Let the city that can barely fucking run itself corner the grocery market.
Couple retarded things:
1. Why not give the private stores the same benefits you plan to give the government ones? (Because government can never actually compete on a level field).
2. Grocery margins are some of the lowest in pretty much any market. Most of them are hardly above charity if they're mainly selling groceries.
Government grocery stores won't actually be cheaper. They'll just be subsidized by the people who are already peacing out of your shitty city.