wikipedia) will nearly double in value by 2016, predicts the Boston Consulting Group (allthingsd.com). They expect that the compound revenues of Internet companies will grow from $2.3 trillion in 2010 to $4.2 trillion during this period.
How boring! This would mean just an annual growth rate of around 10 % (including the compound interest effect). You can do this calculation easily here (.moneychimp.com/calculator).
I reckon this alleged growth rate is way too low. Leading Internet companies like Google, Amazon, eBay, Netflix, Facebook, Twitter, Tumblr, Baidu (China), Yandex (Russia) and others are growing at least 20% annually. And there are many startups and copycats which add to the growth. The Blog Techcrunch sees a "cambrian explosion" in startups which are offering software & services for Internet users (techcrunch.com).
You also could count Apple (revenue growth around 70%) as part of the Internet economy - a least partly. iPhones & iPads are used mainly for surfing the World Wide Web and the Californians are expanding into the huge download-markets for music, films, games and books via iTunes, iBooks et.al.
The prices for tablet computers, smart phones and other internet connected devices are rapidly shrinking - thanks to Moore`s law (wikipedia). These means that billions of people in the emerging markets will get affordable access to the Internet. The combination of globalization & technological progress could lead to an explosion of global use of the Internet.
And more and more consumers and companies are storing their data on the Internet or are using external IT-services (cloud computing) (wikipedia) to save from investing in expensive hardware & software. For instance Amazon.com has or will open data centers in Brazil, India and Singapore to offer cloud services to the fast developing regions.
All these developments should add up to an annual growth rate of at least 20%. Using the compound interest calculator again I get the number of $6.9 billion. If I act a bit more optimistic and dare a growth rate of 25% (in the case that the alleged explosion in the emerging markets will be realized) then the number jumps to $8.8. This would mean almost a quadrupling of Internet fevenues. Time will tell!
Disclosure: I hold stocks in Amazon.com, Apple & Baidu.