A Logical Tax Rate
The question is then what form the tax rate function should be. For context, let’s see what the current real tax rate is as a function of taxable income. Figure 1 shows this information for married couple filing jointly on a logarithmic scale to help highlight the overall shape. We can see that income taxed up to $10,000 is taxed at a flat rate of ten percent, with higher rates slowing creeping up over the middle income brackets and then increasing once you get above $100k before tapping off for the very wealthy. This kind of trend is known as a sigmoid or S-shape curve. As such we, can easily approximate its current shape with many fewer variables than our tax brackets.
I’ve written out the framework of our new continuous function in equation 2 below. We’re down to four variables now instead of the 14 used to define our brackets. R0 and Rm are the minimum and maximum tax rates across the entire range of incomes, while H is the income that pays half the difference between them. The final variable, m, determines how sharp of a transition it is from R0 to Rm. These allow us to create a very good simulacrum of the actual 2021 tax rates, as shown in the following figure. Some of the behavior toward the middle will be different, either plus or minus a few fractions of a percent, but on the whole will provide the same result.
The criticism that would likely be levied against this new method is that it is too complicated of a calculation for the average American do make. This may be correct, but it ignores the fact that the current tax instructions include a tax table with all the numbers up to $100,000 printed out and that it is trivial to implement on a website. So long as the math is hidden, no one will even know the difference. And in return, we have a much simpler system to amend and update every year. At least in one small way.