> that one employer would get all of these great women who are just as productive for a lower price and would take over their market. It only takes two such employers in a market who are competing for those women to get women up to income parity with men.

Yet companies will always want to hire someone for the least possible amount they can - regardless of the manager's personal views.

Two potential employees walk in the door at your hypothetical perfect company. They are perfectly equivalent. One was originally paid $40,000 while the other was paid $55,000 at their previous position. They each want a 10% raise to come to your company. One is a woman, the other is male.

Now you end up paying the woman less than the male, purely because her previous position paid her less. And the cycle continues until eventually you get to some sexist manager back at her first company that thought she wasn't as skilled for some reason or another (apparently).

That's the point I'm trying to make. Your hypothetical situation would not be the panacea to these problems because companies don't offer salaries like that. You're also making the astronomically huge assumption that every person wants to change positions in the first place. Some people like the job they have and stay there for much longer than would be competitively optimal for them.

Systemic sexism is the sexism that manifests in these cycles.