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So there is no minimum for teaching a class. It's not done by ranges 10-20= x 20-30 students =y?
Let's say that teachers are getting paid on a per student basis (this astounds me but I have no reason to doubt that you are correct), Does there electricity go up by 10%? Do non-faculty salaries go up by 10% Does the debt service go up by 10%? No. If faculty pay goes up based upon that number students in their classes then that is a marginal cost increase so is fair to be charged back to the AD, but the rest? Not so much. They don't vary by student.
Can we agree on that?
Yes, there are ranges. Fall below the minimum and the class is canceled. 65% of the budget is faculty pay, so in your example, the reimbursement is 65%. (Note: I don't really see the point in doing it this way, since schools pay for general upkeep just based on what they expect in revenue, based on number of admitted students, which is carefully calibrated, so we run into the same problem.)
While departments don't pay utilities, you might be shocked to find out that they do pay for things like office space, furnishing, painters to paint the walls, computers, refurbishing a department owned classroom for new technology: these are not utilities but each department is tasked with paying building upkeep. Just to give a few examples: if I want my office painted without having my Chair sigh at the request, I will sneak in on a Sunday and paint it myself with my money. In order to set up a smart classroom (i.e. computer, screen, projector, lighting) we recently shelled out $75k. A rip off. We hold events for a program we run downtown at a performance venue owned by the folk singer Ani DiFranco. She gives it to us for free. We do this because the only suitable venues on campus are owned by other departments, who charge $700 for a couple of hours. So instead, we shuttle students downtown on university buses for $200 for the events. It is madness. I am only trying to emphasize that almost every cost outside of utilities is paid for by departments according to their means, and that money is doled out according to the number of students serviced. Remove asbestos from offices? The department pays.
Also, note, in some schools (smaller ones) the number of athletes make up a big % of the student body. Say UConn has 600 athletes. That's 3-5% of the UConn student body. Pretty small. At other schools, it is 10-15%. At some of the small privates, 30%.