My rate varies depending on level of effort to do the job, commuting, my interest in the work, etc. I have a spreadsheet of all my commitments that helps me determine the absolute minimum to charge, based on a 40 week year.
I tend to take the advertised rate as a guide to whether I want to even apply for it. If it's too low, I don't even bother. All the while I have the luxury of being picky, I will. If circumstances change, I'll drop my rate if really necessary.