I went to a school that had essentially this system in place. There wasn't a reverse auction, but rather, full tuition was a significant chunk of change, and as a result, a significant chunk of the student body was there on various merit-based scholarships.

You could usually tell which group a given individual was from, and saying so was a common insult. Either "Your folks may have money, but you're dumb as a post", or "You might be smart but you're poor". There were a select few students where the circles seemed to overlap...