[OkayPhysicist]

At private schools, stated tuition is basically just a (soft) cost ceiling. The majority of students receive some level of aid, either need or merit based, or both. It's a pretty good system, if you want a mix of rich students, academically gifted students, and disadvantaged students who might succeed given the resources.

The existience of merit-based pricing is the big differentator versus public schools.

[chatmasta]

Not sure which way you’re saying the differentiator goes, but “merit-based pricing” is NOT what the top schools have. They are entirely need blind. You don’t get financial aid because you’re good at sports, you get it because you were accepted to the school and if you can’t afford to go there then they will make sure that you can attend. In fact that’s why the Ivies don’t offer scholarships - because if you can’t afford to attend, they’ll reduce your tuition until you can.

I’d call it merit-based admissions, if anything.

(Athletes can still get preference in admissions, with each team given a number of slots, but it’s totally separate from financial aid decisions. And this is actually a disadvantage compared to top, non-Ivy schools like Stanford, because a top athlete from a rich family would go to Stanford for free but would have to pay at an Ivy.)

[OkayPhysicist]

At the very top, schools don't need to worry too much about competing to attract top students, because they're the best schools and the top students are going to be trying to get into them anyway. Private schools below that (like Stanford, USC, etc) use discounted tuition to try and convince top students to attend, leading to the merit-based tuition I described.