As someone else posted, private schools are free to charge whatever they wish. HOWEVER, not all students attending elite ivy league schools are rich kids nor are they necessarily paying anywhere near the published tuition -- and this is where some of that "30k/year or 40k/year" goes.
My younger daughter got her BS at SLU and MS at UAB, paid for thru scholarships (pre-TOPS), part-time jobs, and mom/dad. However, she wanted and in her field needed a PhD. She investigated various programs and schools and ultimately decided that the best program was at Brown University in Providence, RI. BU's published tuition was ~$45K per year for what was expected to be a 4-yr program, and one of the stipulations was that the student was not allowed to work outside of their studies. Fortunately, BU invited my daughter to attend, waived all tuition and fees, and provided her with a stipend of ~$20K/yr. She now works as a research scientist for a major drug company in Seattle. I'm certainly grateful for those folks who did in fact pay full freight for their kids, because I really would have struggled to fund that degree(!)
