  In this paper we extend the work by Ryuzo Sato devoted to the development of
economic growth models within the framework of the Lie group theory. We propose
a new growth model based on the assumption of logistic growth in factors. It is
employed to derive new production functions and introduce a new notion of wage
share. In the process it is shown that the new functions compare reasonably
well against relevant economic data. The corresponding problem of maximization
of profit under conditions of perfect competition is solved with the aid of one
of these functions. In addition, it is explained in reasonably rigorous
mathematical terms why Bowley's law no longer holds true in post-1960 data.
