Tax Brackets

Won't Get Fooled Again

Then I'll get on my knees and pray

We don't get fooled again, no, no

Have we been fooled in the tax rates?

A  change in the range of the brackets in the Tax Cuts and Jobs Act, TCJA, without changing the marginal rates in the TCJA, would lower the tax rate for most incomes. Incomes are not equal, but are distributed according to an exponential function.  Taxes should be expected to follow that same exponential function. The effective, not the marginal, tax rate is taxes divided by the income.  A flat tax rate assumes that all incomes are equal.  So country to popular wisdom, a flat tax is a communistic approach, not a free market approach.

Math is hard.  The Orange Menace’s son made the statement in the past that raising the average (i.e. mean) wealth raises everyone’s wealth because that is how math works.  It prompted a blog post from me https://dbeagan.blogspot.com/2018/08/wonderful-world-dont-know-much-about.html, because unless DJT Jr. was either hungover again in class at UPenn’s Wharton Business School and did not hear correctly,  this is different from the math that I learned, and used, as a graduate student down the street at UPenn’s Towne School of Engineering.  The statement is definitely false.  Whether it is false in a effort to deceive, or false because the speaker was ignorant, I can’t say, but the apple does not fall far from the tree.  The problem is that “Math is Hard” and people get the terms wrong, and people deal with linear equations better than with non-linear equations.

The tax code is one place where the difference between a linear and non-linear equation has dire consequences.  Because a nonlinear equation is hard to compute, when dealing with these equations, it is common to approximate the nonlinear function by a series of linear functions.  But you have to approximate correctly or it will not work correctly.

When approximating an exponential association, such as the tax rate, it is common to use a series of linear equations (e.g. tax brackets).  But math has rules. If you are approximating an exponential association, the range of those linear equations MUST BE EQUAL.  For example, if as in the TCJA, the top bracket is incomes over $539,000 ( $628,300 if married and filing jointly), then the range of the brackets should NOT be variable, but should be equal to the top range divided by the number of brackets minus one ( $89,833, or $104,717 if married and filing jointly).

 

The implication is that the constant term in the linear equation is lower for each tax bracket in the TCJA than it should be. I would like to assume that this was done from ignorance.  And this is the same ignorance that is shown when people are surprised that doubling the diameter of a cake quadruples the amount of a cake, not realizing the amount of a cake is a non-linear function of the diameter of a cake. But  this was done by the same “fine” individuals who also proposed the Texas Abortion Law, which was carefully crafted so that no government officials could be sued, and it has been going on for the last 40 years.   I have to conclude that the taxpayer is Lou Costello and the TCJA Tax Code authors are Bud Abbott, and those authors are taking advantage of poor Lou again.  https://www.youtube.com/watch?v=9udNrOh5DyA.

As shown in the figure above, computing tax brackets correctly will lower the effective tax rate for all incomes, but the lowering is proportionally larger for lower incomes.  This may mean also mean that marginal tax rates have to be raised in order to raise the same amount of total tax revenue, but  there are ways to do this that are  mathematically correct, and hopefully we have learned from our mistakes and won't get fooled again.