Under CEO Jeff Bezos, Amazon.com (NASDAQ:AMZN) has shown a willingness to spend money in the short term to grow its business over the long haul. One of the key ways the company could invest in its future, and ensure its best customers have the widest possible access to its products and services, would be to offer a free Fire TV Stick with a year-long Amazon Prime subscription.

The Stick is a set-top box, albeit one that sits plugged into an HDMI port rather than sitting on the actual set, which allows users an easy way to stream digital content including Netflix, Hulu, and Amazon's own Prime Video service to their television screen. 

Giving away the device might sound like a radical idea since the Fire TV Stick has been such a hit that orders for the $39 device placed today on Amazon.com aren't expected to arrive until after Jan. 15. Making an item that is selling well free may seem counterintuitive, but the lure of a free streaming device should attract on-the-fence customers to sign up for a $99-a-year Prime subscription and giving it to current members who request it would enhance their relationship with the company. 

 Fire Stick

The Amazon Fire Stick retails for $39. Source: Amazon 

Prime members spend more
Having as many Prime members as possible is good for Amazon because the company makes more money from Prime members than it does from regular customers. 

Prime subscribers spend almost $538 a year versus the $320 per year spent by non-subscribers, according to a study conducted by RBC. The survey, conducted in June 2014, was based on the answers of just over 2,000 Amazon.com shoppers -- 708 Prime members and 1,357 non-Prime customers. 

"Some 61% of respondents said they've spent more money on Amazon after becoming Prime subscribers than before," Quartz reported. "And Prime subscribers were more likely to have spent more than $200 over the prior 90 days."

The device can be used to keep people on board
While Amazon would have to add this technology to Fire TV Stick, it could make the free devices only work when connected to a current Prime account. If the customer drops Prime, then the set-top box would stop working. That would create a direct relationship between the device and the account. It would also tie people to Fire Stick TV even if they aren't using it to watch Amazon Prime Video.

For example, if a family has the set-top box on its TV and mom uses it to watch Netflix, dad uses it to stream sports, and the kids watch shows on Hulu, dropping Amazon Prime would mean needing to buy another device to keep using those services on the family's TV. That's not a huge barrier, but if the family is getting some benefits from Prime -- maybe using free shipping and watching a little video -- then it tips the scale toward renewing. 

Having a storefront in your best customer's living room is a good thing
Every customer that uses an Amazon product, be it a a Kindle tablet, a Fire Phone, or a Fire TV device has essentially elected to build a little Amazon in their home. Having a Fire TV stick installed in a Prime member's living room gives Amazon a direct portal to its best customers.

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It's not that crazy
Amazon clearly wants Prime members to buy Fire Stick TV, as it offered the device to them for $19 for the first two days it was on sale. It's not such a big leap to offer it for free with a Prime membership and the company could easily make up the lost $39 sale by the increased revenue which comes from Prime members and the enhanced ability to sell to its customers once they have Fire TV installed.

Offering Fire TV Stick for free could make Amazon a major player in the set-top box world. It would also trump the other players in the field and force them to reconsider their pricing. It would likely allow Amazon to add millions of new Prime members and retain a greater percentage of its existing customer base.

Daniel Kline owns shares of Apple and Microsoft. He owns a Fire TV and has pre-ordered the Fire TV stick. The Motley Fool recommends Amazon.com, Apple, Google (A shares), Google (C shares), and Netflix. The Motley Fool owns shares of Amazon.com, Apple, Google (A shares), Google (C shares), Microsoft, and Netflix. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.