A judge says Apple fixed e-book prices. This chart shows how they did it.

A federal judge has ruled that Apple violated antitrust law by helping five of the nation's six largest book publishers conspire to raise e-book prices.

Judge Denise Cote spends almost 100 pages describing how Apple orchestrated a coordinated change in the e-book pricing model. But the effect of Apple's campaign can be summarized with this chart:

Before 2010, the e-book market worked on a "wholesale" model: Retailers paid a fixed price to publishers and then were free to choose any retail price they wanted. Amazon had doggedly insisted on a $9.99 retail price for new releases, even selling some books below cost to build up the market for Kindle devices. Publishers hated this strategy because they thought Amazon was cannibalizing the market for hardback books and setting a precedent that e-books should never cost more than $10.

Seeing an opportunity, Apple got five of the six publishers to agree to an "agency model," where publishers set the price and Apple got a fixed percentage of the sale price. And Apple's contract with the five publishers included a "most favored nation" clause, stating that if Amazon offered books at a lower price, the publisher would match that price on Apple's e-book store.

The fact that five of nation's leading publishers had all accepted this "most favored nation" clause greatly strengthened their bargaining power with Amazon. Each of them gave the Kindle maker an ultimatum: accept an agency model, and higher prices, or Amazon would lose access to the publishers' books. Amazon would have refused if any single publisher had made this demand. But with five publishers making the same demand simultaneously, Amazon was forced to capitulate.

The result: a sudden spike in e-book prices. The five publishers labeled A through E signed deals with Apple in January 2010, and by April all of them had forced Amazon to accept prices that were $2 to $4 more than they had been previously. The largest publisher, Random House, did not cut a deal with Apple (and, therefore, wouldn't be charged with antitrust violations), and its e-books didn't get more expensive in early 2010. Smaller publishers also didn't see a sudden price increase in the spring of 2010.

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