# 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.