What should the highest income tax bracket rate be?

[TJ in Oregon]

If we're going to have a progressive tax structure, I say we eliminate the bracket system and replace it with a continuous function to determine the rate. I don't think having piecewise discontinuities is a good idea and creates unnecessary distortions, especially when we could just as easily use some other kind of function.

[TJ in Oregon]

Here are a couple plots I just made in Excel. The first is the current US income tax brackets for single filers. The tax rate is shown in black, the income tax paid in red, and the income after the tax in green:



To me this just seems stupid. Why do we need the discontinuities? Was it drawn by someone who never passed high school algebra?

As Wormyguy just pointed out I made a serious mistake in the original version of this. Here is the correct form in which the discontinuities are only in the derivative rather than the function itself. It’s still rather ugly.

 I fit the midpoints from each bracket using the sum of least squares method to an exponential decay function: T=35*[1-exp(-BI)]+A  where 35% is the maximum tax bracket, A = 9.93 and B = 0.0042. The result is shown in the following plot with the same color scheme:



The main reason why I am opposed to a progressive income tax bracket system like the US is that we've created distortions where someone would be financially harmed by getting slightly more income. This isn't limited just to the income tax but is also present in the hard cut-offs for countless government programs. To me it seems like pure sloppiness on the part of our elected officials to allow such discontinities when it only takes like half an hour to eliminate them.

There are still plenty of other programs this statement actually applies to though the income tax is strictly speaking not one of them. I still think we would be better off with a smoother function than that hideous piecewise thing.

 It's not even like this would add any beaurocracy to the process since calculating the income is what takes time and calculating a rate takes roughly ten seconds, ie. no longer than looking it up in a table.

[TJ in Oregon]

Dang! I did all that for nothing then.

Well, in any event that makes it even more unnecessarily complex, though less ridiculous.

Edit: The graphs should be correct now.

[TJ in Oregon]

If we're going to have a progressive tax structure, I say we eliminate the bracket system and replace it with a continuous function to determine the rate. I don't think having piecewise discontinuities is a good idea and creates unnecessary distortions, especially when we could just as easily use some other kind of function.

I've always thought about doing that, but I don't know what the exact effects would be, if any.

People need to use calculus to find out how much tax they owe.

No they wouldn't, just algebra. All you would have to do is type the function into a calculator. No derivatives or integrals would be necessary. The calculation would actually be quicker than the current one.