This seems a very odd question. Hunting Elk is an epxensive proposition for the majority of people. Even up here where I can hunt them every year and very close to home for not much cost, the cost of the rifle and ammo is completely IRRELEVANT. Take three or four tanks of gas at $125 a pop, and even a couple of days off work and the price of ammo doesn't even register. Most guys are spending FAR more than that on their Elk hunts.
My last ten elk, furthest was just under 500 yards, were all shot with a 308, not to save money but I love the lightweight of the LH NULA and it shoots great. I have also shot thew with 300 WM, 7 Rem, 7 RUM, 338 Win, 375 H$H and 45-70, because that was what I happened to be hunting with that year. Pick a gun that suits your fancy and go kill elk.