Engineering Production Functions and Capital-Labor Substitutions in Metal Machining

For some time the theory of the firm has been subject to an unfortunate division: in the classroom we talk about production functions involving physical inputs and a physical output; in our empirical work we are content to estimate cost or production functions from value and accounting data.1 The former have come to be called "engineering production functions,"2 while the latter have been termed "index numbers of production" [3], "distribution functions" [4], and "surrogate production functions" [13]. Attempts to refine these empirical production functions to bring them closer to the physical production functions of the classroom have led to a mass of literature. The difficulties involve such questions as: Under what conditions may factors be aggregated [5]? Should capital be measured as a stock or service?3 Should there be corrections for price changes? (If so, should these entail weighting by (1) constant prices, (2) moving averages, or (3) labor time equivalents [1S]?)