Some preliminary remarks:
I am rather conservative about such question for several reasons such as:
- the canon of the OT was clearly selected with extreme care - much literature was excluded, even some that might be considered beneficial, especially the material in the inter-testamental period (400 BC - 0). That is I trust the ancients that were closer to the events that some 19th century experts who often presumed to know more than those present at the time!
- if a book of the Bible cannot be believed in what it says about itself, then it is unfaithful and should not be part of the canon of Scripture! In the case of Micah, either it was composed by Micah in the 8th and early 7th cent BC or it is not inspired.
- The above does not exclude the possibility that some very minor later editing occurred such as updating the spelling, change of an occasional place name to something that later readers would better understand, etc.
OK, these are general principles; but what evidence , if any, exists that the book of Micah was written by the person it claims at the time it claims? I offer a few morsels:
- Nothing is known of the prophet Micah outside the book bearing his name
- Micah's father is never mentioned suggesting Micah is of rather humble origins
- The fact that Micah only mentions Judean kings suggests that his place and work of ministry was confined to the southern kingdom of Judah.
- I am told that the Hebrew style, while poetical and rhythmical, is rugged, simple and forthright which reinforces Micah's likely peasant background. (A later composition by an educated priest or similar might have used a higher form of Hebrew language.)
- The book of Micah is notable for it frequent figures of speech and puns, again suggesting a hard-working agricultural background.
- A much later composition would make little sense as pseudepigraphal works invariably try to disguise their message about local problems by placing them in the mouths of a much older prophet or dignitary. Micah's message is essential two-fold (a) condemnation of the sins of the people in Hezekiah's time and (b) the glory of the coming Messianic kingdom.
- I am also impressed by the fact that the NT gives credibility to the authenticity of Micah because it quotes Micah as authoritative: Mich 5:2 is quoted by Matt 2:6; and, Mich 77:6 is quoted by Matt 10:35, 36; Matt 23:23, "justice mercy and faithfulness" also appears to allude to Mic 6:8. [Note that Micah 3:12 is quoted by Jer 26:18.]
- The documents found among the Dead Sea Scrolls include commentaries of Micah (eg, 1QpMic, etc) suggesting that the book of Micah is much older than the second century BC and already accepted as canonical then.
Thus, I see nothing in history, the text itself, and other ancient documents that might suggest that Micah is anything other than what it claims to be - a series of prophecies composed by Micah in Judea in the 8th and early 7th century BC, probably a farmer.