The answer probably depends upon how much extra length was left when your current cable was installed. If it is long enough to reach down to the new position of the derailleur, then you're good. If not, then you need a longer cable.

As for price, I typically pay around $6, I think, for Jagwire stainless steel inner cable, which is what I like to use. I've seen galvanized cables go for a couple bucks each.