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Most of us know folks who owe everything they have in life to education. That explains, I suspect, why we nod in agreement whenever we hear somebody describe education as the ultimate antidote to inequality.

Education certainly can serve as a brake on our widening divides. But education, if structured the wrong way, can also reinforce inequality — and perpetuate privilege.

We saw this unfortunate dynamic at work most blatantly back in the days of legal school segregation. “Separate but equal” kept children of color distinctly unequal.

Legally segregated schools no longer scar our nation. But our educational systems are still, in many different ways, perpetuating privilege. And the most powerful perpetuating of all may be taking place at the tippy top of America’s educational order, on the campuses of our nation’s most prestigious elite universities.

We tend to view these elite schools — places like Harvard, Yale, and Princeton — as national treasures. One thing’s for sure: These private universities certainly sit atop treasures. They all boast endowments that run into the many billions of dollars.

In 2012, Harvard, Yale, Princeton, and five other elite schools had endowments worth a combined $112 billion. For this enormous nest egg, elite private schools owe the American people a debt of gratitude. Without us, their endowments wouldn’t be anywhere near as large.

Elite universities, keep in mind, get the bulk of their contributions from wealthy alumni. These alumni — thanks to the generosity of the American taxpaying public — get to deduct charitable contributions off their taxes. This generous tax break gives the wealthy a mighty incentive to donate to dear old ivy. The more they give, the more they can deduct.

With this tax break in place, elite universities get to accumulate vast endowments, and the phenomenally rich get to pay taxes at bargain basement rates — and stay phenomenally rich.

But these same endowments are also creating fabulous wealth — for the money managers and hedge fund kingpins that universities hire to invest their endowment dollars. These money manipulators rake off enormous fees, often many millions of dollars a year.

What about us, the general public? What’s our return on investment for the hefty tax breaks we extend to wealthy people for their college contributions?

University PR staffers have a ready answer. Elite private universities, they assure us, are serving the public interest. Those billion-dollar endowments, these flacks note, fund scholarships that enable students from families of modest means to get the finest educations available anywhere in the world.

Elite universities, the claim goes, are broadening opportunity.

But not by much, a new landmark study makes clear. The academics behind this new research — economists from Stanford, Berkeley, and Brown — examined data for over 30 million students who attended college in the United States between 1999 and 2013. They found that students from lower-income families make up a shockingly paltry proportion of the enrollments at elite private universities.

In fact, 38 elite institutions have more students from families making over $650,000 a year — our top 1 percent — than from the under-$65,000 ranks of the low- and middle-income families who make up America’s entire bottom 60 percent.

We do have colleges in the United States, the researchers also found, that do a good job reaching large numbers of lower-income students and helping them succeed. The vast majority of these colleges happen to be public institutions — places like the City University of New York.

These public schools aren’t sitting on billion-dollar endowments subsidized by tax breaks for mega millionaires. These colleges depend on our tax dollars for their support. What do you think? Maybe they should get more of those tax dollars — and mega millionaires less.