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Functional forms for technical change functions

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Abstract

In this paper we examine the four properties of technical change functions introduced by Sato [1980, 1981], paying particular attention to the composition property. We show by way of examples that two of the properties are independent, but that a third is a necessary consequence of two others. A theorem providing a necessary condition for the composition property is stated and proved. Finally, we identify the general continuous functional form of technical change functions for which the efficiency of factor i is independent of the quantities of all factors j ≠ i. Noting an unappealing characteristic of a member of this class of transformations, we propose an additional property for technical change functions and note that it is independent of the others.

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References

  • Aczél, J.D. (1966). Lectures on Functional Equations and Their Applications. Mathematics in Science and Engineering, Vol. 19, New York: Academic Press.

    Google Scholar 

  • Binswanger, H.P. (1974). “The Measurement of Technical Change Biases with Many Factors of Production.” American Economic Review 64, 964–976.

    Google Scholar 

  • Chambers, R.G. (1988). Applied Production Analysis: A Dual Approach. Cambridge: Cambridge University.

    Google Scholar 

  • Mitchell, T.M. (1984). “A Functional Equation Approach to the Theory of Production, Technical Change, and Invariance.” Zeitschrift für Nationalökonomie 44, 177–187.

    Google Scholar 

  • Mitchell, T.M. (1990). “On the Functional Forms of Technical Change Functions.” In Conservation Laws and Symmetry: Applications to Economics and Finance, R. Sato & R. Ramachandran (eds.), Boston: Kluwer Academic.

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  • Sato, R. (1980). “The Impact of Technical Change on the Holotheticity of Production Functions.” Review of Economic Studies 47, 767–776.

    Google Scholar 

  • Sato, R. (1981). Theory of Technical Change and Economic Invariance: Application of Lie Groups. New York: Academic Press.

    Google Scholar 

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Authors and Affiliations

  1. Department of Economics, Southern Illinois University at Carbondale, 62901-4515, Carbondale, Illinois

    Thomas Mitchell & Daniel Primont

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  1. Thomas Mitchell
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  2. Daniel Primont
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Additional information

The refereeing process of this paper was handled through S.T. Hackman.

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Mitchell, T., Primont, D. Functional forms for technical change functions. J Prod Anal 2, 143–152 (1991). https://doi.org/10.1007/BF00156344

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  • DOI: https://doi.org/10.1007/BF00156344

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