This column is about racial discrimination. But more importantly, it's about how a little arithmetic can go a long way toward settling a controversy.

The controversy I have in mind is, Why do blacks earn less than whites do? The easiest hypothesis is that the employers discriminate. Some commentators have attempted to dismiss that hypothesis on the grounds that discrimination is costly (because it entails a willingness to pay premium wages for white workers) and therefore unattractive to employers with an eye on the bottom line.

But that kind of dismissal is too glib, because it is not based on any estimate of how much it costs to discriminate. Without that estimate, we can't even begin to think about whether the cost is high enough to make much difference.

Iwant to provide the missing estimate, starting with a few assumptions that are reasonably commensurate with reality. First, I'll suppose that blacks constitute 10 percent of the work force. Second, I'll suppose that blacks, because of discrimination, earn 60 percent of what whites earn. Third, I'll make an assumption (again guided by real-world observations) about what happens to corporate revenue: I'll assume that for every dollar paid to the workers, a half dollar gets paid to the bondholders and the stockholders collectively--let's say the bondholders and the stockholders each get a quarter.

To make those assumptions more concrete, suppose you're the manager of a corporation that employs one black and nine whites, paying the black $60,000 and the whites $100,000 apiece. That makes your total wage bill $960,000. The bondholders and the stockholders each receive one fourth as much as the workers, thus each group gets $240,000. So your payouts look like this:

(The specific numbers in the preceding paragraph don't matter. If you assume 100 employees instead of 10, or wages of $6,000 and $10,000 instead of $60,000 and $100,000, the conclusions to follow will remain unaffected.)

Now we can estimate the cost of your discrimination. Notice first that discrimination must be quite common in your industry; otherwise your black worker would have gone elsewhere long ago. That means there are a lot of blacks working for $60,000 in this industry. If you could put aside your racism, you'd fire your nine $100,000 white employees and replace them with some of those $60,000 blacks--cutting your wage bill by $360,000.

Where would the $360,000 in savings go? The same place any corporate savings go--into the pockets of the stockholders, increasing their earnings from $240,000 to $600,000--a 150 percent increase overnight. Your payouts now look like this:

When the return to stockholders rises by 150 percent, so must the price of your company's stock. That's enough to put you on the cover of Time magazine as the financial genius of the century. To continue discriminating is to throw away an opportunity for unprecedented financial success.

In fact, that same opportunity is available to every other corporate manager in the industry as well, and they're rejecting it too (remember that discrimination must be widespread or all blacks would move to nondiscriminatory firms). So in order to believe that discrimination explains the black/white wage differential, you must believe that managers throughout the industry are so blinded by racism that they are willing to throw away a 150 percent gain for their stockholders, and the acclaim of all Wall Street for themselves. Personally, I find that wildly implausible.

That's not an irrefutable disproof that discrimination exists, but it's at least a calculation that needs to be taken seriously. If we had come up with a number like 10 percent rather than 150 percent, it would have been far easier to maintain a belief that employers discriminate.

The figure of 150 percent is based on numerical assumptions that are reasonable but not ironclad. If you juggle those initial assumptions a bit, you'll get a number other than 150 percent coming out at the end, and you might or might not discover a scenario in which discrimination is plausible. (My guess is that you won't, but then again, you and I might have different standards for what's plausible.) Regardless of how that experiment turns out, it's well worth performing. Without some such test, there is simply no way to know whether discrimination is a credible hypothesis.

I f we rule out employer discrimination, there must be some other explanation for the black/white wage differential. Suppose, for example, that there is discrimination not by employers but by customers, who are willing to pay a premium for goods and services produced by white workers. To advocate that theory convincingly, you'd have to estimate the size of the premium and assess whether it's something that consumers would plausibly pay. I invite readers to do their own arithmetic.

Alternative theories posit that blacks earn less because they have fewer marketable skills. Like theories of discrimination, these theories are best judged by quantitative criteria, but now we have to go beyond what can be computed on the back of an envelope and look, for example, at what we can learn from standardized test scores.

According to recent research by Derek Neal of the University of Chicago and William Johnson of the University of Virginia, black/white wage differentials are largely explained by differences in skill levels which are already detectable at an early age. (Richard J. Herrnstein and Charles Murray had previously reported similar findings in their best-selling book The Bell Curve.) To explain those skill differentials, one can try pointing either to training or heredity.

Herrnstein and Murray argued that heredity plays a substantial role, but Neal and Johnson's more recent findings tend to refute that interpretation. For one thing, Neal and Johnson report that the performance gap between blacks and whites is considerably larger for young adults than it is for teen-agers. That's hard to explain if the gap is caused by heredity (why should an inherent difference become larger over time?), but not if it's caused by training (if blacks get inferior schooling, then it's not surprising that the effects are greater after 10 years of schooling than after six).

Much research remains to be done, and is being done, and will be done. All of that research, at least when it is useful, will be quantitative in one way or another. Some of it requires sophisticated techniques and sophisticated measurements. But there are cases--and discrimination is one of them--where the inherent plausibility of a theory can be well tested with nothing more than the back of an envelope and an open mind.