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Is it better to tax goods with inelastic demand? (Atkinson-Stiglitz redux)

Not necessarily.

Bloggers across the political spectrum, from Noah Millman to Ryan Avent, have recently argued that because the demand for oil is inelastic with respect to price, a gas tax is a relatively efficient way to raise revenue. Though I support a higher gas tax, I don’t think this argument is quite right.

It’s true that the deadweight loss from a tax (a standard measure of inefficiency) is intimately connected to the supply and demand of the good being taxed. If either supply or demand is inelastic with respect to price, the deadweight loss will be low. But when designing a tax system, the deadweight loss isn’t the only relevant consideration.

To see why, let’s consider a silly example. Imagine a tax with the lowest deadweight loss imaginable: a tax on breathing, levied at a rate of $10 every day that you take a breath. The demand elasticity here is exactly zero—no one (I hope) is going to stop breathing for an entire day just to avoid paying the tax. This is a wonderfully efficient tax: it has zero deadweight loss.

In fact, this is effectively a lump-sum tax, a tax demanded equally of every individual. Since lump-sum taxes are a perfectly efficient way to collect money, anyone thinking about how to minimize deadweight loss will always raise revenue exclusively through lump-sum taxes. But this is a cheat: obviously we don’t observe lump-sum taxes in practice, even though at the margin it would be possible to implement them. (If the government demanded that everyone coughed up an additional $50, almost everyone could manage to do it.)

The reason why the government doesn’t do this, of course, is distributional: we care about the poor, and it wouldn’t be fair to ask them to pay exactly the same dollar amount as the rich. This is important for even the most conservative fiscal policy proposals—many of them suggest flat taxes, but never a regressive lump sum. And one we realize that this is a key issue, it’s critical for our understanding of optimal taxation, far beyond the observation that lump sum taxes are a bad idea.

A famous result in public finance, the Atkinson-Stiglitz theorem on the optimality of direct taxation, captures this intuition in a striking way. Atkinson and Stiglitz show that if the utility function is weakly separable between consumption of various goods and labor (intuitively, the amount you work has nothing to do with your consumption choices, except insofar as working more gives you more money to spend), then no consumption taxes are needed to attain the optimum. You don’t levy higher taxes on gas than soy milk because soy milk has a higher elasticity; you just determine the optimal tax schedule on income and then stay away.

Why is this? Well, the reason we don’t levy lump-sum taxes is that we’re concerned about distribution. But it’s also a story about information: if we knew exactly what each person was capable of making, we could assign everyone personalized lump-sum taxes, and achieve our distributional goals without distorting any incentives. (“Matt, the government has calculated that you are easily capable of making $1 million a year over the next 10 years; therefore you must pay $300,000 in tax every year, regardless of your actual income.”) Of course, we don’t have this information, and we’re forced to use income as a proxy for ability to pay instead. But then we reach the Atkinson-Stiglitz result: if your exact consumption decisions don’t add any information about this ability, they shouldn’t be part of the tax. Unless gasoline consumption indicates that you have high hidden earnings potential, it shouldn’t be subject to any special charges.

Mapping this result onto the real world is tough, since “income taxes” in practice include taxes on saving (i.e. capital income), rather than the original income itself. Unless propensity to save or access to savings vehicles offer additional information about underlying earning ability, the Atkinson-Stiglitz results suggest that taxes on capital income should be zero, and that our current regime is inefficient. In this context, it might be efficient to raise gas taxes if they’re replacing taxes on capital gains. But it would be even more efficient to replace capital gains taxes with taxes on regular income*, or implement a progressive consumption tax. It’s tough to imagine a world where hiking gas taxes is the fiscally optimal thing to do, or even the second best.

Of course, this isn’t to say that gas taxes aren’t a good idea. If they’re correcting an externality, gas taxes are absolutely appropriate. They’re just hard to justify on fiscal grounds alone.


*Since people with lots of capital tend to be rich, and they acquired that capital under the assumption that it would be taxed, in practice a sudden implementation of this change would represent a windfall gain for the rich. But this could be counteracted either through an explicit one-time expropriation of capital or an implicit expropriation through an increase in consumption taxes.

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