I addressed that below:

it seems to me that retailers currently have margins that competition could eat into, but doesn't. If one of the factors keeping margins above epsilon is the amount of money people are willing to spend, then an increase in that would presumably also increase margins.

Also consider that retailers do in fact have different prices. Instead of Sainburys raising prices, we might find Sainsburys starting to get edged out by Waitrose. (This feels sketchy to me, especially since it's least likely to happen in poor areas, and I'm not about to argue for it specifically. But I do want to suggest that prices can rise from factors other than "retailers decide to raise prices".)