I have said to people--tradesmen that I have an existing and hopefully future relationship with, and friends/family who are serving as tradesmen--"please don't undercharge me. This seems low. Of course I don't want to get ripped off, but I also don't want to be taking advantage of or trading on our relationship. The last thing I would want is for you to end up feeling taken advantage of."
I've also said, "I want to be able to call you back to fix something if it turns out it's needed, without you feeling that I'm overstepping. So charge me a fair price. Fair to you, and fair to me."
And I've said, "If you feel you want to 'cut me a break' because I'm family or a long-term customer, the thing I'd want you to give me is your very best attention and diligence. I'd want you to so an extra good or extra careful or extra thorough job. THAT is the thing I'd hope for in terms of favored status. But I want to pay you an appropriate amount of money."
I also said to the florist for my wedding, when the bill was something like $350, "Are you sure this is right?" in an incredulous tone. The lady got all defensive about how they were "name" roses, and working on the weekend. I had to interrupt her to say, "No, no, I mean, shouldn't it be MORE? Because you made two extras of this, and ran around doing special stuff with that..." I hadn't actually negotiated price beforehand, so I didn't know--I was expecting $1,000.