I often hear statistics about the inequity of income distribution, either in terms of nations or people within nations. The statistics quoted are typically of the form "The top X% of the people (or countries) have Y% of the income", where X is small and Y is large. It is assumed that if this is true, the income distribution must be inequitable.

I am not convinced that this statistic alone proves what it is said to. So, I decided to devise an income distribution that seems equitable from a different measurement, yet also has the property described above.

I am suggesting that my model is either comparable to income distribution with a single country, or when comparing between countries which have been normalized for population. It can be extended to compare people in different countries by considering that in a particular country have income distributions based on the overall income (GDP/GNP) of their country.

I modeled a population of 1296 individuals, assigning each an "income rank" from 0 to 20, with frequencies according to the possible sums of 4 six-sided dice (but numbered from 0 to 5 instead of 1 to 6). An individual's income is actually the square of the income number, which turns a symmetrical "bell" curve into one with a larger right end.

In the first graph, the X axis corresponds to income -- the one person in the simulation with no income is at 0, the one person with the highest income is at 100 -- and the Y axis corresponds to the fraction of people who have that income level. The peak of this curve is at around 25% of the income of the richest (highest income) individual. In fact, the majority of people have an income between 20% and 40% as large as the richest person, which is a whole lot more fair than the American economy actually is. (How many people make 20%-40% as much as Bill Gates?)

In the second graph, the X axis corresponds to the percentile of the population, and the Y axis corresponds to the percentile of the income. Thus, you see that in this simulation that the lower 50% of the population make only 25% of the income, the upper 50% of people make 75% of the income, and that the last 10% make 30% of the income. These are all very much like figures quoted to show that income distribution is woefully skewed towards a few rich individuals.

But we already decided from the first graph that this was a reasonably fair distribution of income. So, I conclude that a statistic of the form "X% of the population makes (only) Y% of the income" is not enough to prove that there is a gross imbalance in income.

I don't wish to claim that there is no problem with income or wealth distribution in the US or in the world, or that this model actually reflects reality, but only that the oft-quoted statistic does not, on its own, demonstrate much.