It’s possible that Tony understands this better than I do, but I have to say that I don’t agree with him regarding “cut down” vs “bring down”. I’m not a native speaker and could be wrong, but this is my opinion:
I consider “cut down”, “bring down” and “reduce” synonyms in this context. None of these words say anything about the speed of the reduction. If one wants to show that the costs are reduced gradually, then one must state it explicitly, by using “gradually” for instance.