The exposition of Langston Hughes's "Thank You, Ma'am" is basically the first three sentences of the story that establish Mrs. Luella Bates Washington Jones as a character and establish the basic setting of the story--11:00 o'clock at night as Mrs. Jones walks home from work alone.
The initiating event, then, is Roger's attempt to steal Mrs. Jones's purse in the fourth sentence.
The resolution comes in the last three paragraphs of the story when Mrs. Jones gives Roger the $10 to buy his blue suede shoes and allows him to leave. Roger is barely able to say "thank you" and never sees Mrs. Jones again.
Both the exposition and the resolution of short stories are essential elements. Interestingly, in "Thank You Ma'am" by Langston Hughes, the exposition is much more developed than the resolution.
The short story's first element is the exposition, which is arguably the most fundamental part of the narrative. It introduces the setting, characters, and situation --information that is essential to understanding the story. The exposition is also an introduction to the main conflict of the narrative. Further, its function is to bring clarity to the narrative, as well as enhance its literary value.
The resolution of a story is the moment when the conflict ends. Many modern stories provide enough information for readers to draw their own inferences as to how the conflict(s) will be resolved.
The exposition of "Thank You, M'am" presents the two main characters, the "large woman" Mrs. Luella Bates Washington Jones and "the boy" named Roger, who tries to steal her purse. This action introduces the main conflict of an adult who respects people and the law and the boy, who tries to satisfy his selfish desires.
In the resolution of "Thank You, M'am," Mrs. Jones, who has taken Roger home with her, fed, and talked with him, then generously and surprisingly gives the boy ten dollars so he can buy the blue suede shoes he desires. With this gift come her instructions not to "make the mistake of latching onto someone's purse "because shoes come by devilish like that will burn your feet."
Mrs. Jones then says that she must rest and urges Roger to behave himself in the future. She closes her door so quickly that Roger can only reply with a quick word of gratitude:
The boy wanted to say something else other than “Thank you, m’am” to Mrs. Luella Bates Washington Jones, but he couldn’t do so as he turned at the barren stoop and looked back. . . He barely managed to say "Thank you" before she shut the door.
Thus, this resolution is one that allows readers to draw their own conclusions about the effect of his encounter with Mrs. Jones and Roger's future behavior.