When I first started working for myeslf, I thought it would be a good idea to charge lower than my local competition. This plan back-fired.
Most people are looking for a deal, but at the same time are expecting to pay an average rate. When you charge at a lower rate, I feel the customer believes you will overcharge on materials, or try to sell them something they dont need to make up the difference.
If you want to attract customers over your competiton, I have found that offering other incentives work better than a standard lower rate. Right now, the highest rate in my area is $75 an hour, the lowest is $60 an hour. I am at $70 an hour but provide free estimates, senior discounts, military discounts, no overtime or weekend charges, $10 off first service call coupons, etc.
As Roger stated, make money, but also make a happy customer base. I have a higher than 50% second job return on average with my customers. This works out for a lot more income than a single overcharge service.