Many Harvard officials, Dr. Faust said, feared that cost was driving the choices students made about graduate school and careers and that it had created what amounted to a two-class system among Harvard undergraduates. Mr. Fitzsimmons referred to it as “the upstairs downstairs syndrome.”

The officials said, for example, that often only the wealthy students can afford to pursue highly valuable but unpaid research opportunities with professors, take unpaid summer internships, study abroad or even spend time with their friends.

Under the new financial aid rules, the university said, a family making $120,000 would have to pay about $12,000 for a child to attend Harvard College, compared with more than $19,000 under current policies. A family making $180,000 would pay $18,000, down from $30,000.

The university also plans to substitute grants for loans in all financial-aid packages and will no longer consider home equity in calculating aid. The change in home equity considerations alone will mean, on average, a reduction of $4,000 a year in cost for those families whose home equity would previously have been a part of the financial aid calculation.

Harvard officials say they do not want families borrowing against their homes  or selling their homes  in order to send their children to the university. “If you had an oil well in the backyard, you could sell the oil,” Mr. Fitzsimmons said. “But you need to live somewhere.”

Currently, 763 students whose family incomes are between $120,000 and $180,000 receive some financial aid from Harvard, which has a total of 6,600 undergraduates. The new policy will apply to them next year, officials said.

Only a handful of universities have anything even remotely close to Harvard’s financial resources, and it was not clear how many could afford to follow. Yale tersely said in response only that it was planning an announcement next month on expanded financial aid.