Answer
The word "author" is the simple subject of the sentence.
and Explanation:
The subject of a sentence is its topic - what the sentence discusses.
In the sentence "The world-famous author will autograph her books at the mall this afternoon," the complete subject is "the world-famous author". A complete subject includes the simple subject and any modifiers accompanying it. In this case, "author" is the simple subject, that is, the main word that refers to what or whom the sentence is about.