[zoolily]

There's much more to higher education costs than Baumol's cost disease. Public universities have much higher tuition because state subsididies to universities have decreased. In 2005, the state paid 3/4 and students paid 1/4 of the cost of instruction at my university. By 2019, those numbers were reversed, with students paying 3/4 of the cost. Total cost of instruction remained the same within a couple percent over that time period.

On the other side, elite private universities are in ever greater demand, driving higher tuitions. Higher tuition is a signal of their elite status, and such universities want to keep their tuition close to that of their competitors. They use financial aid to produce a sliding scale to collect as much money as they can from those who can afford to pay. On the other side, because of that financial aid, raising tuition an amount x may only produce an increase of income of 1/2 x, because the rest goes to increased financial aid. That factor increases the rate at which they raise tuition.