Marginal Tax Rate vs Effective Tax Rate

 

Slow Hand

You want a man with a slow hand
You want a lover with an easy touch
You want somebody who will spend some time
Not come and go in a heated rush

Slow and steady wins the race.

I got especially upset when I heard one of my favorite podcasts, Planet Money Indicator, repeat the falsehood that the tax rate once was as high as 91%. I know that I took macroeconomics more than 50 years ago, but it was math then and it should still be math. Saying the tax rate is 91% is confusing speed with acceleration. The marginal tax rate, second derivative or the rate of change of change for the math geeks in the crowd, might be 91%, but the effective tax rate, the first derivative, the rate of change, was no where near this. Talking Barbie might be right, Math is Hard, but just because it is hard doesn’t mean that it is not true.

If the median, what a statistician would say is normal, tax rate is 20%, then for any normal tax rate, the highest tax rate should be about twice that amount and the lowest tax rate should be about half that amount. If the median tax rate is 20%, then the highest effective tax rate should be 40% and the lowest effective tax rate should be 0%. But the highest marginal tax rate is not constrained to be 40%. It can be as high as 100% if the size of the brackets (increments) are equal and infinite. Math is hard, and it is useful to approximate a complex function such as a tax rate by a series of increments, brackets. The increments should be as small as possible for the approximation to be useful, but they still must be equal.

If the number of brackets is infinite, for a progressive tax rate, which has a first derivative of x% then the second derivative of the highest tax bracket can be 100%. The smaller the number of brackets, the lower that the second derivative appears to be.

Lowering of the marginal tax rate, should have been accompanied by dividing the intervals to highest income bracket into equal amounts.  If the size of the brackets are not equal,  the math is such that the approximation will not work.

I don’t want to know the highest marginal tax rate. I want equal tax brackets. The highest effective tax rate should be twice the median tax rate. The size of the brackets should be equal. When Maverick said in Top Gun, “I feel the need for speed,” he did not mean “I feel the need for acceleration.” The human body does not have a constraint on its maximum speed, but it does have a constraint on its maximum acceleration, G- force. Don’t confuse speed with acceleration… you want a slow hand.