Columbia University has the highest *sticker* price of any school in the country. But most students don't pay that. (Tian Fineberg/AP)

Columbia University doesn’t usually mind college rankings; after all, it mostly does pretty well for itself (it’s tied for fourth with the University of Chicago in U.S. News’ latest college rankings). But it probably wasn’t too pleased to top the Department of Education’s latest College Affordability and Transparency Center report. The DOE ranks Columbia as the most expensive four-year college or university in America, with an annual sticker price of $45,290 for the 2011-2012 school year. And that’s just tuition and fees. Throw in room and board and other related expenses, and Columbia will set you back $61,540 a year.

Or maybe it won’t. Many, if not most, Columbia students don’t actually pay $61,540 a year. Half of the students entering in 2011-2012 received some institutional aid, making the average net price, including room and board, around $21,274 that year. For low-income students, it was lower still. Students from families making from $30,000 to $48,000 a year paid an average of $6,719; those from families making between $0 and $30,000 paid about $12,018

Columbia is among many, many schools that charge vastly different prices for the same education, depending on students’ income, where they’re from, their academic achievement level, and so on.

This has always been the case, at least to a certain extent. Public universities prefer in-state to out-of-state students, both in admissions and in financial assistance. Financial aid has a long history, too. The first scholarship program in the United States was set up at Harvard College in 1643, which also created the first student loan program in 1840.

But today’s system takes that pattern to extremes. In the 2007-08 school year, students from families making $100,000 or more paid an average of $30,159 a year in tuition, fees and room and board to attend private four-year colleges and universities, and they paid $16,871 a year to attend public four-years, according to the College Board. Students from families making under $32,500 a year paid $17,050 a year on average to attend private schools and $9,404 a year to attend publics.

In each case, the poorest students are paying slightly more than half of what the richest ones are paying. The numbers are even more startling when you look at tuition apart from room and board. The typical poor student at a public four-year paid no tuition or fees in 2007-08.

There was actually a wider gap between what poor and rich students paid at private institutions two decades ago. In 2007-08, poor students paid 55.5 percent of rich students’ tuition at private schools; in 1992-93, they paid 45 percent. But public universities, which the great majority of students attend, are doing even more to help poor students than they were in the '90s. In 2007-08, poor students paid 55.7 percent of rich students’ tuition at public four-years; in 1992-93, they paid 67.1 percent.

On the surface, this doesn’t represent an increase of college costs so much as a shift. There’s no reason why you have to raise average tuition for all students in order to charge them different amounts. You can just raise prices for rich students and cut prices for poor students by an equal amount, without affecting the overall trend of average tuition.

But one theory proposes that charging different prices actually drives up the cost of college because it makes the institutions dependent on tuition from wealthy students to cross-subsidize tuition discounts for poorer students. Those wealthy students expect a certain quality of life at their colleges, one that calls for more spending on the part of those colleges and universities. Thus, the underlying price of the college experience rises, which means higher tuition for everybody.

Pierce Hawthorne, one of the rich students that schools have to attract. (NBC)

“You have to recruit some affluent students, and part of the way you recruit affluent students is by having symbols of excellence, like an up-to-date campus center and up-to-date athletic facilities,” says Michael McPherson, president of the Spencer Foundation and a former president of Macalester College. It's analogous to judging banks by whether or not they have marble columns in front of their buildings, he says. “It’s a visible demonstration that they’re not about to go broke.”

“A few years ago we started investing in athletic facilities because we were being told by parents that the facilities weren’t as good as the facilities in their high schools, and their kids wanted to keep playing athletics,” Catharine Hill, president of Vassar College, tells me. “I think the number of singles has increased. We’re seeing increased demand for science enrollment, and so spend more on labs.”

There’s some social science to suggest that McPherson's and Hill’s experiences aren’t unique. The University of Michigan’s Brian Jacob, Brian McCall and Kevin Stange have found that most students are not likelier to attend schools that spend more on instruction (though high-achieving students are). However, all students, and in particular low-achieving and wealthy students, are likelier to attend schools that spend more on amenities like those McPherson and Hill describe. The effect isn’t huge — a 1 percent increase in amenity spending leads to a 0.3 percent increase in a wealthy student’s likeliness to attend — but it is real.

But how much of the increase in college costs can this explain? The Bowen and Baumol Effects leave considerable room for other explanations. Martin and Hill find that the two effects account for 55 percent and 16 percent of the increase in costs between 1987 and 2008. That leaves 29 percent of the cost increase unexplained. Martin and Hill speculate that one of them is “bundling” — that is, the inclusion of greater and greater amenities as part of the college experience.

So does the cost data bear this explanation out? At most research universities, yes. According to the Delta Cost Project, all categories of public school and private research universities saw spending on “auxiliary enterprises” — which include dormitories and meals, as well as hospitals, bookstores, etc. — increase between 2000 and 2010, even accounting for the downturn at the end of the decade. The one exception was private bachelor’s institutions (like, ironically, the institutions McPherson and Hill led).

But in all other colleges there were increases -- often huge ones. Community colleges, which saw costs decline overall, raised their “auxiliary” spending by an astonishing 52.7 percent between 2000 and 2010. Public research universities increased it by 28.7 percent, private research universities by 18.4 percent, and public master’s schools by 17.3 percent. All of those are above the overall growth rate of costs. If you added up all the areas where costs increased over that period in public research universities, “auxiliary” spending represented fully 41.2 percent of the total.

The question remains, though: are rich students that schools want to recruit demanding this spending, or are colleges choosing to devote new revenues here for other reasons? That’s a hard one to answer, but other evidence suggests that the story Hill and McPherson tell of schools recruiting rich kids with nice amenities checks out.

Steven Burd of the New America Foundation found that there’s been a marked shift in recent years toward merit-based aid, for which rich students are eligible, rather than need-based aid. In the 1995-6 school year, 8 percent of public school students reported getting merit aid. By 2007-08, that was up to 18 percent. And over that period, the share of high-income students reporting getting financial aid increased from 13 percent to 18 percent.

And more aid for rich students means less for poor ones. Cornell’s Ronald Ehrenberg, along with Penn State’s Liang Zhang and Jared Levin, found that there’s an inverse relationship between the number of institutionally-backed National Merit Scholarship winners at a school and the number of Pell Grant recipients. Merit-based aid crowds out need-based aid.

So the rise of merit aid suggests that schools are trying to recruit affluent students with generous aid packages. Schools will actually admit this in anonymous surveys. An Inside Higher Ed survey found that 54 percent of admissions directors say they’ll increase recruitment efforts aimed at “full pay” students.

There is plenty of evidence that schools are using increased amenity spending to entice full-pay students. That’s not the main driver of cost increases, and arguably it’s only made possible by the kind of nonprofit budgeting that the Bowen hypothesis implicates as responsible for cost increases. But it does contribute to the problem.