If the surplus of men over women is temporary, say, because of war or upheaval, then the surplus usually leads to an even greater incentive to prostitution.
As permanent residents in a location, men are potential participants in both the marriage market and the sex markets, whereas if they're visitors, only the latter market is generally available and the supply of prostitutes and their incomes rise. The authors cite examples from 12th century crusaders to modern sex tourists.
The model also predicts that how much a woman damages her chances to marry by becoming a prostitute depends on how likely it is that she'll be exposed as one.
The likelihood shrinks if the woman leaves home and migrates to a different part of the country or to a different country altogether. This would also explain why foreign prostitutes are likely to be cheaper than domestic ones.
More generally, the abundance of foreign prostitutes shouldn't come as a surprise. Immigrants generally have difficulty finding employment and, except at the high end of the scale, prostitution does not place much of a premium on language skills. As in other parts of the economy, globalization is controversial and is one reason the number of women trafficked for sexual purposes is exaggerated. (It is considerably smaller than the number of people trafficked for nonsexual labor.)
There are good reasons -- from academic studies to the sheer ubiquity of prostitutes -- to believe that this heinous practice is relatively isolated and that only a small fraction of prostitutes are coerced into prostitution.
One last prediction the model makes is that the income differential paid to prostitutes will rise with the status the culture accords wives.
That is, if wives are valued highly, would-be prostitutes are giving up a lot by becoming prostitutes and will require more money to do so. And if wives have few privileges, would-be prostitutes aren't giving up much to become prostitutes and thus need less inducement to do so.
Cultural tolerance, of course, is a determinant not only of the income differential but also of the number of women who become prostitutes. Compare, for example, Thailand and Afghanistan.
Like any statistical model, this one ignores the diversity of real people and the complexities of love and pleasure, changing social mores, et cetera. Still, once all its equations have been solved, a simple fact remains: Most women enter prostitution for the money.
This being so, legalizing it, regulating it (strictly enforcing laws against pimping, child prostitution, public nuisance and so forth) and improving the economic prospects for women seem to me a greatly preferable approach to it than moralistic denunciation.
Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.