> Good teachers and good nannies aren't easier to replace than good carpenters or construction workers. But since many men who are in charge of setting salaries don't understand that they aren't as well paid.
I'm not sure teachers and nannies are good examples. Public school teachers are largely unionized which would eliminate differences in pay between men and women. And many nannies are effectively small business people who set their own rates.
Being unionized doesn't mean that pay is non-negotiable or anything of the sort. Yes, the union typically establishes a baseline pay based on experience, but individuals can still negotiate their own wages.