Intuiting Large Numbers: A Facebook Exchange

I recently had an interesting exchange with a FaceBook friend, a reasonable person with political views very different from mine. He posted something to the effect that he didn't think a free market society could produce a middle class, and supported it with the claim that at the beginning of the 20th century one or two dozen families held most of the wealth. Pretty clearly, judging by past exchanges, his view was that it was the rise of labor unions that changed that situation. I do not know if he had actual data on the distribution of wealth; if he did, I suspect that "wealth" was limited to forms of wealth, such as stocks and bonds, held mainly by wealthy people. 

What is more relevant is the distribution of income, so I asked if he had data on that. I also suggested that he was being misled by the inability of humans to intuit large numbers. If a hundred people have incomes of a million dollars a year and a hundred million have incomes of a thousand dollars a year, it looks as though the hundred have most of the income. Simple arithmetic demonstrates that they actually have just under a thousandth of it.

He responded with a graph showing the share of income going to the top one percent, .1 percent, and .01 percent of the population. It did not go back quite to 1900, but extrapolating it the share of the top .01 percent then looked to be about 5%. 

The top .01 percent would be about 10,000 people, say 2,000 households. So even after expanding his one or two dozen families by two orders of magnitude, their share of income was still only about one twentieth of the total, making it difficult to see how their existence could have prevented a middle class from coming into existence.

To put the point a little differently ...  . From 1900 to 1905, real GDP per capita increased by about ten percent. So if all of the income of the top 10,000 people in 1900 had been transferred to the rest of the population, their gain would have been equivalent to two or three years of economic growth. If the existence of the rich made the rest of the population too poor to have a middle class in 1900, the problem should have been solved by 1903.

Which I think supports my original point about intuiting large numbers.