Yes, but I would guess most teachers don't actually figure in all the potential expenses that come up, when setting their tuition rates.

How does one run a business without calculating expenses before setting prices?

By becoming a "hobby" teacher.

I understand what you are saying, but I still want to stress strongly what I see as "professional". First and foremost, the teacher has to have skills and knowledge to impart, and know how to bring them across. In other words, he or she has to be able to teach effectively, and make the effort to do so consistently.

A teacher who knows how to make money and run a business is not, in my view, a professional teacher due to that fact. The person may know very little and have few skills, but have a good business sense. Conversely, a teacher may be excellent at teaching, but have a poor understanding of teaching. That teacher in my view is not a "hobby teacher" - just a poor businessperson.

Of course someone who teaches excellently but can't run a business won't last long, but might be able to keep on teaching if the family income is carried by a spouse. So they could run it like a "hobby teacher" -- maybe only teaching part time, charging less than everyone else. In the sense of how they run their business, it's like a hobbyist.

In every profession, not just music teaching, one must know the subject matter. It is a given. What is usually overlooked, especially in the arts, is how to connect with the student. Obviously, this is not more important than the subject matter, but it isn't less important, either. Make no mistake about it, if you cannot connect with the student, all your brilliance and training is for naught. You're no more effective than the teacher with only a high school education.

The business leg of the tripod is rather odd. An artist who cannot manage his personal affairs or run his business is soon out in the cold. What good is that?

All three elements of teaching are needed: knowing the subject matter, knowing how to teach (connecting with the student), and knowing how to run a business. I think we're on the same page.