It's not that they charge more (though I don't have evidence they don't), it's just that international students almost always pay full price. American students

It's not that they charge more (though I don't have evidence they don't), it's just that international students almost always pay full price. American students may receive financial aid either from the government, or the university itself (scholarship or other aid). International students on the other hand usually don't. They pay full price. They make universities, particularly private ones, a lot of money. I went to a good but not top private college on scholarship. Some undergrad majors such as business and the graduate business school were overwhelmingly international students. The law school is approaching 50% international students.