Ignore people like that, they have a market, its probably not the market you want. Just offer your service at a realistic rate and you will get much better clients and have time to sleep and do other things. We all know that generally the cheapest is not the best and if I was searching for a tradesman to install a new shower I am not going to go with the cheapest because chances are the quality will be poor and I would rather pay more and get the job done right the first time.
When starting a business it is easy to focus on the competitors and they will do you head in if you are not careful. Know about them, listen to what the market is saying, but don't give them air or let them worry you. Concentrate on what you bring to the table.
If you plan to advertise in the same paper you could sell your services differently you might say that you are not cheap but offer high quality fast service (or something different to what the competition are offering).