C.E.S. production functions in the light of the Cambridge critique

The Cambridge debate of the 1960s showed conclusively that the aggregation of capital, so as to obtain a surrogate production function according to Samuelson, is not possible in general, with critical implications also for other variants of neoclassical theory. The framework for the demonstration is that of linear activity analysis. There is an individual wage curve in function of the rate of profit for each technique. If these individual wage curves were straight lines, their envelope would define a wage curve resulting from all techniques, from which a surrogate production function could be derived, but all wage curves are straight only, if there is only one industry. And if wage curves are not straight, phenomena such as reswitching show that essential neoclassical hypotheses need not hold. A recent empirical investigation by Han and Schefold has found one empirical example for reswitching and several for reverse capital deepening. A rigorous derivation of surrogate production functions thus is ruled out also on empirical grounds, but the paradoxes seem not to be as frequent as the critics once thought, so that the question arises whether approximate surrogate production functions could be derived, with individual wage curves which would be sufficiently linear to construct approximate surrogate production functions, indicating a relationship between the intensity of capital and output per head which would be sufficiently precise to work with. The paper is part of a wider investigation, in which conditions for the existence of quasi-linear wage curves and the possibility of the construction of approximate surrogate production functions are given. The emphasis here is on the special hypotheses needed to obtain C.E.S. production functions.