As a freelancer, you have made this experience more often than you liked to. No matter what you offer and to whom you offer it to. There is ALWAYS someone cheaper. It is like a law of nature. As sure as day follows night each of your offers is doubled by a cheaper one. Keep calm. I know that the other offer is not really cheaper or at least not only cheaper in price. It is more in the way that today’s cartoon depicts:
By the way, we have more cartoons for you here.
Dieter Petereit is a veteran of the web with over 25 years of experience in the world of IT. As soon as Netscape became available he started to do what already at that time was called web design and has carried on ever since. Two decades ago he started writing for several online publications, some well, some lesser known. You can meet him over on Google+.