College, while not a silver bullet, is still important. Yes, more U.S. workers attaining higher education seems unlikely to significantly reduce income inequality in the near future. But higher levels of education could be beneficial in multiple ways—by increasing productivity and economic growth as well as increasing social mobility.

Let’s concentrate here on that last benefit, mobility, which presumes that access to and attendance at colleges and universities is open to all students with the necessary drive and ability. Unfortunately, plenty of research finds that presumption to be false. Yet new research shows that some optimism is still warranted about expanding the reach of higher education due to new evidence about whether and how low-income students apply and attend selective colleges.

David Leonhardt late last year noted in The Upshot that schools have become more concerned about increasing economic diversity over the past decade or so. Yet many top colleges continue to fail at having an economically diverse student population. So why are these types of universities—think Bucknell, Washington University in St. Louis, and Providence College —so lacking in students from lower-income backgrounds?

The answer might be as simple as this—these students just don’t apply. Research by economists Caroline Hoxby of Stanford University and Christopher Avery of Harvard University shows that many high-achieving students from low-income households don’t apply to selective schools for which they are qualified. Instead, these students apply to and eventually attend schools at which they are overqualified, as measured by their scores on standardized tests.

So how can policymakers get these high-achieving, low-income students to apply to more competitive schools, if at all? Follow-up research by Hoxby and economics and education professor Sarah Turner of the University of Virginia looks at how giving students information about the college application process and the schools they might be a good fit for given their grades and scores influences their decision making. They find that, perhaps not shockingly, better information about the selective schools boosted the application rate of these high-achieving, low-income students to these schools.

But what exactly about this information got these students to apply? Hoxby and Turner released a short paper earlier this year that digs into the data. They find that after receiving information from what they term their “information intervention,” known as the Expanding College Opportunities project, students were more likely to apply when they knew schools had high graduation rates and students with test scores and GPAs that were similar to their own.

What’s particularly interesting is that students also are more likely to apply when they learned about the actual net price of college. When students are applying to a college or university, they can see the gross price of tuition, before financial aid is considered. It’s only after admission to the school that they’ll know the net tuition. The Expanding College Opportunities intervention gives students an estimate of how much financial aid students at their income level could expect to receive from the selective school before knowing whether they had gained admission. Students are more likely to say they will apply after learning the probable net cost.

So low-income students, who in the end will pay quite less than the sticker price of college, avoid applying to these selective schools because of a lack of knowledge about the gap between the gross and the net price. Perhaps schools interested in increasing economic diversity could post a menu of tuition prices for different family income levels. Or the government could require disclosure of these prices if policymakers deem it important enough.