Monday, July 14, 2008

Why Top Earners Earn More

I've always been fascinated with reports on how the top 1% or 10% of people earn as much as the bottom 10% or 50%. I don't see how this is news.

If you take 100 people, and each earns $1, $2, $3, ... $100, i.e. a perfectly flat distribution, then the top earner earns as much as the bottom 13. The top 10 earn as much the bottom 44.

This is because the top earner earns 100 times what the bottom one does. If the top earner earns only 5 times what the bottom one does, i.e. the salaries go from $100 to $500 in steps of $4 (and change), then the top earner earns as much as the bottom 4, and the top 10 as much as the bottom 29.

This assumes a flat distribution. With a natural bell curve, we end up somewhere back to something that looks more like the first case: the top earner is going to earn more than a boat load of people at the bottom. This makes sense.

This doesn't sit well with a lot of people. Either it's because the top earner is presumed to have acquired his wealth/income through unfairly distributed luck, childbirth, or access to resources, or because the top earner should be paying more to help society based on his income.

If everyone paid 10% of his income to taxes, then the top earner is paying 100, or 5, times more than the lowest earner. More is demanded, because even after this payment the richest should be able to afford more. Presumably, this more isn't so much so that, after paying, the richest earner takes home the same amount as the poorest.

So a "fair" amount is enough so that less well-to-do, less lucky, or less hard working people feel that the rich person has contributed more in both absolute and percentage terms, but not so much so that the rich person throws up his hands and says "why bother?" This "fair" amount is going to leave the rich person still richer than anyone else, by several multiples.

So if the highest earning person earns XXX% more than the lowest, or earns as much as X number of lowest earning people, does that mean that something is wrong? Is our goal to make the income of the highest and lowest earners as close as possible? Or to make the life of the lowest earners as good as possible?

Yehuda
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