Don't bother trying to compete with others who undercut the market price. There is a need for all prices of care. If you run a quality program, then charge accordingly. Don't undervalue yourself!
Quite often the ones that undercut the price are running a sub-par program/not following the laws/not declaring income etc. Not always the case, but more often than not.
If you're just starting out, you might go $1-2 dollars a day less than the norm to build your first couple of clients, and then come up to the average as you take on more clients.