In "A Rose for Emily," who was the author writing for, and to what purpose?

It is difficult to pinpoint a single audience or purpose for most literary works, and William Faulkner's "A Rose for Emily" is no exception. First, it may be useful to think about the narrative voice and themes of the story.
The narrator is a sort of communal "we" representing the townspeople who know (or know of, at least) the title figure, Miss Emily Grierson. The narrative voice reports, in a non-chronological order, the major events of Emily's life, as observed from the outside by the town. The story begins with Miss Emily's death and the opening of her home to mourners. Most of the townspeople have never been in the home before this, and they join in the procession mainly out of curiosity. We then hear some background on Emily's relationship with her father and with the town, in which her family was once important and powerful. Eventually, hints are dropped about Emily buying rat poison and a stench coming from her home. At the end of the story, the town discovers that Emily has apparently poisoned a former suitor and kept his body in a bed where she has seemingly slept with him for a number of years. All of the information is presented in an almost gossipy tone. The townspeople talk about Emily but not to her. Their knowledge of her life is based on speculation, rumor, and detached observation. The narrative voice could be addressing any kind of audience. The reader need only be interested in hearing about Emily's story (while also understanding that the story is an interpretation of the character and not necessarily a factual account).
Purpose is another tricky term that seems related to the slippery concept of authorial intent. Many authors do not have one intended purpose, meaning, or message when writing a complex literary text. However, we can discuss some of the themes that emerge from the story and can infer that some of the purposes may be to have the reader think about those themes. First, Emily and her family are considered a tradition in the town, and the outward respect citizens show her is mostly based on her family's previous influence and standing. Now, the house is decrepit and the family is dying out with Emily's demise. The world around the Griersons has evolved and modernized, but Emily tries desperately to hold on to the past. This is seen in several examples but in none more clearly than her symbolic attachment to Homer's dead body. Faulkner is, in large part, drawing our attention to humans' desire to hold on to what they have, particularly when what they have is power and money. Further, in context, Faulkner seems to suggest a larger message about the South trying to hold on to the prosperous society and economy they enjoyed in the antebellum period. More generally, the story could also suggest how little humans really know about one another's lives or psychologies. The story could also possibly be lamenting the human impetus to scapegoat or exile others who are mysterious or different.