So, this piece (here) from GSB news, implies that Garry Becker asks: "Will Women Get Bigger Paychecks Than Men?". If you read carefully the article, Garry Becker never explicitly answers positively. But if he actually thinks so, he is plainly wrong.
Some background for my argument: As all studies show, the average IQ of men and women is (almost) the same, but their distributions are different. Men's IQ has a higher variance than women's. To put simply, there are more "limited" men than "limited" women but there are also more smart men than smart women (this phenomenon explains why there are more men than women in high-end science and engineering positions, as poor Lawrence Summers dared to suggest).
See a visualisation of the different variance here:
Now, in modern information-based economies, jobs that are IQ-intensive tend to pay increasingly much more. At the same time the relevant pay-size of these IQ-intensive jobs (banking, IT, senior management, high-end sciences) is growing compared to non-IQ-intensive sectors (like music, sports etc.). Moreover, the companies or the "invisible hand" in these IQ-intensive sectors have developed very efficient intelligence screening mechanisms. The effect of that is a trend that smarter people are getting higher and higher payments.
Given also that the IQ-payment relationship is not linear but rather exponential and that it is floored on the downside (basic salary) but uncapped on the upside (millions), it is clear that men will always have a higher average payment than women.
In this analysis I do not discuss other factors, like the fact that the testosteronized male brains drive men, more than women, to compete hard for power and status -which usually relates to higher payments.
*All the above assume:
-similar employment rates for the two sexes
-continuation of the trend in modern economies where IQ matters more and more
-no material discriminating intervention from the state
-no material genetic engineering alteration