The average woman’s salary is 20 percent below the average man’s. What should we do about this apparent discrimination?

We should profit from it.

If the gender pay gap is real, an all-female company should have a ten percent higher profit margin than competitors who employ half men. Even if the rest of our business ran at cost, we would be one of the most profitable companies, as well as social justice heroes. And if enough employers did the same, women’s salaries would rise and eliminate the gap.

So what prevents millions of people from pursuing this easy path to praise and riches? The answer is that the gender pay gap is not real. Our attempt to profit won’t work. Payscale, a website that aggregates job market compensation data, found that when salaries are controlled for industry, occupation, experience, job title, etc., the supposed 20 percent gap shrinks down to 2.4 percent. Women doing the same job as men earn virtually the same pay.

[Opinion: Every day is Equal Pay Day]

That remaining 2.4 percent gap is still an extra 12 minutes of work per day. Do men work a little more? According to the 2017 American Time Use Survey by the Bureau of Labor Statistics, men indeed reported working an average 20 minutes beyond their 8-hour day, whereas women reported working about 10 minutes less than 8 hours.

Perhaps the discrimination comes not in salaries, where there is no real gap, but in opportunities. Why are there fewer women than men in high-paying, high-level jobs?

Harvard economist Claudia Goldin found that women take jobs with different characteristics, such as tending to avoid round-the-clock availability or preferring certain working hours. So maybe factors like these keep women from even applying to certain jobs. Maybe it is discrimination of opportunity rather than discrimination of pay.

Consider Uber. Uber doesn’t care about gender with hiring or with assigning passengers. Drivers set their own hours and can quit anytime. Thus, the Uber pay gap should be zero. Yet in a recent paper, economists Cody Cook, Rebecca Diamond, Jonathan Hall, John List, and Paul Oyer found that the women driving Uber still earn about 7 percent less than the men. Mostly, that difference is that men drive slightly faster and do more airport runs. It’s neither discrimination in pay nor discrimination in opportunity. It’s just preference. There’s no social injustice here.

Then why do we see so few female executives? If we look only at people who do not require flexible time, commit exclusively to their career, and have whatever other traits accompany pursuit and success in top roles in companies, surely those people should be equally male or female, no?

Actually, no, this is another statistical illusion. It turns out that small differences in averages between men and women can yield enormous differences at the extremes.

For example, in documenting personality differences across genders on standard one-to-five scales, psychologists Yanna Weisberg, Colin DeYoung, and Jacob Hirsh report that the typical woman rates as 3.89 on agreeableness while the typical man rates as 3.65, give or take half a point on each. If we now look at all people who rate 4.5 or higher on agreeableness, we would see almost three times as many kind women as men. And if we look at all people who rate 1.5 or lower, we would see about ten times as many antagonistic men as women.

If aggression ends up being a trait of those who pursue executive jobs, then you can guess what the result will be. Likewise, it probably isn't due to discrimination that more than 90 percent of registered nurses are women.

You’re thinking there’s still an unanswered question. Why do the female-favoring characteristics lead, on aggregate, to lower-paying jobs, while the male-favoring metrics lead to high-paying jobs? Shouldn’t it be random?

The answer could be leverage. Researchers Rong Su, James Rounds, and Patrick Ian Armstrong show that overall, women prefer jobs involving people, while men prefer jobs involving things. But people-orientation does not scale (you can only help so many people one-on-one), so it pays less than thing-orientation.

The gender pay gap is an illusion. Whoever still thinks it is real should go try to make a fortune today.

Philip Z. Maymin is an Associate Professor of Analytics and Finance at the University of Bridgeport Trefz School of Business and an attorney admitted to practice law in California.