Looking across Wyman Quad to Shriver Hall on the campus of Johns Hopkins University in Baltimore. Photo: Andrew Mangum for The New York Times

When colleges review applications, all but a few consider a student’s ability to pay. As a result, high-achieving applicants from low- and middle-income families are routinely denied seats that are saved for students whose families have deeper pockets. This hurts the son of a farmer in Nebraska as much as the daughter of a working mother in Detroit.

Denying students entry to a college based on their ability to pay undermines equal opportunity. It perpetuates intergenerational poverty. And it strikes at the heart of the American dream: the idea that every person, from every community, has the chance to rise based on merit...