Here are two different articles that talk about schools using merit as a carrot for wealthier families:
https://www.nytimes.com/interactive/2019/09/10/magazine/college-admissions-paul-tough.html
"If colleges were simply giving each student the same 50 percent discount, that would be challenging enough for enrollment managers like Pérez. But the discounts they offer vary widely from student to student. In fact, if you pick any two freshmen at the same college, they are very likely to be paying completely different tuition rates. Those rates are based not on the true value of the service the college is offering or even on the ability of the student’s family to pay. Instead, they are based on a complex calculation, using sophisticated predictive algorithms, of what the student is worth to the college and what the college is worth to the student.
The consultants many colleges hire to perform those calculations — known in the trade as “financial-aid optimization” — are the hidden geniuses of enrollment management, the quants with advanced math degrees who spend hours behind closed doors, parsing student decision-making patterns, carefully adjusting their econometric models, calculating for admissions directors precisely how many dollars they would need to cut from their list price to persuade each specific Chloe or Josh to choose their college. Outside the ranks of enrollment management, the work done by the companies that employ these back-room prodigies is almost entirely unknown. But collectively, they play as big a role as anyone in shaping American college admissions today."
and this one:
https://washingtonmonthly.com/magazine/septoct-2013/merit-aid-madness/
"Either a school offers tuition discounts to students from affluent families, or else those students (and the revenue they could provide) wind up going to other institutions that offer similar or more generous discounts.
There is now a whole industry of consultants who will gladly explain the math—not that it is very difficult to grasp. After all, if a school offers a single low-income student a full scholarship of $20,000, the school may feel good about itself, but it’s out $20,000. But if it can attract four affluent students to its campus instead, by offering them each a $5,000 discount off full tuition, it can collect the balance in revenue and come out way ahead financially. Such competitive discounting to the affluent may not be equitable, and it may not be sustainable over the long term, but once the cycle starts it can be very difficult for any one institution to resist unless they all do.
Today, these tuition discounts usually come in the guise of “merit scholarships,” but often the students who get them are hardly the best and the brightest. For example, 10 percent of college admissions directors at four-year colleges (and nearly 20 percent of those at private liberal arts colleges) admit that they give affluent students a significant leg up in the admissions process—meaning that they are admitting affluent students with lower grades and test scores than other applicants. Indeed, nearly a fifth of all students receiving so-called merit scholarships have less than a B average, and a largely overlapping 19 percent have only mediocre SAT scores, according to a report by the National Center for Education Statistics."