No, you really don't. The following isn't true:

> But in order to arbitrage this, you have to be willing to pay women and men differently.

A very simple way to arbitrage it without discriminating is to set your wages somewhere between what others pay men and women. Women will flock to you, as you pay better than elsewhere, while men will tend to leave to the discriminating jobs. You pay everyone the same, but the result is your cost in wages is lower than your competitors'.