I’m rediscovering my old frustrations with aggregate production functions like the CES. They’re handy, but I have a nagging suspicion, never quite formalized, that they just don’t capture the engineering/thermodynamic realities of substitution. Anyone know any papers on that? I’m aware of critiques of KLEM applications, but not interfuel aggregation.
Click to enlarge. From a google images search for production function.
Your intuition is correct in that aggregate production functions can be misspecified to violate the laws of thermodynamics. Fortunately, there is also a way to get it right by adjusting the factor shares. The following paper does just that.
Representing energy technologies in top-down economic models using bottom-up information
http://globalchange.mit.edu/pubs/abstract.php?publication_id=800