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Negishi on Edgeworth on Jevons’s law of indifference, Walras’s equilibrium, and the role of large numbers: a critical assessment

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  • Franco DONZELLI

Abstract

In developing their pure-exchange equilibrium models, Jevons (1871), Walras (1874-77), and Edgeworth (1881) make use of some version of a law, called law of indifference (or principle of uniformity) by Jevons and Edgeworth and often referred to as the law of one price in connection with Walrasian economics. Edgeworth, in particular, shares with Jevons the idea that the law of indifference must be regarded as an equilibrium property; unlike his predecessor, however, he denies the validity of the law in all economies with a finite number of traders: for him, price uniformity can only emerge and a Jevonsian or Walrasian or competitive equilibrium can only be established when the traders’ number grows unboundedly large. About one century later, Negishi (1982) resumes the time-honoured discussion about the law, striving to prove that, contrary to Edgeworth’s original conjecture, a competitive equilibrium can be attained even in small economies, provided that the true driving force underlying Jevons’s law of indifference, namely, its implicit arbitrage mechanism, be allowed to operate and carry its effects through. In this paper, after reconstructing Jevons’s, Walras’s, and Edgeworth’s respective positions, we critically discuss Negishi’s critique of Edgeworth’s stance on Jevons’s law of indifference, Walras’s equilibrium, and the role of large numbers, showing that his central claim is unsubstantiated.

Suggested Citation

  • Franco DONZELLI, 2011. "Negishi on Edgeworth on Jevons’s law of indifference, Walras’s equilibrium, and the role of large numbers: a critical assessment," Departmental Working Papers 2011-23, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2011-23
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    References listed on IDEAS

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    1. Franco Donzelli, 2007. "Equilibrium and Tâtonnement in Walras's Eléments," History of Economic Ideas, Fabrizio Serra Editore, Pisa - Roma, vol. 15(3), pages 85-138.
    2. Nicholas Kaldor, 1934. "A Classificatory Note on the Determinateness of Equilibrium," Review of Economic Studies, Oxford University Press, vol. 1(2), pages 122-136.
    3. Allan M. Feldman, 1973. "Bilateral Trading Processes, Pairwise Optimally, and Pareto Optimality," Review of Economic Studies, Oxford University Press, vol. 40(4), pages 463-473.
    4. Hicks, John, 2017. "A Market Theory of Money," OUP Catalogue, Oxford University Press, number 9780198796237.
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    More about this item

    Keywords

    ; Walras; Edgeworth; law of indifference; equilibrium; large economies; arbitrage;
    All these keywords.

    JEL classification:

    • B13 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Neoclassical through 1925 (Austrian, Marshallian, Walrasian, Wicksellian)
    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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