BOSTON — The nation’s elite universities have historically nurtured both the social movements that challenge the status quo and the upper crust that maintains it, and the Occupy movement is the latest to highlight that contradiction.

With huge annual tuitions, multibillion-dollar endowments and long lists of powerful graduates working on Wall Street and in Washington, such schools embody the kind of institutions the Occupy movement — with its opposition to undue influence by those in the top tiers of society — was born to protest. Yet their students are joining in.

Members of elite institutions are in a unique position to change them, said Rossen Djagalov, a teaching assistant in history and literature at Harvard University, which costs around $50,000 a year to attend.

“We just want this university to be a better citizen, whether that’s in Cambridge or the whole country, in which Harvard graduates are such prominent people,” Djagalov said.

From its start in September at an encampment in New York, the Occupy movement has drawn broad support from students at top colleges, and they’ve taken public stands.

At Duke University in Durham, N.C., for instance, a small group of students has camped out for three weeks. On Wednesday night at the University of California at Berkeley, dozens were arrested during demonstrations against financial policies they blamed for causing deep cuts in higher education spending.

And in Harvard Yard on Wednesday, protesters gathered in front of the statue of school namesake John Harvard, calling for “a university for the 99 percent.” A few dozen students then set up tents and stayed overnight, although police stopped any non-students from joining them.

Students urged a fair contract for custodial workers at Harvard, argued that it played a role in the financial crisis because of its influence, and should be socially responsible in its endowment investments.

“Harvard should reconsider its status as the training ground for the people who make our political and economic systems less democratic,” said Joe Hodgkin, a senior who has led meditation sessions at Occupy Boston.

Last week, students walked out of a popular introductory economics class, complaining of bias.

The actions have drawn plenty of skeptics, even at the schools themselves. On Wednesday, Harvard students in nearby dorms yelled derisively at the protesters, while another said the yard into which police had locked students was “the richest prison in America.”

Harvard spokesman Kevin Galvin said in an email that the university already pays more to cover custodians’ health care benefits than many other institutions. He did not comment on the students’ other concerns, including endowment investments.

That endowment is the nation’s deepest, at $32 billion, followed by Yale University’s $19 billion.

It makes no sense for students at such wealthy schools to be part of a movement against elites, said Ron Meyer, spokesman for the Young America’s Foundation, a national conservative organization focused on college campuses.

“There’s rampant hypocrisy spread throughout it, of course,” he said.

“It’s a sense of guilt and sense of wanting to sort of be a part of a movement that’s against the system,” he said. “It’s sort of like a hipster movement, basically.”

Students at top schools say that it’s wrong to assume they all come from wealth, or that those with privileged backgrounds — in the so-called “1 percent” — don’t have a stake in a movement targeting societal inequity.

“Even those who don’t fall in the numbers game of the 99 percent can recognize why this sort of economic inequality is dangerous to all of us,” said Yale senior Alexandra Brodsky.

Duke senior Shreyan Sen, who’s been camping out with Occupy Duke, said fellow students have accused him of protesting a system he’s part of. Sen said that acknowledging he’s part of that system, and has benefited from it, doesn’t mean he can’t speak against it.

“If you realize you’re part of something bigger that you think is unfair, there’s two things you can do: You can either go to the woods, like Thoreau, or you can say, ‘All right, I realize something is wrong, I’m going to now start to protest, I’m going to work against this,’ ” Sen said.

Last year, Harvard said it distributed $166 million in financial aid, indicating that plenty of students aren’t from wealthy households, and President Drew Faust has emphasized public service careers.

Still, plenty of Harvard grads head into the financial sector that the Occupy movement has bashed. The numbers have dropped in recent years, but a survey of post-graduation plans by the Harvard Crimson in 2009 put the number at about 1 in 9 graduates.

Yale’s Brodsky said people aligned with the Occupy movement have a duty to try to stop fellow students from entering finance, or force the people who may eventually be in the 1 percent to face the “moral repercussions of their decisions.”

Brown University junior Lily Goodspeed said a key part of the Occupy movement on her campus is getting today’s students thinking differently about what they have and how they’ll chose to use it.

“I think this is the first time people are forcing Brown students to look at what they have, and what are the responsibilities that come with those privileges,” she said.

Still, some collegians are rejecting the movement, whose critics say suffers from incoherence and hasn’t offered specific remedies to income equality.

“As a pretty well-read Harvard student, I still am confused about what the message is,” said freshman Ned Whitman.

Sophomore Will Poff-Webster mocked the crowd gathered in Harvard Yard this week, saying, “I’ve never been prouder to be a student of Harvard than tonight. I know some people here today are courageous and prepared to get arrested, but unfortunately, I have a Spanish quiz tomorrow.”