A friend told me how his father had been in a similar situation. He was offering a superior service that was, in many cases, lower than what the prospects were already paying. After being turned down repeatedly he finally asked why. He was told that he couldn't possibly be able to deliver the quality promised for the price he was asking. The low price created a perception of lower quality-- lower than what people were willing to accept for that price. So, they'd tell him it was too expensive or they just weren't interested.
I doubled my rate and not only got more work but better work. You could try it. The worst that will happen is people will still say no and you can always let them negotiate down a bit. Still, like others have said, it depends on the going rate where you're doing work.