I'd thought that price fixing was when huge companies like breweries, supermarkets or oil companies get together and agree to charge fixed prices so they avoid getting into a price war. That way they agree not to compete with each other, but rather to divide up the pie amongst themselves.
Now THAT is unethical.
What most of us do is to decide on an amount that we need to charge in order to earn a decent wage and give the customer choice whether to take it or leave it.
If your price is very similar to my price it just shows that we both value our time and effort the same.
That is perfectly ethical.
Anyway, I don't believe that price comes into it a great deal with the best customers. It's whether they like and trust you or not.