Well, I've been working freelance for approaching four years now, and just a few days ago I passed one particular milestone: an attempt to undercut me and 'gazump' work from me.
My client was open and honest enough to say what was happening, and my instinctive reaction to 'justify' my work - my price and my schedule - in the face of competition from a more experienced, bigger hitting campaigner, was, initially, overwhelming.
However, I calmed myself down, took a long hard look at what they were offering and what I was offering, and came up with the following statements that were useful to me in this situation, and hopefully will prove useful in future situations. (This situation, surely, is only the tip of the iceberg in terms of what hazards lie ahead.)
The way I work is the way I work. The values that I have are a part of what makes it my work. I can't work how somebody else does, and that is a good thing.
The value that I place on my work means, generally, that somebody else will always be able to do the same work, quicker. This is neither a good nor a bad thing, it's just different.
Different people (clients) value different things. Of course, there is the person out there who can do all of i) cheaply, ii) quickly, iii) brilliantly, but that person isn't me. Don't sweat about that too much.
The fee that you charge is reasonable / going rate for the work and the talent and the expertise that you're bringing. Remember that.
Relationships do matter, and if your client really, really wants to take their business elsewhere because they want a better (or a different) relationship, as hard as it may be knowing that, it means that you will have to work harder in the future, to maintain that relationship.
Relationships do matter. If you've invested in that relationship and the client values that relationship, another professional coming along and saying, 'Hey, I can do it quicker,' isn't necessarily going to swing the deal. Remember that.
In this particular case, I didn't even have to utter a word of 'justification', which is just as well really, because my work - anyone's work - should speak much, much louder than any words you can use to describe it. So it proved in this case. However, I know that there will be other instances where all the above the statements are true and the client still goes elsewhere. That is the game that is played and, when the time comes, I'll have to learn to it accept; be a bit mad about it, yes; but move on from it, and work past it.