If your son or daughter is accepted at Yale this year, you probably won't have to borrow a dime to pay for that Ivy League education, thanks to Yale's expanded financial aid for middle- and upper-middle-income families.

But only a fraction of students manage to gain admission to Yale, which hasn't raised the size of its freshman class in 40 years. The same is true for other elite schools that have also liberalized their aid plans. Harvard, which will provide aid to families with incomes of up to $180,000, has received 27,000 applications.

The number of freshman slots? About 1,650.

Though some other private colleges have taken modest steps to aid more families, they can't begin to match the Ivies' financial bounty. Most middle-class families, experts say, won't find any additional aid on the table.

Some aid analysts also worry that some private schools, to try to stay competitive with the Ivies, will use more of their endowments to attract the best and brightest students. Those students are likely to come from relatively well-off families.

That approach "could take resources from the same pot of money that really should be going to low-income students," warned Robert Shireman, president of the non-profit Institute for College Access & Success.

Looming in the background are fears that the economic downturn could force states to cut funding for state colleges and universities, which could lead to sharp increases in tuition. More than 65 percent of full-time undergraduate students — including a majority of low-income students — attend state colleges and universities.

A 2006 study by the Center for the Study of Education Policy at Illinois State University found that state funding for higher education declined during three of the past four recessions. After the 2001 recession, the study found, state appropriations for higher education fell 8.6 percent.

Several states are also wrestling with gaping budget deficits, which could deepen the cuts, said Luke Swarthout, advocate with the U.S. Public Interest Research Group's Higher Education Project. When states face a budget crunch, he said, "higher education frequently finds itself in the position of being one of the first programs cut."

In an interview last month, Yale President Richard Levin said Yale's expanded financial aid program "is giving a strong signal that opportunity is available to the most talented in the country. Americans like to have ambitious targets."