Marginal vs Average Tax Rates

Both candidates claim to be in favor of cutting taxes, although Obama's people concede that his plan would raise taxes on a small minority of very high income tax payers. But a recent study from the Tax Foundation finds that both candidates' proposals would raise marginal rates for many middle income tax payers. Can both claims be true? If they can, which matters?

The answer is that both can be true and both matter. What the candidates claim is that most individual taxpayers will pay less money under their plans. That may well be true, at least if we look only at income taxes and ignore indirect effects on taxpayers of other proposed changes in the tax code. If you want to know much poorer you will be with a given income as a result of having to pay taxes, that is the fact that matters.

On the other hand, if you want to know how much poorer the country as a whole will be as a result of their plans, the marginal rate may be more important. It tells you how much you will be able to keep of each additional dollar you earn. That is one of the things that affects your decision, and other people's decision, of how hard to work at doing things that they can paid for, what quantity of goods and services to produce. It's also one of the things that affects the decision of how much effort to put into avoiding taxes, whether in legal or illegal ways.

If the point is not obvious, consider a very simple and highly graduated tax system. The rate is 0% on the first $40,000, 100% on everything above that. Faced with that set of rates, most people now earning more than $40,000 would cut back by working fewer hours, taking longer vacations, accepting pleasanter jobs with lower wages, or in any of a variety of ways reducing their income to $40,000. The only reasons to earn more than that are that you like contributing money to the government or that you enjoy the work enough to do it even when you are no longer being paid for it.

Everyone currently earning $40,000 or less and some people now earning more than that would pay less in taxes under that system than under a more conventional set of rates. But the country as a whole would be much worse off, because we would be producing and consuming a lot less. And, of course, the government would be collecting very little in taxes.

The same holds for less extreme versions. High marginal rates give taxpayers an incentive to substitute leisure for income even when the value of what they could produce is more than the value to them of the leisure, since they are only getting part of that value. That is a part of what economists refer to as the dead weight loss due to taxation—a cost to the taxpayer that is not matched by revenue to the government.

How does Obama manage to lower average rates while raising marginal rates—in some cases, according to the Tax Foundation, to over 50%? He does it by lowering taxes at the low end of the income scale—to well below zero.

If, using invented numbers to explain the logic of the situation, a taxpayer with zero income receives $10,000 from the government and a taxpayer making $20,000 receives and owes nothing, then raising your income from zero to $20,000 makes you only $10,000 better off, corresponding to a marginal rate of 50%. And if you only start paying taxes at $20,000, then the rate above that has to be higher than if you started at (say) $10,000 in order to bring in the same amount of money from a taxpayer making $30,000.

Some readers may find a graphical explanation of the point useful. The figure shows two different tax systems, each in the form of a graph of after tax income as a function of before tax income. The red line is a flat rate tax; everyone pays the same fraction of his income. The blue line is a flat rate tax plus a demogrant, meaning that everyone starts at income zero with a fixed amount of money from the government and pays a fixed fraction of each additional dollar of income to the government. As you can see, everyone on the graph ends up with at least as much money after taxes under the blue system.

The slope of the blue line is lower; for each additional dollar you earn your after tax income goes up by less than it does on the red line. That corresponds to a higher marginal rate. So your incentive to earn income is less under the blue system.

Everyone is paying less under the blue system, so the government is collecting less money. But it is collecting it in a way that has a larger negative effect, a greater excess burden aka deadweight cost, on the total amount that taxpayers choose to earn.

[I have focused on Obama's proposal because it is easier to explain its logic, but according to the Tax Foundation both plans raise marginal rates for many middle income taxpayers.]