That’s a facile assumption, but I don’t think it’s right. Per each school’s most recent Common Data Set, 44.8% of Amherst’s students are full-pays; at UMass it’s 43.5%. Of course, with a higher sticker price at Amherst, need-based financial aid goes higher up the income scale, so a lot of students who would be full-pay at UMass would get need-based FA at Amherst College (if they could get in, of course; I’ll readily acknowledge that most students at UMass couldn’t get into Amherst, but that’s a separate issue, and not the point turtle17 was making in claiming that LACs don’t get more applicants because they’re too expensive).
More to the point, here are the average net costs by income bracket, per the US Dept. of Education College Scorecard:
Household income – average net cost
$0-$30K – UMass $11,064, Amherst College $3,700
$30K-$48K – UMass $12,008, Amherst College $4,840
$48K-$75K – UMass $15,611; Amherst College $10,759
$75K-$110K – UMass $21,127; Amherst College $20,406
$110K+ – UMass $24,338; Amherst College $40,438
So it’s really only among the more affluent, at household incomes of $110K and up, that Amherst College becomes more costly. For those at or below the median household income, Amherst College is significantly cheaper, on average, though of course YMMV in individual cases depending on, e.g., merit scholarships at UMass.
And not only is UMass less generous in awarding need-based FA, but the composition of the FA awards is dramatically different. At UMass, the average need-based scholarship and grant award in 2016-17 was $9,905 and the average need-based loan was $4,568, while at Amherst College the average need-based scholarship and grant award was $50,380, while the average need-based loan was $478. In short, the main reason Amherst College grads come out of college with less debt is not because they went in with higher SES, but because those who didn’t have high SES just didn’t need to borrow very much, since the college’s generous need-based FA policy mostly took care of them through grant aid.
Also revealing are the aggregate figures. In 2016-17, UMass-Amherst students received $105.7 million in scholarship and grant aid from all sources (including $89,7 million in need-based aid and $16 million in non-need-based scholarships); but they took out even more in loans ($117.3 million). Amherst College students received $54.7 million in scholarship and grant aid, almost all of it ($54 million) need-based, but they took out only $3.4 million in loans