My partner works at a private school where the students pay more than a typical university to attend - lots of business and celebrity parents. I was surprised to find out that some of the teachers are indeed paid less than they would be if they worked at a public school. If they've worked there a long time, then their pay is significantly better, so there is incentive to stick with it at one location.
However, the perks are better. For one, if they have children, they can attend the school for free. They also get very sophisticated lunches that only cost them $5/day.
