Just two nights ago I saw a very interesing short documentary on this subject. It is not just the elk, and other game, wolves kill to eat that is causing problems. It are the animals the wolves harrass while trying to kill just one. Elk, in particular, are spooked and chased to often they work off their fat stores which allow them to survive cold, harsh winter conditions. If that fat is worn off, which happens when wolves are around, the elk do not survive the winter. That is what is reducing elk and deer populations and harming the genetic quality and reproduction rate of the survivors.
I favor total wolf eradication.