That is less about inflation and more about pricing power. An Egg McMuffin is a low-grade foodstuff in one community (probably higher income), but a "treat" or extravagant breakfast in another (probably low income). The Egg McMuffin has far more pricing power in Detroit than it does on Rodeo Drive.

This happens with things like Medium Ground Beef as well. But T-bone steaks can be quite cheap in lower income areas, and massively overpriced in more expensive parts of town.