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C.E.S. production functions in the light of the Cambridge critique

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  • Schefold, Bertram

Abstract

The Cambridge debate of the 1960s showed conclusively that the aggregation of capital, so as to obtain a surrogate production function according to Samuelson, is not possible in general, with critical implications also for other variants of neoclassical theory. The framework for the demonstration is that of linear activity analysis. There is an individual wage curve in function of the rate of profit for each technique. If these individual wage curves were straight lines, their envelope would define a wage curve resulting from all techniques, from which a surrogate production function could be derived, but all wage curves are straight only, if there is only one industry. And if wage curves are not straight, phenomena such as reswitching show that essential neoclassical hypotheses need not hold. A recent empirical investigation by Han and Schefold has found one empirical example for reswitching and several for reverse capital deepening. A rigorous derivation of surrogate production functions thus is ruled out also on empirical grounds, but the paradoxes seem not to be as frequent as the critics once thought, so that the question arises whether approximate surrogate production functions could be derived, with individual wage curves which would be sufficiently linear to construct approximate surrogate production functions, indicating a relationship between the intensity of capital and output per head which would be sufficiently precise to work with. The paper is part of a wider investigation, in which conditions for the existence of quasi-linear wage curves and the possibility of the construction of approximate surrogate production functions are given. The emphasis here is on the special hypotheses needed to obtain C.E.S. production functions.

Suggested Citation

  • Schefold, Bertram, 2008. "C.E.S. production functions in the light of the Cambridge critique," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 783-797, June.
  • Handle: RePEc:eee:jmacro:v:30:y:2008:i:2:p:783-797
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    1. Avi J. Cohen, 2003. "Retrospectives: Whatever Happened to the Cambridge Capital Theory Controversies?," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 199-214, Winter.
    2. Zonghie Han & Bertram Schefold, 2006. "An empirical investigation of paradoxes: reswitching and reverse capital deepening in capital theory," Cambridge Journal of Economics, Oxford University Press, vol. 30(5), pages 737-765, September.
    3. Harcourt,G. C., 1972. "Some Cambridge Controversies in the Theory of Capital," Cambridge Books, Cambridge University Press, number 9780521096720, April.
    4. P. Garegnani, 1970. "A Reply," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 439-439.
    5. Jonathan Temple, 2006. "Aggregate Production Functions and Growth Economics," International Review of Applied Economics, Taylor & Francis Journals, vol. 20(3), pages 301-317.
    6. Steedman, Ian & Tomkins, Judith, 1998. "On Measuring the Deviation of Prices from Values," Cambridge Journal of Economics, Oxford University Press, vol. 22(3), pages 379-385, May.
    7. P. Garegnani, 1970. "Heterogeneous Capital, the Production Function and the Theory of Distribution," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 407-436.
    8. Bertram Schefold, 2005. "Reswitching As A Cause Of Instability Of Intertemporal Equilibrium," Metroeconomica, Wiley Blackwell, vol. 56(4), pages 438-476, November.
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    Cited by:

    1. Chirinko, Robert S., 2008. "[sigma]: The long and short of it," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 671-686, June.
    2. Saverio M. Fratini, 2010. "Reswitching And Decreasing Demand For Capital," Metroeconomica, Wiley Blackwell, vol. 61(4), pages 676-682, November.
    3. Frieling, Julius & Madlener, Reinhard, 2016. "Estimation of Substitution Elasticities in Three-Factor Production Functions: Identifying the Role of Energy," FCN Working Papers 1/2016, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN), revised Sep 2016.
    4. Miguel A. León-Ledesma & Peter McAdam & Alpo Willman, 2010. "Identifying the Elasticity of Substitution with Biased Technical Change," American Economic Review, American Economic Association, vol. 100(4), pages 1330-1357, September.
    5. Jesus Felipe & John S.L. McCombie, 2013. "The Aggregate Production Function and the Measurement of Technical Change," Books, Edward Elgar Publishing, number 1975.
    6. Iliadi, Fotoula & Mariolis, Theodore & Soklis, George & Tsoulfidis, Lefteris, 2012. "Bienenfeld’s approximation of production prices and eigenvalue distribution: some more evidence from five European economies," MPRA Paper 36282, University Library of Munich, Germany.
    7. Saverio M. Fratini, 2009. "Reswitching and Decreasing Demand for Capital in a Model with a Continuum of Linear Techniques," EERI Research Paper Series EERI_RP_2009_26, Economics and Econometrics Research Institute (EERI), Brussels.
    8. Mariolis, Theodore & Tsoulfidis, Lefteris, 2010. "Eigenvalue distribution and the production price-profit rate relationship in linear single-product systems: theory and empirical evidence," MPRA Paper 43716, University Library of Munich, Germany.

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