Subsidies can’t make things unaffordable

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….)

Elasticity and the Law of Supply

JDN 2457292 EDT 16:16.

Today’s post is kind of a mirror image of the previous post earlier this week; I was talking about demand before, and now I’m talking about supply. (In the next post, I’ll talk about how the two work together to determine the actual price of goods.)

Just as there is an elasticity of demand which describes how rapidly the quantity demanded changes with changes in price, likewise there is an elasticity of supply which describes how much the quantity supplied changes with changes in price.

The elasticity of supply is defined as the proportional change in quantity supplied divided by the proportional change in price; so for example if the number of cars produced increases 10% when the price of cars increases by 5%, the elasticity of supply of cars would be 10%/5% = 2.

Goods that have high elasticity of supply will rapidly flood the market if the price increases even a small amount; goods that have low elasticity of supply will sell at about the same rate as ever even if the price increases dramatically.

Generally, the more initial investment of capital a good requires, the lower its elasticity of supply is going to be.

If most of the cost of production is in the actual marginal cost of producing each new gizmo, then elasticity of supply will be high, because it’s easy to produce more or produce less as the market changes.

But if most of the cost is in building machines or inventing technologies or training employees which already has to be done in order to make any at all, while the cost of each individual gizmo is unimportant, the elasticity of supply will be low, because there’s no sense letting all that capital you invested go to waste.
We can see these differences in action by comparing different sources of electric power.

Photovoltaic solar power has a high elasticity of supply, because building new solar panels is cheap and fast. As the price of solar energy fluctuates, the amount of solar panel produced changes rapidly. Technically this is actually a “fixed capital” cost, but it’s so modular that you can install as little or as much solar power capacity as you like, which makes it behave a lot more like a variable cost than a fixed cost. As a result, a 1% increase in the price paid for solar power increases the amount supplied by a whopping 2.7%, a supply elasticity of 2.7.

Oil has a moderate elasticity of supply, because finding new oil reserves is expensive but feasible. A lot of oil in the US is produced by small wells; 18% of US oil is produced by wells that put out less than 10 barrels per day. Those small wells can be turned on and off as the price of oil changes, and new ones can be built if it becomes profitable. As a result, investment in oil production is very strongly correlated with oil prices. Still, overall production of oil changes only moderate amounts; in the US it had been steadily decreasing since 1970 until very recently when new technologies and weakened regulations resulted in a rapid increase to near-1970s levels. We sort of did hit peak oil; but it’s never quite that simple.

Nuclear fission has a very low elasticity of supply, because building a nuclear reactor is extremely expensive and requires highly advanced expertise. Building a nuclear power plant costs upward of $35 billion. Once a reactor is built, the cost of generating more power is relatively trivial; three-fourths of the cost a nuclear power plant will ever pay is paid simply to build it (or to pay back the debt incurred by doing so). Even if the price of uranium plummets or the price of oil skyrockets, it would take a long time before more nuclear power plants would be built in response.

Elasticity of supply is generally a lot larger in the long run than in the short run. Over a period of a few days or months, many types of production can’t be changed significantly. If you have a corn field, you grow as much corn as you can this season; even if the price rose substantially you couldn’t actually grow any more than your field will allow. But over a period of a year to a few years, most types of production can be changed; continuing with the corn example, you could buy new land to plant corn next season.

The Law of Supply is actually a lot closer to a true law than the Law of Demand. A negative elasticity of supply is almost unheard of; at worst elasticity of supply can sometimes drop close to zero. It really is true that elasticity of supply is almost always positive.

Land has an elasticity near zero; it’s extremely expensive (albeit not impossible; Singapore does it rather frequently) to actually create new land. As a result there’s really no good reason to ever raise the price of land; higher land prices don’t incentivize new production, they just transfer wealth to landowners. That’s why a land tax is such a good idea; it would transfer some of that wealth away from landowners and let us use it for public goods like infrastructure or research, or even just give it to the poor. A few countries actually have tried this; oddly enough, they include Singapore and Denmark, two of the few places in the world where the elasticity of land supply is appreciably above zero!

Real estate in general (which is what most property taxes are imposed on) is much trickier: In the short run it seems to have a very low elasticity, because building new houses or buildings takes a lot of time and money. But in the long run it actually has a high elasticity of supply, because there is a lot of profit to be made in building new structures if you can fund projects 10 or 15 years out. The short-run elasticity is something like 0.2, meaning a 1% increase in price only yields a 0.2% increase in supply; but the long-run elasticity may be as high as 8, meaning that a 1% increase in price yields an 8% increase in supply. This is why property taxes and rent controls seem like a really good idea at the time but actually probably have the effect of making housing more expensive. The economics of real estate has a number of fundamental differences from the economics of most other goods.

Many important policy questions ultimately hinge upon the elasticity of supply: If elasticity is high, then taxing or regulating something is likely to cause large distortions of the economy, while if elasticity is low, taxes and regulations can be used to support public goods or redistribute wealth without significant distortion to the economy. On the other hand, if elasticity is high, markets generally function well on their own, while if elasticity is low, prices can get far out of whack. As a general rule of thumb, government intervention in markets is most useful and most necessary when elasticity is low.