Last week, George Washington University became the first school in the country to charge undergraduates more than $50,000 a year.

The university, which is in Washington, D.C., will charge about $39,000 in tuition plus another $11,000 in mandatory fees (including housing), making it the most expensive in the country – but not by much and not for long. About a year ago, several other private schools pushed their costs above the U.S. median household income, now $46,326. With fee increases consistently exceeding inflation, many more schools can be expected to join the $50,000 club long before this year’s freshman class graduates.

Overall, tuition and fees at four-year institutions increased 35 percent over five years (and that’s after being adjusted for inflation), according to the College Board.

What’s more, many prestigious schools are raising prices at a time when they have more money than ever. The same day George Washington announced its tuition increases, for instance, the school boasted that its endowment for the first time had surpassed $1 billion.

So why are they doing it? Don’t expect an easy answer from those whose presumptive mission is to tackle society’s toughest problems.

University officials claim they need every penny they have just to get by. Tuition and fees, they’ll tell you, cover only about two-thirds of what it costs one of our leading private institutions to educate a student. The rest of that cost is covered by the university’s endowment, annual gifts and other outside sources.

Schools contend that their expenses mandate steep tuition increases. Not only do they face typical expenses such as rising employee health care and benefits costs, but they must invest heavily in state-of-the-art facilities (gyms, libraries, museums and the like) to lure and retain first-rate faculty and students and to support their ambitious academic pursuits.

The rising fees are misleading. In fact, the pricing scheme at the nation’s most elite schools actually resembles that of a car dealership: Most people don’t pay the sticker price, discounts abound and more and more customers borrow heavily to make their payments.

At George Washington, for instance, fewer than half of undergraduates pay full price; about 40 percent of students there receive need-based aid. They are from the vast majority of American families that simply cannot afford to pay close to $50,000 a year.

But that generosity is offset by more self-interested price-cutting as well. George Washington University, like its peer institutions, including Washington University in St. Louis, New York University, Emory or the University of Southern California, also has invested heavily in “merit scholarships” that cut tuition for students whose families otherwise could afford to pay full price. (Roughly 20 percent of students at George Washington didn’t qualify for need-based aid but received merit scholarships averaging about $19,290 a student.)

By using discounts to attract students with high grades and test scores, these colleges and many others have enhanced their status in all-important rankings, such as the U.S. News & World Report list.

That’s not necessarily such a good policy. Yet such status-climbing is contagious. Merit scholarships were far less common a generation ago. But schools content in the 1980s with being respected now want to be desired – and this drives up costs for all students and reduces the pot of money available for needy students.

Indeed, enrollment of low-income students at selective private colleges and universities has been steadily dropping.

According to its self-reported data, George Washington spends about $20 million a year on merit scholarships. Presumably, it and other schools with hefty merit scholarship offerings simply could drop the costly awards and use the money to charge everyone less in tuition and fees.

For a college without Ivy League cachet, however, a hefty tuition break can be a powerful recruiting tool. Rather than charging a lower tuition rate, a school that sets an artificially high price and then awards a merit scholarship can tell a student he or she has earned a prize worth thousands of dollars. Hopefully, the student will return the flattery by enrolling.

Along with such cash incentives, schools – which are also ranked for “quality of life” by college guides – are piling on costly amenities for students. Espresso bars and fully equipped exercise gyms are more the rule than the exception at the fashionable schools.

Margaret Soltan, an English professor at George Washington, enjoys her comfortable office and floor-to-ceiling windows on an increasingly luxurious campus. But she also points out that the university relies increasingly on part-time instructors rather than investing in full-time faculty positions.

Soltan sees the posh atmosphere on her campus and others like it as a byproduct of the broadening gap between the wealthy and the rest. “You’ve now got this class of hyper-rich people in this country whose kids are attracted to chic urban schools like NYU and GWU, which are full of well-dressed sophisticates just like them,” she said.

As colleges become more like luxury items, students and their families are paying for them the way they would a pricey house or car. Student loans taken through private lenders now make up 20 percent of educational borrowing, according to the College Board. Ten years ago, the figure was 4 percent. Private loans are not guaranteed by the government as are federal student loans, and they frequently carry higher interest rates, especially for borrowers with poor credit ratings.

It seems colleges and universities will continue to raise tuition and fees as long as society is willing to pay, and ordinary students will have a harder time paying their way. Perhaps, at some point, universities full of great economists, ethicists and business school efficiency experts will figure out how to lower their prices. But so far, our finest institutions, including several with multibillion-dollar endowments, say they don’t know the answer.