Thursday, October 10, 2013

The Zeros Tax; a Modest Proposal

             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 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 - (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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