Gore Vidal is famous for his biting criticisms of modern society. Visit to a Small Planet is a play intended to satirize mid-20th century American society, a society that had lost itself to fear and the belief that a "simpler time" was something that could be reclaimed. Vidal is eager to illustrate the foolishness of the American people by showing their behavior through the eyes of the aliens.
The occupations and social classes of the characters are as important to this story as they would be to any. By providing this information, the author is trying to provide the reader with as information that will shape a reader's analysis of the characters. How a character behaves or how people treat him has to be influenced by every trait the author provides.
Furthermore, as American society is capitalistic, the experiences of people in different occupations and social classes will vary. We are not all alike. Therefore, Vidal's portrayal has to show these differences in order to show an accurate picture of American life.