This is a story I read as a child in the early 80s, very likely a short story in a collection and not the first story in the collection. I don't 100% remember the name of the hero, but I think he was called Chris.
Chris is a young boy in a future society who lives on the lowest level, Level 3, with his parents where they lead a middle-class life. Chris asks his parents questions like 'Where do the spoons come from? What happens if we lose one?' which they have no interest in - 'They came with the apartment'.
One day Chris spots two scruffy boys a little older than him in the corridors, and when they see him they dive into a garbage chute. Curious, he follows them down the chute onto Level 4, a level he didn't know existed. The boys aren't there, but he's quickly spotted by two men in uniforms who shout at him, and to get away he dives into another garbage chute that takes him down to Level 5. This is a dark factory where they deal with the garbage from the levels above.
Chris is grabbed by the supervisor who listens to his story then rounds up all the workers. He asks Chris to pick out the two boys that he saw on level 3, which he does. The supervisor orders two men (by surname) to 'process' one of them. That one is carried away screaming and (it's implied) fed into one of the grinding machines and killed. The supervisor thanks Chris. Chris asks the supervisor how he can get back to his parents on Level 3, but the supervisor tells him he can't – he works on Level 5 now.
Thanks for any pointers!