In the story, Half a Day, the author uses this 'grandpa' at the end to create a shocking realization by the reader that what has been happening in the tale is not something that has 'just' happened. In teh beginning of the story, the boy is helped by the father, an older man. But, at the end, the old man is helped by the young boy. This grandpa at the end IS the young boy who has now become an old man.