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Comment by tunesmith | Hacker News Reader

I got interested in the utility of money a while back and how the "value" of money is roughly logarithmic as it goes up. I found a couple of thought experiments regarding a "logarithmic flat tax". Anyway, going by that I think it's about right - it might still be a little bit high, though. Depending on how you calculate it those plans can be configured so that he should have paid more in the 35-40% range.

Basically, you take revenue, divide it by the poverty level (he's got six kids, so around $45k - $50k), take the log base 10, and multiply by some constant that would be the same for everyone to match the government spending level - that constant these days is probably around 9 or 10. The result is your fair tax rate.

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Do you mean "fair" in the sense that it tries to be equally painful for everyone?

That seems like a reasonable interpretation of fair.

It taxes an equal amount of utility-of-money, I suppose.

Sounds like reasonable policy but incredibly obtuse. All taxpayers should be able to calculate and file their own taxes. The more complicated the easier to game and manipulate.

I'll go as far as to say simplicity should be the driving motivation, not equality.

The proposed system seems a whole lot simpler than the existing one to me.

It's implemented as a literal table lookup anyway, so it wouldn't be any different from the taxpayer's standpoint.

This proposal, given it can be described in a single HN post, is vastly simpler than the present tax code. It would similarly be trivial to make a calculator for this and present it on the IRS site for those who don't feel like calculating it.

https://en.wikipedia.org/wiki/Marginal_utility#Diminishing_m...

Interesting.

Can you add a little detail, perhaps a formula?

Do you mean that if someone earns R, they pay $C*log10(R/P), where P is some poverty level for them and C is a constant around 9?

Yeah. It's a bit simple - like, we're not going down to infinite negative income tax for people below poverty, just assume zero tax paid for them.

To find C, you have to sum up the log10(R/P) for everyone (including corporations) in the nation and divide that into what the government needs. There's various ways to calculate what the government needs, perhaps you separate FICA and payroll tax income entirely if you keep that, or perhaps you just look at entire Federal spending, I believe around 3.8 trillion.

But to sum up the log10(R/P), you need income distribution data. Someone else did that very roughly with a spreadsheet, I haven't tried it myself. A few years ago when they did that, they figured 3.7 trillion for spending, and C was something like 8.86.

C would also be a bit higher if you were also trying to pay down the debt over a period of time.

Unfortunately, I don't understand the logic behind this. I would have thought that a flat tax in terms of utility would solve for the amount of taxes T in log10(R/P) - log10((R-T)/P) = C for some constant C across the population. That would correspond to taxing everyone an equal amount of utility, assuming a logarithmic model of utility.

If the tax itself is proportional to the utility function, that has the effect of taking much less utility from people with greater R. I'm also unclear on how your C works out. The largest company in the world makes less than $1 trillion per year, so even if P is $1, log10(R/P) is bounded above by 12. Given a US budget of several trillion USD, that seems to make C multiple orders of magnitude bigger.

Sorry if I'm missing something. That was my original reason for asking for a formula above.

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