MIT subsidises all undergrads. It costs them about $70,000 to educate them, the full sticker price is $45,000. They can do this because they have an enormous endowment. I don't know about funding of grad students.
I'm skeptical of this claim. I started college in the 80s. The cost of a year at my private seven-sisters college went from 10K the year before I started to 20K the year I graduated. So it doubled in five years.
Every year, they told us that "tuition doesn't begin to cover the cost of your education." They've been repeating that line ever since. With the exception of the last couple of years or so, tuition increases have risen at more or way more than the cost of inflation, so I have a lot of trouble accepting that tuition hasn't caught up with actual costs yet.
What I suspect is really going on is that the "whole cost of your education" claim is referring to the costs of the new dorms, the new rec center (with lazy river!), the new horsey barn, and all those shiny new research buildings. As for those buildings, undergraduates may or may not even
enter them during their four years, much less make use of them beyond a possible summer gig or a fourth-year project.
That and the colleges are gouging parents, and in many cases, students through non-dischargeable-even-in-death student loans. In other words, they raise tuition because they can.
So tuition at MIT is $43,720. If a student takes 8 classes in a year (4 per semester), this means that each class costs roughly $5,500
per student, or $110,000 for 20 students. I have trouble believing that even a course in cell culture or molecular biology could cost that much, let alone general chemistry or...a math class.