This turned out to be one of those rabbit hole questions. The more I looked, the stranger it got. I knew there was prior work on the question -- but I didn't know the magic words Google needed. Eventually I reinvented enough economic theory to connect my simple question to Coase's 1937 (!) theorem, 1970s work on 'the theory of the firm', Brad DeLong's 1997 writings on The Corporation as a Command Economy , and Akerloff's 'information assymetry'. 
Among other things I realized that modern corporations are best thought of as feudal command economies whose strength comes more from their combat capacity and ability to purchase legislators and shape their ecosystems than from goods made or services delivered.
Think of the Soviet Union in 1975.
All of which is, I hope, an interesting review -- but why did I title this 'Strange loop'?
Because I used that term in a 2008 post on how Google search, and especially their (then novel) customized search results, was changing how I thought and wrote. This five year recursive dialog is itself a product of that cognitive extension function.
But that's not the only strange loop aspect.
I started this blog post because today I rediscovered DeLong's 2007 paper  as a scanned document. I decided to write about it, so I searched on a key phrase looking for a text version. That search, probably customized to my Gordon-identity , returned a post I wrote in 2008. 
That's just weird.
- fn -
 Oddly the full text paper is no longer available from Brad's site, but a decent scan is still around.
 There are at least two Nobel prizes in Economics in that list, so it's nice to know I was pursuing a fertile topic, albeit decades late.
 John Gordon is a pseudonym; Gordon is my middle name.
- Gordon's Notes: The Modern Firm - a review 4/2012 ties some of this together. That 2008 paper was a gift that kept on giving!
- Gordon's Notes: Browsing the blog backlist - we need a new app 6/2012. Reading that old blog posts of mine reminds me that we still need a tool for resurfacing old blog posts.