I agree with all the factors listed in post#1.
But also add: vanity pricing
How to Raise a University’s Profile: Pricing and Packaging
http://www.nytimes.com/2015/02/08/education/edlife/how-to-raise-a-universitys-profile-pricing-and-packaging.html?_r=0
I think there’s a perception now that if a private school doesn’t charge a high sticker price, then you’re getting Walmart goods.