Chalk this up as another example of the free market not working.
It turns out, there is a mathematically fairest distribution of salaries among any company's employees. And, it turns out, the salaries of 90 to 95% of employees in US companies actually follow the theoretically fairest distribution.
Guess which 5% to 10% don't?
Did you just guess that it's the highest-paid 5 to 10 percent whose salaries don't follow the fairest distribution?
And did you guess that those who deviate from the fairest distribution do so on the overpaid side instead of the underpaid side?
No prizes for getting this right, except the joy of working for a boss that isn't earn his keep.
But that's not really what's surprising. Yes, some people (in any company) deserve to be paid more. Yes, often (perhaps always) the CEO's are among those favored few. And yes, most Americans recognize that CEO's are paid way too much.
It's the obscene magnitude of just how much more they're getting than they're really worth that really takes your breath away.
Chief executives in 35 of the top Fortune 500 companies were overpaid by about 129 times their "ideal salaries" in 2008, according to a new type of theoretical analysis proposed by a Purdue University researcher to determine fair CEO compensation.
Let me put it this way: if a minimum wage waitress was as overpaid as much our top CEO's, her salary would be $1,945,320 per year.
Technical stuff follows.
The utility of money is not linear: the more you have, the less useful any given amount becomes. Having a million would be great. Having a second million, once you already have the first? Not so much. In fact, studies have shown that the utility of money varies by the logarithm of the amount.
If everyone is paid the same, there is little incentive to do better, or even to do well. Productivity suffers and the company suffers. (This is the trap of unrestrained socialism). If everyone is paid the minimum wage except the CEO, who gets all the rest, there is not only little incentive to to better, but there is also a good reason to quit and work for someone else. This is the trap of unrestrained capitalism.
We've all had a gut feeling that CEO salaries have been unfair for a long time. But what is "unfairness" in an economic sense? And isn't a free market supposed to prevent that from happening?
A market only functions where there are multiple potential buyers for every seller, and multiple potential sellers for every buyer. If that's not the case, the "free" market can become skewed, distorted, and even manipulated. If there's only one seller, for example, you have a monopoly: the seller doesn't charge what the market will bear, he charges whatever he damn well wants.
That's essentially the situation with CEO's. The market is very thinly traded -- meaning that there are very few companies at any one time actually looking to hire a CEO, and there are even fewer CEO's with a track record who are looking for a job at any one time. Hence normal market forces don't work, because there is no real market.
Ideally, one might imagine there should be a classic "normal" distribution of salaries: the bell-shaped curve with a lot of people in the middle and a few at the tail ends of high pay and low pay. However, because the utility of money is logarithmic, this isn't really the case: the bell-shaped curve exists, but it's not your salary that's on the x-axis, it's the logarithm of your salary. This is called a "lognormal" distribution.
The lognormal distribution is useful in a lot of ways, and one interesting way it's useful is in the study of entropy. Entropy is a measure of the disorder in a thermodynamic system, or of uncertainly in an information system. What the author of this study, Venkat Venkatasubramanian, has done is to apply the concept of entropy to economics, by formally equating entropy to the concept of economic fairness.
And it turns out that for most workers, that 90 to 95%, salaries do indeed fall on a lognormal distribution of maximal fairness. For top CEO's, they usually don't. Depending on the size of the company and the range of employee salaries, the lognormal distribution implies that a fair salary for the top person in any company should be roughly 8 to 16 times the salary of the lowest paid person.
"It's interesting to note that Warren Buffett, CEO of Berkshire Hathaway and an outspoken critic of executive pay excesses, drew an annual salary of $200,000 in 2008," Venkatasubramanian said. "This makes his pay ratio 8-to-1, assuming a minimum employee salary of $25,000 per year, which fits the ideal benchmark estimate for fair CEO pay almost exactly. Mr. Buffett's instincts about fairness seem to be amazingly accurate. The top pay set by Mr. Feinberg for the AIG executives is almost exactly the amount recommended by the new theory."
In the US, CEO salaries used to be about 20 times the lowest-paid employees back in the 1960's. In this decade, they have been as high as 300. And for Fortune 500 companies it's even worse: CEO's are taking home salaries that are very likely 1000 or even 2000 times those of their lowest paid employees.
Entropy theory shows not only that this is unfair, it shows just how grossly unfair it is.
Links:
News article here.
Abstract here.
Full paper: Entropy 2009, 11(4), 766-781; doi:10.3390/e11040766. For a copy (pdf, 222 KB) click here.