It seems that they have something everyone wants: prestige. Who wouldn't want to go to Harvard or Yale, for example? And then these schools seem to know what everyone is willing to pay and then they charge it. This is all explained in the WSJ article
Why Top Colleges Squeeze You Dry by ANDREW MANSHEL. Here is an exerpt:
"I learned that the most prestigious and desirable institutions have a good deal of information about the shape of the demand curve for the families seeking to obtain elite higher education for their offspring. These schools have the capacity to estimate with some precision how many applicants will go elsewhere for each additional dollar they charge in tuition and fees. Each sets its tuition so as to produce a targeted "yield"—the percentage of accepted students who actually enroll there. If in any year we over- or under-estimated the price changes made by the other schools, and we had moved up or down in rank, we corrected the following year by raising or lowering tuition by more or less to compensate. We essentially followed the price leadership of the wealthiest, most prestigious institutions."
There is some financial aid. But that amounts to basically charging different students different prices based on their ability and willingess to pay. Economists call this price discrimination.
Why price discrimination raises profits
1. If a firm can get a higher price from some customers than others they increase their profits.
2. If a firm can lower the price for others who might not have bought the product to begin with, they also increase their profits.
Necessary Conditions for Price Discrimination
1. The firm must face a downward sloping demand. Monopolies do but firms in perfect competition do not (their demand, also their MR line, is flat).
2. The firm must be able to readily (and cheaply) identify buyers or groups of buyers with predictably different elasticities of demand (senior citizens have a more elastic demand and will shop around more since they have more time so restaurants might give them a discount).
3. The firm must be able to prevent resale of the product or service. If a student can buy a movie ticket for $6 while everyone else pays $8, the firm will lose money if the students turn around and sell their tickets for $7. So the theater can prevent resale by checking student IDs to make sure people holding the lower price ticket really are students.
What do the schools do with all the money they get? It mainly goes to the faculty and administrators. 60%-75% goes to salaries and benefits. Schools also spend alot of money on "...the "arms race," the constant effort to refurbish and build new physical facilities."