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Best Techniques Leave Little Room for Substitution. A New Critique of the Production Function


  • Kersting, Götz

    (Johann Wolfgang Goethe-Universität)

  • Schefold, Bertram

    (Johann Wolfgang Goethe-Universität)


Samuelson assumed a linear wage curve for each of a continuum of techniques such that their envelope was a monotonically falling wage curve for the economy, from which an aggregate production function fulfilling the marginal productivity conditions could be derived. But the capital intensities of the techniques chosen at each rate of profit are not necessarily lower at higher rates of profit, if the wage curves are not linear, a possibility exemplified by reswitching. This critique of the capital controversy does not rule out Samuelson’s construction as an approximation, since the paradoxes have been shown to be rare. Instead, a possibility is likely that has so far not been noticed: the envelope of the wage curves will in the relevant range of the rate of profit be dominated by a small number of efficient techniques of approximately equal capital intensity, leaving little room for substitution. A new mathematical theorem demonstrates that the expected number of techniques that appear on the envelope is given by (2/3) ln s.

Suggested Citation

  • Kersting, Götz & Schefold, Bertram, 2020. "Best Techniques Leave Little Room for Substitution. A New Critique of the Production Function," Centro Sraffa Working Papers CSWP47, Centro di Ricerche e Documentazione "Piero Sraffa", revised 22 Dec 2020.
  • Handle: RePEc:ris:sraffa:0047

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    Cited by:

    1. Tsoulfidis, Lefteris, 2021. "Capital Theory Debates: New Developments and Direction," Centro Sraffa Working Papers CSWP51, Centro di Ricerche e Documentazione "Piero Sraffa".
    2. Schefold, Bertram, 2022. "What Remains of the Cambridge Critique? Potential Conclusions and Directions for Further Research Following from Recent Investigations in Capital Theory," Centro Sraffa Working Papers CSWP53, Centro di Ricerche e Documentazione "Piero Sraffa".
    3. Petri, Fabio, 2021. "What Remains of the Cambridge Critique? On Professor Schefold's Theses," Centro Sraffa Working Papers CSWP50, Centro di Ricerche e Documentazione "Piero Sraffa".

    More about this item


    Capital theory; production function; substitution; reswitching;
    All these keywords.

    JEL classification:

    • B24 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Socialist; Marxist; Scraffian
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • D57 - Microeconomics - - General Equilibrium and Disequilibrium - - - Input-Output Tables and Analysis

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