Isegoria

Brian Albrecht explains why you can’t just compare tax rates between, say, income taxes and tariffs:

Double a tax rate, and you quadruple the deadweight loss. This is a standard result in public finance, and it suggests we should spread our tax burden across many bases rather than concentrate it in one place.

Here’s the intuition. When you impose a small tax, you only kill off marginal transactions—deals that barely made sense in the first place. The buyer was almost indifferent about purchasing, or the worker was almost indifferent about working that extra hour. These marginal transactions don’t create much surplus, so losing them doesn’t cost much.

But as you increase the tax rate, you start killing off transactions with larger and larger surplus. Beyond eliminating the deals that barely made sense, you’re now eliminating deals where both parties really wanted to trade, where there were substantial gains from the exchange. The surplus lost from these inframarginal transactions is much larger.

This is why deadweight loss grows with the square of the tax rate. Double the tax, and you lose transactions that had twice the surplus. The effect multiplies. A 10% tax might eliminate deals that create $1 of surplus each, but a 20% tax eliminates deals worth $1 and deals worth $2. The total loss is 4x, not 2x.

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If you want to compare across markets, you need another basic idea from taxation: deadweight loss depends on elasticities.

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Some supplies are essentially fixed—you can’t create more of them no matter how high the price goes. Other goods can be produced in unlimited quantities at constant cost. Some demands are highly elastic (people readily substitute to alternatives), while others are inelastic (people need the good regardless of price). These elasticities determine how much distortion a given tax rate creates. The tax rate alone tells you nothing.

More elastic demand or supply curves generate larger deadweight losses. The flipside is the classic Ramsey result: tax less elastic goods more heavily.

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Consider taxing a good with a perfectly inelastic supply—say, land in a specific location. The supply curve is vertical. No matter what price landowners receive, they supply the same amount of land because they can’t create more of it. By definition, there is no deadweight loss. The tax doesn’t change behavior.

What happens when we increase the tax rate on land? The tax raises revenue, but it generates no deadweight loss. Landowners absorb the entire tax through lower prices, but the quantity of land traded doesn’t change. There’s no distortion in the allocation of resources. You could tax land at 100%, and the deadweight loss would still be zero.

This demolishes the idea that you can look at tax rates in isolation. There is no nice connection between tax rate and deadweight loss that transcends the specific good being taxed.

Now compare this to a tariff on imported goods, where supply and demand are both elastic. The tariff creates a wedge between what consumers pay and what producers receive. This wedge distorts both consumption decisions (people buy less than they would otherwise) and production decisions (domestic producers make more than they would in an undistorted market). We get the classic deadweight loss triangle.

And it’s not just that imports aren’t perfectly inelastic. They’re very elastic! Estimates vary but one recent paper puts the long-run elasticity at 14, implying a huge deadweight loss.

The formula that deadweight loss increases with the square of the tax rate applies to both taxes. It tells us doubling tariffs with quadruple the deadweight loss. But it tells us nothing about which tax we should increase and the deadweight loss across the two markets. The land tax, even at a 100% rate, might generate zero distortion. The tariff, even at a 2.5% rate, creates real costs because of the huge elasticities. Elasticities matter. You can’t compare tax rates across different bases without accounting for how responsive behavior is to each tax.

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But tariffs are worse than general consumption taxes because they tax only some goods—and imports are a small share of total consumption.

In the US, imports are roughly 10% of consumption. This means tariffs apply to a base that’s one-tenth of a general consumption tax would. When Lott compares a 2.5% tariff to a 40% income tax, he’s ignoring that these rates apply to completely different denominators.

Think of it this way: if you want to raise $100 from a tax that applies to everyone’s $1,000 of consumption, you need a 10% rate. But if you want to raise that same $100 from a tax that only applies to $100 of imports (10% of consumption), you need a 100% rate. The narrow base means you need a much higher rate to raise equivalent revenue.

This logic applies to any narrow excise tax.

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