MRC is basically the greatest distance per kg fuel.
LRC is approximately 99% of this distance and is generally a more stable cruising speed than MRC.
Now lets look at Cost Index, this is designed to save MONEY, its a trade off between the aircraft cost and fuel. In our case fuel is cheap so we should fly as fast as possible, using more fuel and saving time!
So i can truthfully say that in our theoretical case, LRC saves more fuel than Cost Index!!!!
For a reference, look at the top of this thread for the J_T list of useful sites, then look for the "Airbus, getting to grips with Cost Index"...
Mutt