Economies of scope created AWS

Amazon Web Services is one of the biggest success stories around.

Less than a decade old, ... Cloud computing — remote computing, or web services, as cloud computing is sometimes called — has been so wildly successful that it’s increased the pace of technology innovation, the rate of technology adoption, and the volume of data in the world by many fold. Today mobile startups can go global in a snap, ...

Like many innovations, it's began with a problem, that it took too long and too much effort to plug "merchants" (sellers who use their own supply chain to fill orders) into the Amazon platform.

Providing a solution for Target, for example, one of Amazon’s early merchant.com deals, was “far more painful than we thought it would be,” .... 

According to the book Machine, Platform, Crowd, Amazon stopped customizing solutions for each new merchant on its platform by "hardening" its API's, developing a standardized and well documented set of protocols that essentially decoupled parts of the web platform. For example, they separated back-end data from the presentation layer so that their merchant associates could control the consumer interface without creating more work for Amazon on the backend. Customers who used the new API increased conversion rates on their web properties by 30%.
 
Initially, hardening the API's created more work for Amazon, but when they had finished, they realized that they had a reliable, world-wide, web infrastructure that would enable developers to build their tech infrastructure on top of Amazon's cloud computing platform.  It turns out that there was a huge demand for the service:

First one, then two, then three CEOs declared infrastructure services a top priority and asked Amazon to take a hard look at helping them with data warehousing. It was too expensive, hard to manage, required too much commitment and was riddled with pricey upgrades. It seems in these early days of widespread Internet adoption, a collective grumbling emerged over how much hardware was required to operate at “web scale” — interact globally in real-time with huge user bases. No one had the stomach for the banks of servers they’d have to swallow in order to operate a global online presence.

Amazon continues to "spin off" ideas developed to solve internal problems, like "API Gateway, ... a tool for creating, publishing, scaling and securing APIs. The idea is to let enterprises get the same advantages from using APIs as Amazon does, thereby paving the way for faster development and innovation...":

"Inside your company, if you're able to offer your different services via hardened APIs that are well documented, it frees up all the other teams that want to consume your services, to use those just as building blocks, as if they're external services," Jassy said. "Once we got into that mode inside Amazon, it dramatically changed the speed with which we were able to innovate."

References:

• Andy Jassy's Trillion Dollar Baby
• Andy Jassy, Amazon's $6 billion man