Determination of all Hicks-neutral production functions depending upon capital, labor and time (state of technology). The translation equation

Abstract

We come now to the case n = 2, the Hicks-neutral production processes originally envisaged by Hicks [32], Robinson [37], and Sato-Beckmann [68], who took capital and labor (in addition to the time or state of technology) as production factors. As we will see, homogeneity will play an important role here too, as it did in section 3 (see, for instance, Proposition 3.4). We will prove the following (cf. Aczél-Gehrig [86], where an arbitrary open rectangle I₁ × I₂ stands in place of ℝ²₊₊, just as in Theorem 5.7 above).