Princeton has $2.86 million in endowment per student, which would yield about $140k per year in interest for every undergraduate. Princeton could charge no tuition if its goal were to maximize accessibility. On the other hand, Princeton received 32,000 applications last year, so it could easily fill a highly-qualified class with people who could pay its full tuition price–or much more than that–if the university’s goal were to maximize tuition income. Princeton could also double or triple its size or create a new campus in another state or country if it wanted to maximize both accessibility and revenue.

Of course, a university sees itself as doing more than providing education. It also generates research, arts and culture, public service, etc. Every dollar that it collects from a student can go to those other purposes. But any endowment money that it spends on those other purposes could have gone to financial aid.

Meanwhile, prospective students also want a bundle of things, including prestige. Prestige comes with selectivity and sticker-price. Imagine you have a choice between paying the basic in-state tuition at UW-Madison ($10,725) or the same amount to Stanford after receiving financial aid. Stanford might look like a better deal, since its tuition sticker price is $55,473. It seems like you are being given $44k. However, it is unlikely that the marginal cost per student at Stanford is really 5.5 times higher than the cost at UW-Madison. More likely, Stanford knows it can charge a base tuition of $55k because many families will pay that much; and asking for less would be leaving cash on the table. Stanford with financial aid is arguably a better deal than UW-Madison’s full price, not because Stanford offers a better (or more costly) education in the classroom but because attending a college that is extremely selective and expensive looks better.

In short, the demand curve rises with price. The more other people pay for a given college, the more valuable it is to you, holding your own costs and the quality of the education constant.

It sounds as if college is a Veblen good, one that rises in perceived value the more it costs. But that logic does not exactly apply. If a college that regularly turns away 94% of its applicants decided to fill its seats with people who could pay full price, it would look less academically selective (as well as less diverse), and it would become less desirable. Many of the people who could pay to attend would now try to go elsewhere. In other words, if you pay full price, you are better off the more of your fellow students do not. Financial aid demonstrates that the college is selecting on criteria other than wealth. This is not typical of a Veblen good, which looks more desirable if only rich people buy it.

As Frank Bruni amusingly postulated, a college could win the prestige sweepstakes by deciding that no one was qualified for admissions. Bruni imagines the day when Stanford finally admits zero applicants:

At first blush, Stanford’s decision would seem to jeopardize its fund-raising. The thousands of rejected applicants included hundreds of children of alumni who’d donated lavishly over the years. …

But over recent years, Stanford administrators noticed that as the school rejected more and more comers, it received bigger and bigger donations, its endowment rising in tandem with its exclusivity, its luster a magnet for Silicon Valley lucre.

In fact just 12 hours after the university’s rejection of all comers, an alumnus stepped forward with a financial gift prodigious enough for Stanford to begin construction on its long-planned Center for Social Justice, a first-ever collaboration of Renzo Piano and Santiago Calatrava, who also designed the pedestrian bridge that will connect it to the student napping meadows.

One of the anomalies that Bruni is pointing to is that people who attended a college in the past now underwrite it voluntarily with their donations. Usually, you pay in order to obtain a good. Here, you get the good and then you pay for others to get it–in part so that it can be withheld from as many applicants as possible, thus raising its value even more on your own resume.

These are strange incentives ….