**The Zeros Tax; a Modest Proposal**

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 I will be proportional to I^(-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 99

^{th}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 - (N - k(N+D))*(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.

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.

Of course you can 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, as Friedman recommended. 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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