You also need to consider that most students don't pay the "sticker price" with Ivies (and many schools). Financial aid (need-based) is significant.

An interesting point though is the achievement gap. I went to Cornell, which was the perfect choice for me, and although I was GT and worked my tail off, I graduated with a 3.2 in Economics. Had I attended a lesser school, I would have likely gone pre-med and wound up probably attending an Ivy medical school. I half-joked about this with my sons' pediatrician, who went to Yale and Harvard Med, and he concurred - that I probably could have done quite well at Yale or Harvard for med school even though I couldn't come close to cutting it in pre-med at Cornell.

If you're considering post-grad work, it may pay to go to a top research school that isn't as competitive as the Ivies.