If GW's demographic profile matched the actual distribution of high-achieving students - that is, if there were one bottom-quartile student for every two top-quartile students -- GW's revenue would plummet by about 20 percent. The school would have to raise its tuition for students that are paying full price. But there would be far fewer of them. To take in the same amount of money as they currently do, GW would have to raise its price by approximately $30,000 per full-pay student, for a sticker price of about $90,000 a year. The actual increase would likely need to be more, given that families making $120,000 per year are classified as high income but cannot afford a college cost that would consume three-fourths of their annual income.

This is not a sustainable model. Colleges will not be able to raise sticker prices to these levels while preserving enough aid for low- and middle-income students. They will either raise prices across the board or recruit more affluent students.

Either way, the unequal system will remain.

How to Keep Prices Down: Be Really Rich

Not all colleges, however, would need to raise tuition drastically to pay for a larger number of low-income students. Schools with large endowments can cover the shortfall in tuition by drawing money from these reserves. But keeping tuition constant and paying more from the endowment is only an option for schools with monstrous endowments.

Many writers cite Amherst College as a success story, which has "aggressively recruited poor and middle-class students in recent years" and has increased its share of low-income students. But Amherst has a very large endowment for the size of its student body. Its strategy is only viable when backed with an endowment of more than three quarters of a million dollars per student from which it can draw additional funds to cover its costs while remaining competitive in its levels of spending.

Amherst is better than others, however. Some schools that already do have sizable endowments and could increase aid are instead decreasing it. Cornell, which has an endowment of about $5 billion, took $35 million from its endowment in 2009-2010 to fund financial aid. It is now changing its policy to draw less from the endowment, which includes lowering its financial aid policies.

For GW, with $1.33 billion in its endowment (about 1/18 of Amherst's per student), it's more difficult to use the endowment as a primary backstop. GW only has around 11.7 percent of its endowment, or $155 million, available for student aid. As such, GW - and most selective schools - would only be able to preserve student revenues by raising tuition.

The Public College Crisis

This problem is not reserved for private colleges and universities like GW. In fact, the problem is even worse at public universities.

In addition to competing with private schools, public universities are dealing with cutbacks in public funding as state governments turn to austerity to restore their balance sheets. State funding for colleges and universities dropped substantially after the 2001 and 2008 recessions. States are now spending 28 percent less per college student than they were in 2008, according to the Center on Budget and Policy Priorities, and the College Board reports that average state appropriations for higher education per $1,000 in personal income have declined from $9.74 in 1990 to $5.63 today. These budget cuts have forced states to raise their tuitions in turn. Over just the last 10-year period, combined tuition, fees, and room and board at public 4-year universities have increased 45 percent in inflation-adjusted dollars.