# Neutral Inventions and CES Production Functions

• Frank Stehling
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 99)

## Abstract

In the literature of economic theory the most frequently used classes of (macroeconomic) production functions with completely substitutable factors are the CD functions 2) and ACMS functions 3) defined respectively (for two arguments, usually interpreted as capital and labour) by
$$F\left( {K,L} \right) = c{K^a}{L^b}\quad \quad \quad \left\{ \begin{gathered} a,b,c\;positive,\;const.; \hfill \\ K>0,\;L>0 \hfill \\ \end{gathered} \right)$$
(0.1)
and
$$F\left( {K,L} \right) = {\left( {{c_1}{K^{{ - \rho }}}} \right)^{{ - \frac{1}{\rho }}}}\quad \left\{ \begin{gathered} {c_1},{c_2}\;pos.,\;\rho \ne 0,\;const.; \hfill \\ K>0,\;L>0, \hfill \\ \end{gathered} \right)$$
(0.2)
or, if a time variable t is involved4, by
$$F\left( {K,L,t} \right) = c(t){K^a}{L^b}\quad \quad \quad \left\{ \begin{gathered} a,b\;pos.,const.; \hfill \\ c(t)>0;\;t>0,\;K>0,\;L>0 \hfill \\ \end{gathered} \right)$$
(0.1′)
and
$$F\left( {K,L,t} \right) = \bar{c}(t){\left( {{c_1}{K^{{ - \rho }}} + {c_2}{L^{{ - \rho }}}} \right)^{{ - \frac{1}{\rho }}}}\quad \left\{ \begin{gathered} {c_1},{c_2}\;pos.,\;\rho \ne 0, \hfill \\ const.;\;\bar{c}(t)>0; \hfill \\ t>0,\;K>0,\;L>0. \hfill \\ \end{gathered} \right)$$
(0.2′)
.

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