sale at any given time. At some retailers (such as Art Van Furniture and Jos. A. Bank clothing), literally almost everything is almost always on sale.

There is a very good explanation for this in terms of cognitive economics. It is a special case of a more general phenomenon of asymmetric nominal rigidity. Asymmetric nominal rigidity is the tendency of human beings to be highly resistant to (rigidity) changes in actual (nominal) dollar prices, but only in the direction that hurts them (asymmetric). Ultimately this is an expression of the far deeper phenomenon of loss aversion, where losses are felt much more than gains.

Usually we actually talk about downward nominal wage rigidity, which is often cited as a reason why depressions can get so bad. People are extremely resistant to having their wages cut, even if there is a perfectly good reason to do so, and even if the economy is under deflation so that their real wage is not actually falling. It doesn’t just feel unpleasant; it feels unjust. People feel betrayed when they see the numbers on their paycheck go down, and they are willing to bear substantial costs to retaliate against that injustice—typically, they quit or go on strike. This reduces spending, which then exacerbates the deflation, which requires more wage cuts—and down we go into the spiral of depression, unless the government intervenes with monetary and fiscal policy.

But what does this have to do with everything being on sale? Well, for every downward wage rigidity, there is an upward price rigidity. When things become more expensive, people stop buying them—even if they could still afford them, and often even if the price increase is quite small. Again, they feel in some sense betrayed by the rising price (though not to the same degree as they feel betrayed by falling wages, due to their closer relationship to their employer). Responses to price increases are about twice as strong as responses to price decreases, just as losses are felt about twice as much as gains.

Businesses have figured this out—in some ways faster than economists did—and use it to their advantage; and thus so many things are “on sale”.

Actually, “on sale” serves two functions, which can be distinguished according to their marketing strategies. Businesses like Jos. A. Bank where almost everything is on sale are primarily exploiting anchoring—they want people to think of the listed “retail price” as the default price, and then the “sale price” that everyone actually pays feels lower as a result. If they “drop” the price of something from $300 to $150 feels like the company is doing you a favor; whereas if they had just priced it at $150 to begin with, you wouldn’t get any warm fuzzy feelings from that. This works especially well for products that people don’t purchase very often and aren’t accustomed to comparing—which is why you see it in furniture stores and high-end clothing retailers, not in grocery stores and pharmacies.

But even when people are accustomed to shopping around and are familiar with what the price ordinarily would be, sales serve a second function, because of asymmetric nominal rigidity: They escape that feeling of betrayal that comes from raising prices.

Here’s how it works: Due to the thousand natural shocks that flesh is heir to, there will always be some uncertainty in the prices you will want to set in the future. Future prices may go up, they may go down; and people spend their lives trying to predict this sort of thing and rarely outperform chance. But if you just raise and lower your prices as the winds blow (as most neoclassical economists generally assume you will), you will alienate your customers. Just as a ratchet works by turning the bolt more in one direction than the other, this sort of roller-coaster pricing would attract a small number of customers with each price decrease, then repel a larger number with each increase, until after a few cycles of rise and fall you would run out of customers. This is the real source of price rigidities, not that silly nonsense about “menu costs”. Especially in the Information Age, it costs almost nothing to change the number on the label—but change it wrong and it may cost you the customer.

One response would simply be to set your price at a reasonable estimate of the long-term optimal average price, but this leaves a lot of money on the table, as some times it will be too low (your inventory sells out and you make less profit than you could have), and even worse, other times it will be too high (customers refuse to buy your product). If only there were a way to change prices without customers feeling so betrayed!

Well, it turns out, there is, and it’s called “on sale”. You have a new product that you want to sell. You start by setting the price of the product at about the highest price you would ever need to sell it in the foreseeable future. Then, unless right now happens to be a time where demand is high and prices should also be high, you immediately put it on sale, and have the marketing team drum up some excuse about wanting to draw attention to your exciting new product. You put a deadline on that sale, which may be explicit (“Ends July 30”) or vague (“For a Limited Time!” which is technically always true—you merely promise that your sale will not last until the heat death of the universe), but clearly indicates to customers that you are not promising to keep this price forever.

Then, when demand picks up and you want to raise the price, you can! All you have to do is end the sale, which if you left the deadline vague can be done whenever you like. Even if you set explicit deadlines (which will make customers even more comfortable with the changes, and also give them a sense of urgency that may lead to more impulse buying), you can just implement a new sale each time the last one runs out, varying the discount according to market conditions. Customers won’t retaliate, because they won’t feel betrayed; you said fair and square the sale wouldn’t last forever. They will still buy somewhat less, of course; that’s the Law of Demand. But they won’t overcompensate out of spite and outrage; they’ll just buy the amount that is their new optimal purchase amount at this new price.

Coupons are a lot like sales, but they’re actually even more devious; they allow for a perfectly legal form of price discrimination. Businesses know that only certain types of people clip coupons; roughly speaking, people who are either very poor or very frugal—either way, people who are very responsive to prices. Coupons allow them to set a lower price for those groups of people, while setting a higher price for other people whose demand is more inelastic. A similar phenomenon is going on with student and senior discounts; students and seniors get lower prices because they typically have less income than other adults (though why there is so rarely a youth discount, only a student discount, I’m actually not sure—controlling for demographics, students are in general richer than non-students).

Once you realize this is what’s happening, what should you do as a customer? Basically, try to ignore whether or not a label says “on sale”. Look at the actual number of the price, and try to compare it to prices you’ve paid in the past for that product, as well as of course how much value the product is worth to you. If indeed this is a particularly low price and the product is durable, you may well be wise to purchase more and stock up for the future. But you should try to train yourself to react the same way to “On sale, now $49.99” as you would to simply “$49.99”. (Making your reaction exactly the same is probably impossible, but the closer you can get the better off you are likely to be.) Always compare prices from multiple sources for any major purchase (Amazon makes this easier than ever before), and compare actual prices you would pay—with discounts, after taxes, including shipping. The rest is window dressing.

If you get coupons or special discounts, of course use them—but only if you were going to make the purchase anyway, or were just barely on the fence about it. Rarely is it actually rational for you to buy something you wouldn’t have bought just because it’s on sale for 50% off, let alone 10% off. It’s far more likely that you’d either want to buy it anyway, or still have no reason to buy it even at the new price. Businesses are of course hoping you’ll overcompensate for the discount and buy more than you would have otherwise. Foil their plans, and thereby make your life better and our economy more efficient.

Elasticity and the Law of Demand

pnrj core principles, critique of neoclassical economics , , , , , , , , ,

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.