Imagine the economy were a pizza parlor

A pizza analogy shows how doubling the tax rate could quadruple economic harm.

By , Guest blogger

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    Guest blogger Donald Marron uses a pizza analogy to show how raising taxes can hurt both consumers and the government.
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At last Wednesday’s hearing on tax reform, three witnesses–Rosanne Altshuler, Larry Lindsey, and I–invoked a famous rule of thumb about taxes. We each told the Senate Budget Committee that high tax rates are disproportionately harmful for the economy and that:

If you double tax rates, you quadruple the resulting economic harm.

If a 10% tax rate on some activity does a certain amount of economic damage, for example, then it’s a reasonable guess that doubling the tax rate to 20% would multiply that damage by a factor of four.

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It was nice to hear such agreement among the panelists, but judging by the senators’ reaction, this idea is not intuitive. So let me try to explain with a simple example.

Suppose there are five people who might buy a pizza. The first person values a pizza at $14.50, the second at $13.50, the third at $12.50, the fourth at $11.50, and the fifth at $10.50.

If pizzas cost $10, all five people will buy one. The first person gets a net benefit of $4.50, since the pizza was worth $14.50 to her, but she paid only $10. The second person gets a benefit of $3.50, and so on. Add it all up, and the benefit of the pizza market is $12.50 (= $4.50 + $3.50 + $2.50 + $1.50 + $0.50).

Now suppose that the government levies a 10% tax on pizzas; that lifts the price to $11. Now only the four consumers who place the highest value on pizzas will buy them; Mr. $10.50 won’t buy. The four remaining consumers now benefit by $3.50 + $2.50 + $1.50 + $0.50 = $8.00 from buying pizza. The government collects $4.00 in revenue, so the total economic benefit of the pizza market is $12.00, $0.50 less than before. That 50-cent loss falls on the hungry guy who no longer buys a pizza. The $1 loss for each of the four buyers isn’t lost to the economy; instead, it transfers to the government.

Now suppose, instead, that the tax is 20%; pizzas now cost $12 each, and only three consumers will buy. Their total benefit is $4.50 (= $2.50 + $1.50 + $0.50). The government collects $6.00 in revenue, so the total economic benefit is $10.50. That’s $2.00 less than without a tax.

So there you have it. When you double the tax from 10% to 20%, you quadruple the economic harm from $0.50 to $2.00.

Why does this happen? Because doubling the tax doubles the number of consumers who drop out (from 1 to 2) and doubles the average economic value of the pizza sales that never happen (from $0.50 to $1.00). Two times two is four, so the overall effect is to quadruple the economic harm.

Put another way, the value of the second lost pizza ($1.50) is three times larger than the value of the first one ($0.50). So the economic harm of the 20% tax is four times the harm of the 10% tax.

This is a big deal when you design a tax system for the entire economy. To avoid needless economic harm, you should aim for low tax rates and the broadest possible tax base. If you need to raise $6.00 from our mythical food economy, for example, it would be far better to levy a 5% tax on pizzas, tacos, and hamburgers, than a 20% tax on pizzas alone.

I hope that whets your appetite for base-broadening tax reform.

P.S. Did I cook the pizza example to get the increase to be exactly a factor of four? Of course. In the real world, the actual multiple will vary. If the fifth person valued the pizza at only $10.25, for example, the loss from the 10% tax would have been $0.25, and the loss from the 20% tax would have been seven times larger at $1.75. Conversely, if the fourth person valued the pizza at only $11.00, the loss from the 20% tax would have been $1.50, only three times larger than the $0.50 loss from the 10% tax. The double/quadruple rule of thumb assumes an even spread of consumers and their values — a reasonable starting assumption until you have more information.

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