Income doesn’t fit a bell curve, at least not at the high end. The bottom 5% of U.S. households have incomes below \$10,000, the median U.S. household has an income of \$67,463, the top 1% earn \$504,000 a year, while Elon Musk sold at least \$4 billion in stock this year . Assuming about 122 million households in the U.S., if household income fit a bell curve, it would look like this:

\$10,000 = -1.66 SD (standard deviation) (bottom 5% of bell curve)

\$67,463 = 0 SD (middle of bell curve)

\$504,000 = +2.33 SD (top 1% of bell curve)

\$4 billion = +5.66 SD (top one in 122 million on bell curve)

But as we can see, most of the data points are nowhere near the line of best fit:

To make the distribution more normal (which is useful for regression analysis), scientists often take the natural log of income instead of income itself. If we do this, we get the following:

9.21 = -1.66 SD (bottom 5% of bell curve)

11.12 = 0 SD (middle of bell curve)

13.13 = +2.33 SD (top 1% of bell curve)

22.1 = +5.66 SD (top one in 122 million on the bell curve)

When we use the natural log of income, it relates to normalized Z scores in a much more linear way.

Perhaps Elizabeth Warren or some other left-wing politician could propose a tax bill where people could keep 100% of their household income, as long as it didn’t exceed the natural log multiplied by \$10,000. That way the middle class and below would not have to pay anything, but the top 1% could only keep \$130,000 of their \$504,000 a year, and Elon Musk could only keep about \$220,000 of his \$4 billion stock sale.

Of course such a law would probably destroy the economy but at least Marxists would finally have an intelligent answer to the question “what’s my fair share?” when they demand rich folks pay it.

Your fair share is how much the bell curve says it should be. The bell curve is natural law.