Akaky's worn out old cloak is the objective correlative of his identity, his belief - his being. It is dull, cold, and easily permeable by the North wind (symbolizing change) - it is weak and lacks assertion. His life, his everyday life under that coat is drab and each day is same as the day before or the next day to come. The narrator ruthlessly describes him as "a horse to a mill", who could not stand up to anything challenging. The narrator describes a certain time in his life when certain officer desirous of rewarding him and paying "attention" to him asked him to do a little more than copying, i.e. change heading and some words in an already concluded report! Akaky failed the test and the author writes, "After that they let him copy on forever" (Gogol 4). Thus, the narrator describes him as a man who "indulged in no kind of diversion" and he was "content with his lot" (Gogol 5). He had a vegetative existence and trivialized him further by saying, "Having written to his hearts content, he lay down to sleep, smiling at the thoughtof what God might send him to copy on the morrow." (Gogol 5)
The narrator, like the teasing officer...
But, when it became a necessity, Akaky compromised and saved more to cater to a "new" cloak - his new identity. The narrator almost sympathizes with the hero when he says that, "to tell the truth, it was a little hard for him at first to accustom himself to these deprivations." Here, the narrator's comic tone stings as the reader understands that actually Akaky is a poor man in Russia, who cannot afford to have an identity. He has to remain amorphous and the little choice he is granted becomes a life-changing experience for him. Hence, the comic exaggeration is necessary to hold such a trivial incident under spotlight, without which Akaky's whole life would go to a waste and it would not even rise up to a tragedy!
Akaky's new cloak becomes the only one reason in his life to add to the firmness of his character, it makes him lively and ultimately he sets "himself a goal" (Gogol 13). The narrator comically describes his discussion with Petrovich as a "conference" that he indulged in every month, and after a hard labor and forced savings from his meagre livelihood Akaky affords a new cloak and a new identity of a man, who makes a choice for himself. This trivial addition to his life imparts a new mood and an "internal satisfaction" (Gogol 15). Akaky even drinks and rejoices the attention that his new cloak helps him to get.
The cloak consumes whatever identity he had and takes on a new persona - the loss of which leaves him bereft of his old identity and makes him a ghost. His burial, like his birth, was done out of "necessity" and a pine coffin was ordered - only because its cheap (Gogol 24). Thus the narrator describes with tragic humor that Akaky died uttering the most violent curses (Gogol 25), which