About 2,500 students gathered on the quadrangle of American University in Northwest Washington yesterday to protest a proposed 18 percent increase in tuition and 19 percent hike in campus housing costs this fall.

The demonstrators, led by members of the university's student confederation, waved signs and shouted slogans protesting the proposed increases as well as federal cutbacks in aid to higher education.

A college education, speakers at the rally said, is becoming a luxury affordable only to the rich. They said that many students would be unable to complete their degrees at the school if the tuition increases are implemented.

The proposed increases, announced two weeks ago, would raise tuition at American University by almost $1,000 a year, from $5,240 to $6,198. The cost of a dormitory room would go up more than $300 annually, from $1,628 to $1,940, making student rent on a shared room more than $240 a month.

University president Richard Berendzen said that the increases are necessary to keep pace with inflated operating costs, to offset losses in federal funding and to fund a10 percent pay raise for teachers and staff. Last year, tuition rose 13 percent. Berendzen said this figure had proved to be too low and, as a result, the university is "cash thin."

The university is expected to lose several million dollars as a result of federal cutbacks, chiefly in the area of aid to students, Berendzen said. The school's 1983 budget of $65 million calls for an increase of $200,000 in aid to students, which he pointed out is hardly enough to offset federal losses. Nevertheless, Berendzen said, he expects most students will make up the difference somehow, rather than drop out or transfer to another school.

"I hope that it doesn't turn out to be very many who leave ," he said. "What I wonder is, where are they going to go? We're going up, but the other schools are, too."

Georgetown University also plans an 18 percent increase in tuition next year, and an increase of19.5 percent is scheduled at George Washington University.

Yesterday's demonstration was unusually large for American University, which, students acknowledged, has gained a reputation over the years for affluence and complacency. Students took obvious delight in the balmy weather and the chance to be out of classes. And despite the purpose of the gathering, there was an air of good-natured resignation to the economic demands ahead.

At several points, however, Berendzen was interrupted by boos and catcalls. Student leaders pressed the administration for a complete accounting of the university's finances.

"Apparently President Reagan is not the only man in town practicing voodoo economics," said Steve Tillet, student confederation vice president.

"I think we'd be happy to pay the 18 percent if we could see the justification for it," said Gary Cohen, assistant comptroller of the confederation. "At least we've showed them that we care, and that's a lot around here."