One particular approach that can be taken when discussing the characterizations offered is the idea that economic conditions have a profound impact on how people view reality and one another. Roger snatches Mrs. Jones' purse, presumably, because he is poor. At the very least, he is economically challenged. It is with this in mind that his characterization takes on such a strong manner in the short story. Roger's social and economic challenges enable him to be receptive to the caring that Mrs. Jones gives. The cleaning, the food, and even the discussion that he shares with her impacts him profoundly. Presumably, Roger does not receive this in his conditions of being in the world. This impacts his characterization because he is seen more than just a kid who makes a wrong choice. The condition in which he lives helps to guide him to make decisions that don't play a role in his development as a human being.
For Mrs. Jones, the characterization offered is a challenging one in terms of finances. She alludes to this in her discussion with Roger that there are things that she has done in her life because of the lack of money or for money that she regrets. This bring a wider dimension to her characterization. It is one that Hughes is brilliant in bringing out, but one into which there is no delving. He leaves it to the reader to understand that her own condition is one in which financial hardship has been evident. It is for this reason that she responds to Roger the way she does and for this reason that she is who she is. Through the lens of financial condition, Hughes is able to develop the characterization of both characters in the short story.