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Why can't I offer my ebook for free?

It depends on whether or not you are in KDP Select, obviously, which gives you 5 free days for each 90 day period. But I don't think that is the question you are asking. Here is the correct question:

Q: Does Amazon offer an option to distribute free books?A: Maybe.

If you have a print version of a photo book, then you may want to offer a free ebook version with tiny pictures to tease the reader into buying the print version. If you have a fan fiction book, you may want to distribute the book in print at cost, and free as an ebook. If you want to release an expensive book free for a few weeks to encourage reviews, then you may

Amazon is not in the business of publishing free books. Google has a service that you can use, called Google Books. And you can also release your book at Smashwords for free.

What most people do is offer a CreateSpace book for say $15, then in the description announce that for a limited time the ebook is available at Smashwords for free. Then, after a few weeks, pump up the price both at Amazon and Smashwords. Now cross your fingers and hope that you did not just give away all the copies that the market will consume. Don't forget to log back in to CreateSpace and change the description to eliminate the promotion.

How do people get their books down to $0.00 without using KDP Select?

Authors send an anonymous note to Amazon that they just purchased a book at Amazon, and later discovered that at xxx.com, it is free. Amazonthen lowers the price down to that of the competition, even down to $0.00

This is not worth the effort, and you may find that Amazon refuses to lower the price. The best option is simply to promote the free ebookversion at xxx.com (in your print version description), and let Amazon make a few bucks off the print version. I do this, and it works

* Jon (13 April 2012) https://kdp.amazon.com/community/message.jspa?messageID=249426