Brecht made a crucial change from the Chinese play which was his source. In it, it is the child's birth mother who lets go and wins custody of the child. Near the end of the prologue, the Singer says that this is an old story of Chinese origin, but with a modern re-write.
The play is sometimes played without the prologue, and it was always played that way in the US during the McCarthy era. (The first US production to include the prologue was in 1965.) There is some dispute about how integral the prologue is to Brecht's conception of the play. Some claim that he regarded it as an integral part of his play, and it was present in the earliest drafts. Others claim that it was only included in later drafts. However there is agreement that he originally intended to set in the 1930s, but later updated it.
The setting of the play is clearly Georgia in the Caucasus, although it is described as "Grusinia" (a Russian variant name) in the main play. Most of the characters have Georgian (or Georgian-like) names, and Tiflis and the poet Mayakovsky are mentioned in the prologue. However the city where much of the action takes place, Nuka, is in modern Azerbaijan, although it was under Georgian rule for a time in the Middle Ages. There are also Iranian elements in the play, including the name of the character Azdak, who says he comes from there.
Brecht did not necessarily intend his play to be a realistic portrayal of either contemporary or medieval Georgia. Even in the Soviet Union, some people found it more German than Russian or Georgian, and pointed out that it did not accurately portray the decision-making procedures in Soviet agriculture.