I relay like your idea…
After all because I had nearly the same

But I would give it more features…
X Online Service for the markets where they can register the products with barcode and price
-„POI“ Database with geodata of the markets
-Markets can enter special offers
X Online „Community“ section
-Users can Post reviews and vote for products
-Users can vote for markets / stores
-Users can enter alternate products
X Private section for Users
-You can make your grocery list an search for alternate products
-You can enter an amount of saving and a distance you would go for
So the system could give you a shopping tour
Now to the Phone App
X The App can download your grocery
X You can make a Live price comparison with the barcode
-The app could give you a market / store, it would consider your amount of saving and a distance you would go for
X You can do a live vote for Products and Stores
X You can enter a grocery list
X You can search for alternate products
X The app would use the geodata and GPS