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Lee Clarke
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Introduction to Sociology Everyone must log into sakai.rutgers.edu
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The L-Curve
©David Chandler
Through teaching introductory astronomy over the years I have come to realize that most people cannot distinguish the relative sizes of millions and billions. If you're not quite sure how to picture a billion, as compared to a million, CLICK HERE.
Big numbers aren't just for astronomers. If you can't understand big numbers you can't understand the economy and you will be at the mercy of propaganda mills when you walk into the voting booth.
Consider this picture:
The income distribution of the United States
Partial Graph
of the U.S. Income Distribution.
The graph represents the population
of the United States lined up,
left to right, according to
income. The height of the graph
at any point is the height of
a stack of $100 bills equaling
that person's income.
Imagine the population of the United States stretched across a football field in order of income, from poorest to richest. Now imagine a stack of $100 bills representing each person's income. (A 1 inch stack of $100 bills is $25,000.) The red line represents the heights of those stacks compared to a football field. I call this graph the "L-Curve."
The red line in the first picture is the beginning of the U. S. income distribution. On the scale of the football field the line slopes gradually from zero on the left to less than 2 inches high at the 50 yard line ($39,000), to about 4 inches high at the 95 yard line ($132,000). On this scale the entire graph is less than one pixel high, up to this point. It is not until you are well past the 99th yard line that you hit the $million mark: a stack of $100 bills 40 inches high. There were over 144,000 people who turned in IRS returns in 1997 with adjusted gross incomes of $1 million or more.
It is impossible to show the whole graph meaningfully on a single diagram.
Partial Graph
of the U.S. Income Distribution.
This is a continuation of the
previous graph. On the scale
of this picture each pixel (dot)
represents 250 meters (273 yards),
so the football field is invisible.
Here is the top of the "L-Curve". Ordinary millionaires don't even show up! (One pixel on the vertical scale of this picture represents $250 million.) $1 billion is a a stack of $100 bills 1-kilometer (0.6 miles) high. Bill Gates' wealth increased from about $50 billion to $100 billion in one year recently, so in that year he had an income of at least $50 billion*. Bill Gates, personally, is not the point. He is one of (currently) hundreds of billionaires in this country who happens to have particularly high name recognition.
The graph illustrated in these two pictures represents income, not wealth. The distribution of wealth is even more skewed. Quoting from a not-yet-published manuscript by economist David Schweickart,
If we divided the income of the U.S. into thirds, we find that the top ten percent of the population gets a third, the next thirty percent gets another third, and the bottom sixty percent get the last third. If we divide the wealth of the U.S. into thirds, we find that the top one percent own a third, the next nine percent own another third, and the bottom ninety percent divide up the rest. (Actually, these percentages are slightly out of date. The top one percent are now estimated to own between forty and fifty percent of the nation's wealth.)