Mark Perry and Andrew Biggs argue in the Wall Street Journal that

These gender-disparity claims [the claims that women are paid 23% less than men for the same work] are also economically illogical. If women were paid 77 cents on the dollar, a profit-oriented firm could dramatically cut labor costs by replacing male employees with females. Progressives assume that businesses nickel-and-dime suppliers, customers, consultants, anyone with whom they come into contact — yet ignore a great opportunity to reduce wages by 23% [by hiring women instead of men].

Well, first of all, even if we take the gender disparity claims at face value, this doesn’t add up to an opportunity to reduce wages by 23%. Only about half the work force is female, so the average firm, if it replaced all of its men with women earning 23% less, would reduce its wage bill by only about 11.5%.

Beyond that, the Perry/Biggs argument appears to founder on the observation that lazy and incompetent managers do in fact manage to ignore profit opportunities all the time. Why, then, is it so hard to imagine that they’re ignoring this one?

Fortunately, I’m here to fill the gap —- by figuring out just how big a profit opportunity we’re talking about.

Continuing to take the alleged gender disparity at face value, a typical firm pays about 77 cents to female employees for every dollar it pays to males. (This uses the observation that there are roughly equal numbers of males and females in the work force.) This adds up to a total wage bill of $1.77 per dollar paid to a male employee

Next it’s helpful to know that, as a general rule of thumb, wages soak up about 2/3 of company revenue. The remaining third is paid out to bondholders and stockholders.

So for every $1.77 paid to the workers, about half that much — call it 88 cents — is paid to the capitalists. Some quick Googling (and a more careful Googler in the audience might want to refine this calculation) suggests that, in the U.S. (and hence at the average American firm), about 40% of that 88 cents goes to bondholders, which means the stockholders get about 53 cents.

Now: What about that profit opportunity? If you replace your male workers with females, you save 23 cents per dollar paid to a male. That 23 cents, of course, goes to the stockholders. (Where else could it go?). The return on your company’s stock, and hence the value of that stock, just went up from 53 cents to 53 + 23 = 76 cents — an increase of about 43%.

So, yes, lazy and incompetent managers overlook small profit opportunities all the time. But do they overlook opportunities to increase their companies’ share prices by a whopping 43%? That pretty much strains credulity to the breaking point — and makes the gender disparity claims just about as implausible as Perry and Biggs say they are.