the design seems to be flawed. Is really one BUYER supposed to buy at most one AUTHOR? Additionally, in the second paragraph you are mentioning BOOKS (which makes more sense in real world), however there is no table representing this entity.
I am afraid that there is no way to obtain the required information from the mentioned tables only. If the missing tables (BOOKS and SALES for respective entities), it is as simple as comparing the count of BUYERs with the count of rows in SALES (the new one) table with the given BOOK.