Colleges have NO IDEA how much it costs to educate a single kid. They have their gigantic operating expenses and use every means they have to meet those expenses every year.
This makes no sense.
Schools know what everything costs and are challenged to find the balancing point where they attract as many of the best students they can get as they can afford to educate. They need the volume to fall in certain range to make the formulas work, so things like enough incoming tuition money to pay staff and bills, not needing to hire additional staff, not needing to build classrooms or dorms, etc. They have a fairly fixed aid budget with which to purchase the best quality kids possible, whether it be lower income kids with need or higher income kids with merit. A school’s mission will affect that calculus.
They know how many seats they need to fill and they know what aid it’ll take to fill them, more or less. The difficulty is when the aid money doesn’t go as far as it used to and the kids have to self-select themselves out of the running. That may be unfair to the kids or society or adjunct profs or whomever, but it’s not some huge mystery.