Part II: do a very good job, which means taking the problem off their hands and solving it completely. Folks contract out work because its a thorn in their side; eliminate the thorn, without becoming one yourself.
Then, when they have another thorn, they'll think "That contractor worked great before; lets use them again". Raise your rate 10%. Repeat.
Then, when they have another thorn, they'll think "That contractor worked great before; lets use them again". Raise your rate 10%. Repeat.