A very interesting story has surfaced at ShiftyJelly about what it means to a developer who gets their app featured as the Amazon Appstore Free App of the Day. Clearly, the free app of the day is a move by Amazon to increase the traffic to the Appstore in hopes of selling other apps as well. You might expect that the developer that offers the app for free gets some payment out of the deal, but that would not be correct.
Since Amazon makes no money on the app, it pays no money out. For some apps that might not be a big deal, the hope is that the exposure will help the developer sell more copies of the app after it runs as App of the Day. The ShiftyJelly app that was featured as the Free App of the Day was Pocket Casts. According to the devs they would have made $54,805.14 from their 20% of the app sales had they actually been paid for the 101,491 copies of Pocket Casts that were given away. Instead, they got nothing.
The developers also say that the two weeks after the promotion that they were moved to the Appstore main page Amazon cut the price of their app to 99 cents costing them money again. In the case of Pocket Casts, the app uses a server to parse podcast feeds and the new influx of free users meant that they had to buy new hardware and maintain that hardware. In the end, the Free App of the Day deal cost the developers money. After the promotion ended, their sales went back to the same levels that were seen before all it started. The only difference is they have more expenses as a result.