On aggregate production functions

This reference Aggregate production functions-a pervasive but unpursuasive fairy tale appears in another interesting discussion of Piketty at Crooked Timber. In the comments Bruce Wilder refers to a new review by J.W. Mason and comments on the reasons for popularity of the book "Piketty does not take a heterodox theoretical view — though he’s highly critical of the scholarly habits of the mainstream — and takes care to respect the conservative conventions regarding the marginalist analysis of the returns to capital, and the correspondence of financial “capital” claims to physical capital resources. JW Mason notes how this gives the book’s narrative something of a split-mind quality, with a lightly-committed theoretical frame at unremarked odds with the descriptive summary of painstakingly established facts.

I think the book’s enthusiastic reception by the mainstream rests on this odd split. Paul Krugman would never have reviewed it so favorably, if Piketty had challenged the textbooks. Jamie Galbraith, by telling contrast, took a more critical view of Piketty’s conservative conceptualizations of “capital”."

There is a discussion of average  production functions in my favourite review by Seth Ackerman who recommends this book 'The agregate production function and the measurement of change 'Not Even Wrong'".