This is a strong topic. While there is no mention of wealth and material privilege in Jackson's short story, I think that a clear case can be made that the focus on the narrative is the presence of "insiders" and "outsiders." The "insider" in Jackson's story is the one who holds political and social power. Old Man Warner, Mr. Sommers, and Mr. Graves would represent the privileged positions of the insiders. They have political power in the village because of their status in the village. It can be assumed that they are relatively wealthy, or well off. They are the insiders because of their authority figure. In a larger sense, Jackson merges most of the village with the "insider" status. The condition of being an insider is what affords the individual to have power, relative wealth, and authority in the process of stoning.
At the point of drawing, the members of the village enjoy the relative equality of condition that permeates the hamlet. Yet, when a name is drawn, they become the outsider. The "rules" that are constantly referred to are ones designed to "fairly" assign who is the outsider. Tessie Hutchinson is that outsider. She is not necessarily poor and is not a social outcast. In fact, she is shown to be quite the opposite. At the start of the drama, she is a part of the "insider" group. She rushes to get "her place" in the drawing, and as she engages in banter with other members of the community, it is evident that she enjoys the perks of a particular social condition. It is only when her name is drawn that she is "the outsider." Her protests about how "It isn't right" or "It isn't fair," is a reminder of how much of an outsider she actually is. In this condition, Jackson designs the social configuration of the village to be one where the insiders are designed to exist at the cost of the outsiders. Those who are on the outside are the ones targeted. Status, wealth, and power are all constructed based on this dynamic.