(My answer to this question at Quora.com)
Micah was the youngest of four prophets of the Hebrew Bible who lived in the latter half of the 700s BCE (the others being Hosea, Amos, and Isaiah). The similarities of language (the use of tongue twisters, alliteration, rhetorical questions) are due in part to the fact that they are contemporary, and in part (according to certain Talmudic commentaries) that Micah was one of Isaiah’s disciples (limudim) which case, that would explain it.
A typical example of similar wording (more compelling in the original Hebrew than in the English translation) is the following:
נִצָּב לָרִיב ה’ וְעֹמֵד לָדִין עַמִּים; בְּמִשְׁפָּט יָבוֹא, עִם-זִקְנֵי עַמּוֹ וְשָׂרָיו; וְאַתֶּם בִּעַרְתֶּם הַכֶּרֶם? גְּזֵלַת הֶעָנִי בְּבָתֵּיכֶם? מלכם (מַה-לָּכֶם) תְּדַכְּאוּ עַמִּי, וּפְנֵי עֲנִיִּים תִּטְחָנוּ?!
THE LORD standeth up to plead, and standeth to judge the people. / THE LORD will enter into judgment with the ancients of his people, and the princes thereof: for ye have eaten up the vineyard; the spoil of the poor is in your houses. / What mean ye that ye beat my people to pieces, and grind the faces of the poor? saith the Lord GOD of hosts.
כִּי רִיב לַה’ עִם-עַמּוֹ, וְעִם-יִשְׂרָאֵל יִתְוַכָּח; עַמִּי, מֶה-עָשִׂיתִי לְךָ, וּמָה הֶלְאֵתִיךָ? עֲנֵה בִי!
Hear ye, O mountains, the Lord’s controversy, and ye strong foundations of the earth: for the Lord hath a controversy with his people, and he will plead with Israel. / O my people, what have I done unto thee? and wherein have I wearied thee? testify against me.
But there are many differences between the two—primarily due to the fact that Isaiah was of a high-ranking family in Jerusalem, while Micah was from a modest background from the small peripheral town or village of Moreshet, and thus avoided, for example, addressing issues of international relations or political policy.