Amateur Instructors

How do we assess pricing?

As a rising senior at Brandeis University studying Economics while playing violin on the side, I find myself with more and more violin lesson requests. A little about my mindset:

• I am in no way a professional musician or even considering myself to be one.
• I choose to play violin for fun.

 When I get lesson requests to teach violin, I try to determine what is a "fair" price both for myself and for the student. During the school year, I taught basics and fundamentals to two beginner students in third grade at $10/hr. My peers, parents, and friends urged me to raise the rate, but I did not think my commitment made a higher price worth it.
Throughout the semester, however, I found it to be more enjoyable to teach the student who was more genuinely interested in learning violin. It didn't matter at all to me that I was getting only $10 since it made me happy that the student wanted to learn. On the other hand, I would have wanted to impose a higher rate to teach the other student since my job was seemingly 'harder'.

These considerations make it difficult to determine how to price instruction. A violin teacher of mine from the New England Conservatory Preparatory School once said, "pay what you think is fair". Should this be from the perspective of the student and parent or should it be from the point of view of the teacher's time and their personal accomplishments?