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On the Samuelson–Etula Master Function and the capital controversy


  • Ariel Dvoskin
  • Saverio M. Fratini


The paper addresses the ambiguity that surrounds the conception of capital and its role in neoclassical price-and-distribution theory. The difficulties encountered in the various attempts to define the marginal product either of capital or of a capital good are recalled and the conclusion is drawn that neither concept appears theoretically sound. This historical reconstruction is combined with critical discussion of the recent attempt by Paul Samuelson to determine income distribution by means of the “Master Function†, a device previously developed and presented by Samuelson himself with Erkko Etula, and its “non-neoclassical†marginal products. Rather than the existence of a continuum of alternative technical possibilities, this construction assumes the simultaneous use of a discrete number of methods of production for the same commodity. Even though each technique employs the inputs in fixed proportions, the coexistence of various techniques permits the full employment of an arbitrarily given vector of input endowments. As is shown here, however, the coexistence of methods required for the differentiability of the Master Function can take place, if heterogenous capital goods are used in production, neither in the case with stationary relative prices nor in the non-stationary Arrow–Debreu framework.

Suggested Citation

  • Ariel Dvoskin & Saverio M. Fratini, 2016. "On the Samuelson–Etula Master Function and the capital controversy," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 23(6), pages 1032-1058, November.
  • Handle: RePEc:taf:eujhet:v:23:y:2016:i:6:p:1032-1058
    DOI: 10.1080/09672567.2016.1186920

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    References listed on IDEAS

    1. Stefano Zambelli, 2004. "The 40% neoclassical aggregate theory of production," Cambridge Journal of Economics, Oxford University Press, vol. 28(1), pages 99-120, January.
    2. Paolo Trabucchi, 2011. "Capital as a Single Magnitude and the Orthodox Theory of Distribution in Some Writings of the Early 1930s," Review of Political Economy, Taylor & Francis Journals, vol. 23(2), pages 169-188.
    3. Paul A. Samuelson, 2007. "Classical and Neoclassical harmonies and dissonances," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 14(2), pages 243-271.
    4. Pasinetti, Luigi L, 1969. "Switches of Technique and the "Rate of Return" in Capital Theory," Economic Journal, Royal Economic Society, vol. 79(315), pages 508-531, September.
    5. Paul A. Samuelson, 1959. "A Modern Treatment of the Ricardian Economy: I. The Pricing of Goods and of Labor and Land Services," The Quarterly Journal of Economics, Oxford University Press, vol. 73(1), pages 1-35.
    6. Samuelson, Paul A. & Etula, Erkko M., 2006. "Complete work-up of the one-sector scalar-capital theory of interest rate: Third installment auditing Sraffa's never-completed "Critique of Modern Economic Theory"," Japan and the World Economy, Elsevier, vol. 18(3), pages 331-356, August.
    7. Kurz,Heinz D. & Salvadori,Neri, 1997. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521588676.
    8. Pierangelo Garegnani, 2007. "Samuelson's misses: A rejoinder," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 14(3), pages 573-585.
    9. Saverio M. Fratini, 2013. "Real W icksell Effect, Demand for Capital and Stability," Metroeconomica, Wiley Blackwell, vol. 64(2), pages 346-360, May.
    10. Tatsuo Hatta, 1976. "The Paradox in Capital Theory and Complementarity of Inputs," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 127-142.
    11. Paul A. Samuelson, 1962. "Parable and Realism in Capital Theory: The Surrogate Production Function," Review of Economic Studies, Oxford University Press, vol. 29(3), pages 193-206.
    12. Hahn, F H, 1975. "Revival of Political Economy: The Wrong Issues and the Wrong Argument," The Economic Record, The Economic Society of Australia, vol. 51(135), pages 360-364, September.
    13. Luigi L. Pasinetti, 1960. "A Mathematical Formulation of the Ricardian System," Review of Economic Studies, Oxford University Press, vol. 27(2), pages 78-98.
    14. Saverio M. Fratini, 2007. "Reswitching of Techniques in an Intertemporal Equilibrium Model with Overlapping Generations," Contributions to Political Economy, Oxford University Press, vol. 26(1), pages 43-59.
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    Cited by:

    1. Saverio M. Fratini, 2019. "Neoclassical theories of stationary relative prices and the supply of capital," Metroeconomica, Wiley Blackwell, vol. 70(4), pages 723-737, November.
    2. Enrico Bellino & Christian Bidard & Saverio M. Fratini & G.C. Harcourt & Arrigo Opocher & Ian Steedman & Naoki Yoshihara & Heinz D. Kurz, 2017. "Symposium on Arrigo Opocher and Ian Steedman (," Metroeconomica, Wiley Blackwell, vol. 68(4), pages 586-624, November.
    3. Dvoskin, Ariel & Feldman, Germán David & Ianni, Guido, 2018. "New-Structuralist Exchange-Rate Policy and the Pattern of Specialization in Latin American Countries," Centro Sraffa Working Papers CSWP28, Centro di Ricerche e Documentazione "Piero Sraffa".

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