THIS YEAR, wealthy private colleges and universities...

THIS YEAR, wealthy private colleges and universities fiercely competed less for quarterbacks and perfect SAT scorers than for smart, low-income freshmen. Harvard led last year when it said it would not ask parents making less than $40,000 a year to contribute to their children’s education. Last week, it raised the line to $60,000 and announced an offer of substantial reductions in costs for families earning up to $80,000. Yale’s line is $40,000, Stanford’s $45,000 and Penn recently came in at $50,000. Families with annual incomes of up to $60,000 can also get substantial discounts from these schools’ high tuitions.

It’s gratifying to see intercollegiate competition heat up for something more valuable to society than won-loss records -- something like equality of opportunity for able low-income students that removes any cost barrier to getting an excellent higher education and does it with a policy that can fit on a bumper sticker, say, “Family income under $60,000? For you, Harvard is free!”

But irrational exuberance is sneaking in when it’s suggested, as an article on these pages did, that Harvard should not charge any student for its education. It can afford to be free to all students -- and think what a “moral leadership” message that would send, said the article’s author, Peter Hong.

Would a free education really be a good way for Harvard and other very wealthy schools -- Stanford, Williams, Yale, etc. -- to help able low-income students? Or would it be similar to eliminating poverty by ending the capital gains and inheritance taxes?

Some basic facts are needed about the way these schools set their prices and the availability of highly able, low-income students.

These students already pay less because of the colleges’ long-standing policies that award financial aid on the basis of need, defined largely by family income. Newspaper reports often mention the “sticker price” (about $42,000 a year for tuition and room and board) and compare it with median family income (about $44,000 a year), thus implying that such a family would have to spend almost all its total annual gross income to send one child to Harvard. Great for shock effect and circulation but inaccurate, because a student from a median-income family pays nowhere near the sticker price.

We recently published a study of actual prices (net after financial aid grants) at 28 of the richest private colleges and universities in the U.S. and found that students from a median-income family paid only 34% of the full price but that students from the poorest families (bottom 20%) paid only 22%. Recent changes in financial aid policies at these schools have further reduced prices for the lowest-income students.

So who would pocket the $190 million a year Harvard would give up by making its education free? Or the $3 billion that the 28 wealthy and selective schools would donate?

In these schools, 70% of the students come from the top 20% of family incomes, and 10% come from the bottom 40%. Combine that with the fact that low-income students already pay much lower prices than their high-income counterparts, and it’s clear that the largest part of the savings from zero tuition would go to high-income families -- 86% of it. Only a fraction of the total -- 3.2% -- would flow to those in the bottom 40%.

But the hope is that a zero-cost education would attract more low-income students to such colleges as Harvard. For a lot of reasons, though, not many students from low-income families are academically qualified for success at these highly demanding schools. When one looks, as we recently did, at the family incomes of students who score well on standard admissions tests, only a small proportion of them come from poor families.

Consider these numbers. Of all high school seniors taking the SAT or ACT in 2003, among those scoring 1,420 or higher, 3.7% were from the bottom 20% of family incomes, and another 9.1% from the next 20%. So, less than 13% of the students were, by any stretch of the definition, “poor.” At the other end, 46% of these high-scoring students came from the richest 20% of U.S. families.

Although low-income, high-ability students are scarce in the national population, they are even more scarce on elite campuses. The prospect of a zero-cost education might attract more of these students to the Harvards and Yales. But even if these colleges’ enrollments shifted to accommodate a full share of high-ability, low-income students, families in the top-income quintile would still be the main winners from a zero-cost education. Defining high ability as a score of 1,300 or above, 45% of the benefits of a free college education would still flow to top-quintile families. Families in the bottom 40% of the income distribution would get only 10.5% of the benefits.

There are more effective and efficient ways to increase equality of opportunity for able low-income students at the nation’s most selective colleges and universities. One could further expand existing policies that make college costs much lower for these students. Or instead of giving merit scholarships and other awards to wealthy students, use that money to try to increase the proportion of high-ability students who come from poor families.

Achieving that goal by spending some of the $190 million a year that Harvard would give up to provide a free education for all might be a very good social investment. Giving $4.50 to families with top incomes in order to funnel a dollar to those at the bottom doesn’t seem similarly wise.