Sunday, November 20, 2011

Birthday Announcement and Modest Proposal: Zeros Taxation.

I interrupt this blogging of “Underfables” for an announcement and a modest proposal.

The announcement is:
Today, November 20, 2011, is my 54th birthday. 

That means that, as of today, I have survived:
54*365 days + 13 leap-days  =  19,723 days
which equals
19,723 * 24  =  473,352  hours
473,352 * 60  = 28,401,120 minutes
28,401,120 * 60 = 1,704,067,200 seconds.

One point seven zero gigaseconds old! Time sure flies.

I am having a minimalist birthday today. I figure that I don’t have to do anything to turn 54, other than survive the day, so I’m taking it easy. All I plan is to mail some letters and share a cake with wife and daughter. No big birthday party; I hate the stress. I’d rather treat a birthday as a milestone rather than as a deadline.

About those letters; they contain small presents for friends. I figure that I’m old enough, and internally rich enough, to give on my birthdays rather than get.  It’s a matter of self-expression. The presents in question are small enough to mail, but original enough that I am sure that my friends have never seen the like in their lives. They’ll get “tribands”, made by linking three hairbands in a Borromian link. A triband is a curious item; I’ve seen them as topological diagrams but never before as a physical object to play with. They are fun toys,  yet they also have unique practical uses. I’ll discuss them on this blog after finishing Underfables, once I figure out how to add pictures and video links.

As further self-expression, I here give you, dear reader, the following Modest Proposal: the Logarithmically Flat Tax, a.k.a. Zeros Taxation.


The distribution of incomes in America is a hybrid of Gaussian and power-law. For low to moderately-high incomes the distribution is  nearly Gaussian; so it is as if people were adding and losing sums of income, at random. But the far right tail of the distribution is “fat” - that is, extremely high values occur more often than you’d expect. For the right tail the distribution resembles a power law; that is, the  number of people with income X will be proportional to X^(-p), where p is the power. Here it is as if the extremely rich got that way by multiplying and dividing their income by factors, at random,  instead of adding and subtracting terms, at random. And this  makes sense, given that the upper end of the economy is dominated by finance, where compound interest rules. The 99% adds and subtracts their money; the 1% multiplies and divides their money.

I therefore propose the following hybrid tax code: for up to the 99th percentile the tax shall be flat proportional after deductions; for the top percentile the tax shall let the rich retain an after-tax income proportional to the 8/9th power of their pre-tax income.

Mathematically, the tax code is:
for X = income, and N = 99th percentile of income;
if X < N, then tax = k * (X - D),   where k is the flat proportional tax rate and D is deductions;
if X > N, then tax =  X  -  K * X^(8/9),  where K is calculated to match the tax curves where they meet, at N.

Therefore K equals  (1- k)*N^(1/9) - k*D*N^(-8/9) .  You can also say that tax =  X - ((1-k)N - kD)*(X/N)^(8/9)  ;  so that the 1% can in effect “multiplicatively deduct log(N) zeros”, and pay only one out of every nine zeros thereafter. It’s a logarithmically flat tax.

The dividing line between proportional and 8/9th power taxation is given by a percentile rather than a prestated amount, and hence is stable under inflation and other changes.

You can of course change 8/9ths for other powers.

Note that this leaves a taxpayer in the 99% an after-tax income of (1-k)*X + kD. For those with an income below D, this is a negative  income tax; an incentive-preserving substitute for welfare, recommended by Milton Friedman. But also note that it leaves a taxpayer in the 1% an after-tax income of K * X^(8/9); their income rises by the 8/9th power. Thus a billionaire will make “only” K hundred million dollars.

I therefore call this a “zeros tax”; the government takes one out of every nine zeros.

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