What is the author's purpose of the book? Explain how you know.

Since Tales of a Fourth Grade Nothing is a work of fiction, there is little we can learn directly from reading the story. We should not assume that any of the characters act as a mouthpiece for the author.
Discovering facts about the author's autobiography and reasons for writing is best done by researching what she herself has said about the topic. The first place we should go to research this is Judy Blume's own website. On this site, she discusses herself as a writer in her own words. Since it is her site, she chooses what information to share with us and ensures that it represents her deepest convictions.
First, we should note that she is a professional writer. This means that she writes to earn her living just as a car mechanics repairs cars to earn a living. She was attracted to writing quite early. On one page on her website, she describes how she loved to read as a child and how she enjoyed making up stories in her head. When she had children, she enjoyed making up stories to entertain them. This habit of story telling evolved into a writing career. Her focus on writing for children stems from her own experience as a mother, although she also writes for adults.
This particular book focuses on sibling rivalry, in particular, the way that an older sibling can feel left out or neglected when a new baby arrives. As someone who has a B.S. in education as well as having children herself, I am aware of the conflicts that can occur between siblings. Blume approaches Peter's life with humor, sympathy, and imagination and the family's efforts with their toddler with affection and ingenuity. She says on her website that "Fudge was based on my son, Larry, when he was a toddler," so we can assume that part of her purpose in writing was sharing and expressing some of her own experiences. 
http://www.judyblume.com/