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′)
.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Aczél, J.: Lectures on Functional Equations and Their Applications. Academic Press, New York, London 1966.Google Scholar
  2. [2]
    Allen, R.G.D.: Macro — Economic Theory. Mac Millan, London, Melbourne, Toronto 1967.Google Scholar
  3. [3]
    Arrow, K.J., H.B. Chenery, B.S. Minhas, R.M. Solow: Capital — Labour Substitution and Economic Efficiency. Review of Economics and Statistics 43 (1961), 225–250.CrossRefGoogle Scholar
  4. [4]
    Beckmann, M.: Invariant Relationships for Homothetic Production Functions. This volume 1974.Google Scholar
  5. [5]
    Cobb, C.W., P.H. Douglas: A Theory of Production. American Economic Review 18 (1928), Supplement, 139–165.Google Scholar
  6. [6]
    Daróczy, Z., L. Losonczi: Über die Erweiterung der auf einer Punktmenge additiven Funktionen. Publ. Math. Debrecen 14 (1967), 239–245.Google Scholar
  7. [7]
    Eichhorn, W.: Theorie der homogenen Produktionsfunktion. Lecture Notes in Operations Research and Mathematical Systems, Vol. 22. Springer — Verlag, Berlin, Heidelberg, New York 1970.Google Scholar
  8. [8]
    Eichhorn, W.: Characterization of the CES Production Functions by Quasilinearity. This volume 1974.Google Scholar
  9. [9]
    Eichhorn, W., S.-C. Kolm: Technical Progress, Neutral Inventions, and Cobb — Douglas. This volume 1974.Google Scholar
  10. [10]
    Krelle, W.: Produktionstheorie. J.C.B. Mohr, Tübingen 1969.Google Scholar
  11. [11]
    Sato, R., M. Beckmann: Neutral Inventions and Production Functions. Rev. of Economic Stud. 35 (1968), 57–66.CrossRefGoogle Scholar
  12. [12]
    Schips, B.: Substitutionselastizität und Produktionsfunktionen. Operations Research — Verfahren 9 (1970), 105–115.Google Scholar
  13. [13]
    Uzawa, H.: Neutral Inventions and the Stability of Growth Equilibrium. Rev. of Economic Studies 28 (1961), 117–123.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1974

Authors and Affiliations

  • Frank Stehling

There are no affiliations available

Personalised recommendations