Graduates of Baruch College participate in a commencement program June 5, 2017, at Barclays Center in Brooklyn. (Bebeto Matthews/AP)

The American Dream is in such bad shape that it’s even been losing what should be one of its easier battles in the war against our new Gilded Age: getting poor kids with good grades into the right schools.

Or really any schools, for that matter.

The depressing reality, as Stanford University’s Caroline Hoxby and Harvard Kennedy School of Government’s Christopher Avery have shown, is that most high-achieving low-income students don’t apply to any selective college or university at all. Which, it’s important to understand, doesn’t just mean places such as the Ivy League, but rather any four-year institution that doesn’t accept everyone. They instead go to community college — if that.

Now, this is hardly the only reason that our elevator of social mobility has gotten stuck recently, but it might be the worst one. These are kids, after all, who don’t need any help in school. They just need help picking their next school — a decision that we know can make an enormous difference in their lives. Indeed, public colleges in particular have played a pivotal role in catapulting generations of working-class kids into middle-class futures. And as the New York Times' David Leonhardt points out, they continue to do a better job of that than a lot of Ivies do today despite having to contend with deep budget cuts the past 10 years.

So why aren’t these 17-year-olds — many of whom don’t have parents, teachers, or guidance counselors who know a whole lot about the college admissions process — applying to the type of top schools they should be? Well, when you put it like that, it isn’t much of a mystery, is it? Especially not when you consider the fact that, as Hoxby and Avery report, the high-achieving low-income kids who do end up applying to selective colleges tend to come from big-city magnet schools that not only have a lot of experience dealing with all this, but also get actively recruited by the colleges themselves.

It’s almost as though schools should reach out to qualified low-income kids to encourage them to apply — and, more to the point, let them know that, thanks to generous financial aid packages, it’d be free for them to go if they’re accepted.

That’s exactly what a couple of University of Michigan professors decided to do. They identified low-income Michigan students whose high grades and test scores made them competitive candidates for the university, then ran a simple experiment: They sent some of them a personalized letter, emphasizing three things. First, that these students should apply; second, that they were guaranteed four years of free tuition and room and board if they did get in; and third, that they wouldn’t have to fill out any paperwork to get this financial assistance. None of this, it’s worth pointing out, was a new promise. It was all part of an existing scholarship. But that doesn’t mean that it wasn’t new information to these students and their families.

The results were about as big as you’ll see in social science. About 67 percent of the students who received a packet decided to apply to the University of Michigan, compared to just 26 percent among the similar students who didn’t get one. Even better, 27 percent of that first group ended up enrolling, versus 12 percent of the second. And best of all, this increase didn’t seem to come at the expense of students going to other selective schools. In other words, it got kids who wouldn’t have gone to any college at all to instead go to one of the best public universities in the country.

Mass mailings, then, might not be the secret to saving the American Dream, but they could be a secret for doing so. Or at least for keeping it from becoming even more of a myth. That’s because while there are two high-achieving high-income students for every one high-achieving low-income student, there are somewhere between 8 and 15 of that first group applying to selective colleges for every 1 of that second group who is. We need to do better at both if we’re going to keep our society from calcifying along class lines, but the simple story is that it’s a lot harder to get more high-achieving low-income kids overall than it is to get more of the high-achieving low-income kids there already are to apply to college. The first is a matter of helping parents, improving schools, and stabilizing communities. The second involves sending letters.

It doesn’t seem like too much to ask of our most elite educational institutions, which often have more students from the top 1 percent than they do from the bottom 60 percent.

The American Dream is worth spending 50 cents — the cost of a stamp.