With his “you didn’t build that" remark, President Barack Obama walked into a broad philosophical debate over taxation.

Most people would say that taxes ought to be “equitable,” but there are many views about what that means.  The two most common principles of equity are the “benefit principle,” which holds that people should pay more in taxes the more they benefit from government services, and the “ability-to-pay principle,” which holds that people with more resources should pay more.

Every tax system makes an effort to balance these two principles. Conservatives tend to favor the former and liberals the latter, because the latter is more aligned with progressive taxation.

The interesting thing about “you didn’t build that” is that it’s an argument from the benefit principle, not the ability-to-pay principle. The president was contending that rich people should pay more in tax because they were the beneficiaries of government actions that helped them get rich, not simply because they are rich and can therefore pay more.

This is a good point, as I argue in the Boston Globe this morning. Yet middle-class people are also drawing increasingly valuable and expensive benefits from the actions of the federal government, and Obama has steadfastly refused to tell them they need to pay more.

Of course, the president could simply back away from the benefit principle and make purely redistributive arguments for progressive taxation. The problem is that you need a tax code that leans heavily on the benefit principle if you hope to finance a large and active government. As I wrote in the Globe, there’s a reason that countries with big welfare states also have big, regressive taxes like VATs.

This is because -- and forgive me for getting wonky here for a second -- the deadweight loss of a tax (the economic value that is lost because the tax causes people to change their behavior) is a function of the square of the tax rate.

Here’s what that means. Imagine that a widget costs $100 to produce and is subject to a 5 percent sales tax. You will only buy the widget if it is worth at least $105 to you. Some beneficial trades are lost to the tax -- people who would have valued the widget at $102 won’t buy it. But the economic losses are small, because only a small number of consumers fall within the dissuaded range.

Now imagine that widgets are subject to a 25 percent tax. There will both be a lot more sales lost to the tax -- consumers valuing the good for less than $125 won’t buy, and that’s a larger fraction of the market -- and there will be more loss of welfare from each lost sale. Think of the welfare losses per sale this way: It’s a bigger economic problem when a policy prevents sales of $100 widgets to people who value them at $120 than when it prevents sales of them to people who value them at $102.

This example uses a sales tax, but the principle works the same way with an income tax; you can think of labor as being the good sold by the worker to the firm. With income taxes, higher marginal rates both dissuade more people from working, and dissuade people whose output increasingly exceeds their wages from working.

Roughly, you can expect that when you double a tax rate, the deadweight loss due to the tax increases by a factor of four. Eventually, the economic cost of a tax becomes very large relative to the revenue it generates. That’s why the CBO estimates that the president’s plan to extend most of the tax cuts would be worse for the economy than Republicans’ plan to extend all of them, even though the president’s plan would have grown the public debt less -- the president was proposing to sunset cuts in marginal tax rates on high earners.

And this is why welfare states tend to go hand in hand with efficient, regressive taxes like VATs. As the government gets larger and needs more revenue, the efficiency problems created by progressive taxation get more and more pressing, and regressive taxation is needed.

This is something U.S. liberals have not gotten comfortable with. You can think of liberals having two goals on tax policy: The government should collect more revenue, and it should do so more progressively. Those goals are in tension with each other, and liberals have chosen to focus on the latter. Unless they learn to love middle-class taxes, they will find that a devotion to progressive taxation makes progressive spending programs unaffordable.

Obama’s speech made clear that he knows how to argue for taxes based on the benefit principle. Now he needs to take that argument to the middle class -- and when he does, he should probably find a less scolding way to put it.

(Josh Barro is lead writer for the Ticker. Follow him on Twitter.)

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