It would be a terrible law.

There are many problems with higher education in the United States, but the greatest and most destructive is the significant inequality of access to education on the basis of race and economic status, which are often though not always intertwined. The goal of any good public policy should be to use finite public funds to reduce this inequality.

While eliminating tuition at all public colleges and universities, from the smallest community college to flagships like the University of Virginia and the University of Michigan, would indeed benefit many lower-income students, it would also, and probably to a greater extent, be a boon to students from the upper-middle and upper classes.

Moreover, the policy would not alleviate and would probably worsen the most striking inefficiency in our system of public education: the abysmally low rates of graduation.

In short, tuition-free college would be a hugely inefficient use of public resources and might actually make inequality of access worse.

The median family income at Virginia is $155,500, and 67 percent of students come from the upper economic quintile. At Michigan the numbers are $154,000 and 66 percent, and at the University of Minnesota — economically diverse by comparison — $110,000 and 50 percent. By contrast, the median family income at Minnesota’s private colleges is $83,000, or slightly below the state median.

Unsurprisingly, a recent study shows that affluent students disproportionately benefit from scholarships and grants offered at these flagship public institutions. Over time these universities have become more selective, more dependent on tuition revenue as state funding has been reduced, and thus less accessible to many of the lower-income students they were ostensibly intended to serve. They behave very much like elite private colleges and universities.

Here is almost certainly what would happen if these public universities were to become tuition-free: The absence of tuition would sharply increase the number of applications they received and would make them even more selective than they are now. Already Virginia and Michigan accept fewer than 30 percent of their applicants.

Unless those elite universities completely changed their admissions practices, an increase in selectivity would benefit primarily the high-achieving students who attend private and well-funded suburban high schools. Nothing in the “free tuition” plans addresses the capacity of these universities to enroll more students, so the applicants most likely to be squeezed out would be those from precisely the economic backgrounds that the plans are intended to help.

Nor does anything in these plans address the quality and efficiency of education provided at public institutions, so the graduation rates at the less selective, woefully underfunded institutions would remain low or get lower. The current six-year graduation rate at four-year Minnesota state universities is 49 percent. Among students of color it is 44 percent. More than half of the students who would attend such a college free would not receive a degree from that college.

Absent the ability to charge tuition, and given the likelihood that federal and state subsidies would be unable to keep pace with rising costs, the most likely outcome is that these already low graduation rates would decline over time. Absent any plan to address racial inequality, the achievement gap between white students and students of color would persist.

There is no simple way to deal with the problem of inequality of access to education in the United States, given the deep and complex roots of that problem in everything from racism to fiscal policies that have come increasingly to favor the wealthy. But any policy change should focus on ensuring that the greatest benefit accrues to those who are most in need, that is, those from the lower income levels.

A good start at a sensible policy change would in fact be relatively straightforward: increase the size of the federal Pell Grant, currently available to students whose family income is below $50,000. These grants may be used at both public and private colleges and go directly to the students most disadvantaged by the systemic inequities in our society.

When the Pell Grant was created in 1978, the maximum award, in 2017 dollars, was $5,620, which at the time made a pretty serious dent in the cost of college. For the 2019-20 academic year, the maximum award is $6,195. For a fraction of the cost of the inefficient free-tuition proposals, Pell Grant funding could be sharply increased and the program could again be one that made college, public or private, much more affordable to the students with the greatest financial need. Increasing the size of the Pell Grant by 50 percent would cost far less than the $47 billion that Bernie Sanders estimates would be the federal cost of his free-tuition plan (exclusive of the $23 billion cost to states).

There is, however, one problem: “Increase the size of the Pell Grant” might be too long to fit on a bumper-sticker.

Brian Rosenberg is president of Macalester College.