The Illusionist

The story is set in 1959 and is told with only a few brief snatches of dialogue, much of it in Gaelic. A down-on-his-luck illusionist (known by his stage name, "Tatischeff") watches his popularity and employment in Paris dry up. He packs his meager belongings and props, including an ill-tempered white rabbit, and moves to London. There he finds himself as the irrelevant act following a popular rock band. Despite his wounded pride, he adopts a nothing-to-lose attitude and continues plying his trade at yet smaller gatherings in bars, cafÃ©s, and private parties.
He accepts the invitation of a drunken party patron, taking a long, slow journey to a remote Scottish island (Iona in the Inner Hebrides). The small village's pub has only recently been wired for electricity, and he and his rabbit are appreciated for a time. Living modestly in a room above the pub, the illusionist encounters a young girl named Alice who is captivated by his otherworldly abilities and kind gestures, including a gift of new red shoes. Competition from more modern forms of entertainment follow the illusionist even to this idyll, and he soon moves on.
Alice believes the downtrodden performer possesses genuine supernatural powers, and follows him to Edinburgh, where he performs at a modest, out-of-the-way theater. They book a room in a rundown guest house favored by other fading performers (a trio of acrobats, a clown, and a ventriloquist). The illusionist sleeps on a small couch and the girl keeps busy by cleaning and cooking food that she shares with the neighbors. The girl's affections even tame the rabbit, but the illusionist's increasingly meager wages, lavished on a series of gifts for Alice, lead him to pawn off his magic kit and secretly take on more demeaning jobs. The other traditional performers become similarly depressed and destitute.
Unable to muster the courage to tell his starry-eyed admirer the truth about his fading trade, the illusionist continues giving until he has nothing more to offer. Alice meanwhile discovers the affection of a handsome young man, and once he sees them walking together, the illusionist opts to leave her with money and move on. His final message is a letter that says "Magicians do not exist." Alice subsequently moves in with her new boyfriend. The illusionist releases the rabbit on the verdant hillside of Arthur's Seat, where many other rabbits are seen. He is last seen on a train, where he declines one final opportunity to perform a magic trick for a child by returning a short pencil that the child has dropped, but not replacing it with an identical, but longer, pencil of his own.
The illusionist looks longingly at a photo throughout the film, though it is never revealed to the audience during the film. At the end of the film, a photo appears dedicating the film to author Tati's own daughter. During the final train trip, the illusionist looks at the photo for a last time, and his hand drops down where the photo can be vaguely seen, particularly in the Blu-ray release. It is apparently the same picture of Tati's daughter seen at the end of the film.

Question: What was the object the child dropped?
Answer: A short pencil