> What's actually stopping the elite schools from doubling their tuition in a single year?
If a school doubled tuition, it would be less competitive and fewer of the best students would choose to apply and enroll there. That would make that school less elite.
> What forces would actually cause colleges to lower their tuition?
They might apply, but certainly won't attend if they are admitted to Stanford, Yale, etc. The higher the price differential, the more likely people would be willing to take a 'prestige' hit and go to the lower cost school.
Anyone applying from a family making 400k a year (top 2%) would still be sensitive to an 80k vs 240k/year sticker price change.
Operation Varsity Blues (https://en.wikipedia.org/wiki/Varsity_Blues_scandal) suggests there are plenty of individuals willing to pay plenty more. Some would even break the law and risk prison. If it were legal, probably many more would pay.
This would be true for those whose contribution would be capped based on parental earnings/assets, since their effective price would not increase. And it would be true for extremely wealthy folks whose parents can spend $1M on college and not worry about it. But for the marginal applicants who would be paying full freight under the old price but can't easily toss out another $150k/yr on tuition, there would definitely be a drop in application rates.
If a school doubled tuition, it would be less competitive and fewer of the best students would choose to apply and enroll there. That would make that school less elite.
> What forces would actually cause colleges to lower their tuition?
Increased supply and/or lowered demand.