I have a Masters degree in performance and I teach private lessons as an adjunct at a local 4-year college. I’m only paid $30 per hour. Just goes to show you how vastly different academic pay can be from self run studio teaching. It’s only my side job though, so it doesn’t bother me too much. There might be other factors that weigh into that $40 she is charging. Is she running her own studio? That $40 also has to cover expenses to run her business and some of it will go to taxes, so she may not really be seeing all of that as true “money in her pocket.” Although even if she is basing your $15 per hour rate against what her true “take home pay” per lesson is, it seems like she might be low balling you just a bit, especially if you live in an affluent area where higher lesson fees are the norm. Hopefully that all made sense.