i mean do colleges even care about it? I plan on majoring in econ and I want to take a writing course there
If it is a paid summer program then it isn't as impressive as at least say "RSI" which is a summer program that requires an application and has a low acceptance rate. You can apply for it but keep in mind that it might not be as impressive if you paid for it, especially for top schools like the Ivy´s and the top 40 schools.
Hope that helps!
It's really a question of what are you giving up by doing it? The financial / prestige point below absolutely holds, but a further consideration is as follows: if you want to take a writing course but that means it takes away from a summer of improving in one of your extracurriculars, or setting yourself up for a really good fall sports season, that's an opportunity cost you need to think about.
In less vague terms, summer at Brown is not prestigious just because it is affiliated with Brown. If you want to major in econ (and writing doesn't end up being any part of your applications profile), then that writing course at summer at brown will end up looking a little like a missed opportunity. Don't take that as a "don't do it" though -- only you know all the relevant factors in how to make the decision!
To keep this community safe and supportive: