<p>Generally, schools offer merit scholarships to attract students they wouldn’t otherwise get. Some of them sweeten the pot with other perks, such as honor dorms, stipends for study abroad, etc. This is how Duke (for example) is able to get some high-achieving kids who would otherwise go to HYP.</p>
<p>The more interesting question is: why do they want to get these kids? I think they do want to raise their profile, prestige, ratings, etc. But I would also say that some of these scholarships–especially those funded by rich alumni–are based on the idea that the school is already great, and should have great students as well.</p>