If you are a graphic designer do not fall for this trick. Because you want to know something this is a very old trick. The trick is that the person who told you this they are wanting something done for nothing. Them promoting you is just a way to tell you want you want to hear.
The best thing that I would do is to tell the person no. If you are doing work for them and you know your work is valuable then you should be getting paid. But you have to have the work to show. By that I mean you should have a collection of your work “a portfolio” that showcases your skill.
But if you do happen to fall into one of these situations and the client does not agree to your quote you can do one or two things. You do not want to discount your work. Just think about it for a second. How valuable would you find a graphic designer who always gives people discounts? Not very valuable.
Now how to do with the situation of clients who do not agree to your quote. The mentality of full price or free is a good one. Taking this approach can be very defeating. By defeating you can feel as if you are being taken advantage of with the project. If that does happen with the client you should just go ahead and fire them.
Another thing you can do is just say may be later on we could have the opportunity to work together. The situation is very simple, plain and straight to the point. But if the make the conversation about some cheap design service then they are not serious about their business or project.
So learn how to deal with the people who will promise a lot but do not deliver. There is a lot of those people out there. They will say they are going to do something but then they never will do it. I tend to just search if people are actually following through with what they say. I rarely see that being the case.