Pricing is hard. In fact, I find it the hardest part of being a Valued Artist. Artists have to put a price on the way we express ourselves, which is kind of like assigning a dollar amount to yourself. How in the world are you supposed to do that?
One tempting way to set prices is by figuring out how much time it takes to produce your art, determining an hourly rate, and factoring in the cost of materials. Don't do that. I could practice hopscotch for 10,000 hours, but that doesn't mean anyone will give me money for it.
Your customers aren't paying for the work you put into your art, they're paying for the experience that comes out of it. That means you have to find out what it's worth to enough people that you're satisfied with the income. It's still not easy, but it's a start.
What did I do? First, I started somewhere. I gauged what other pianists like me were charging (and that was the only time I based my prices off others), and set a competitive rate. Since then I've continued to offer greater value, so I've been able to require more value in return.
It still stings when you get turned down because you're 'too expensive'. I recently had someone tell me that they had found someone else to play because the other pianist's fee was "more reasonable." Does that make me unreasonable for asking more? No, because I'm worth that much to enough people that I'm as busy as I need to be.
I rarely regret turning down opportunities I'm not excited about, but I often wish I hadn't accepted offers that weren't to my liking (for financial or other reasons). So I make sure to give as much value as possible and ask for a price that allows me to stay busy. That's the best strategy I've come up with. If you have a better one, let me know.