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Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibria

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  • Khan, M. Ali
  • Sagara, Nobusumi

Abstract

Whereas “convexification by aggregation” is a well-understood procedure in mathematical economics, “convexification by randomization” has largely been limited to theories of statistical decision-making, optimal control and non-cooperative games. In this paper, in the context of classical Walrasian general equilibrium theory, we offer a comprehensive treatment of relaxed economies and their relaxed Walrasian equilibria: our results pertain to a setting with a finite or a continuum of agents, and a continuum of commodities modeled either as an ordered separable Banach space or as an L∞-space. As a substantive consequence, we demonstrate that the convexity hypothesis can be removed from the original large economy under the saturation hypothesis, and that existing results in the antecedent literature can be effortlessly recovered.

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  • Khan, M. Ali & Sagara, Nobusumi, 2016. "Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibria," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 95-107.
    • Handle: RePEc:eee:mateco:v:67:y:2016:i:c:p:95-107
    DOI: 10.1016/j.jmateco.2016.09.004
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    5. Niccolò Urbinati, 2020. "Walrasian objection mechanism and Mas Colell's bargaining set in economies with many commodities," Working Papers 07, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
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    7. Jang, Hyo Seok & Lee, Sangjik, 2020. "Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 57-64.
    8. Cea-Echenique, Sebastián & Fuentes, Matías, 2024. "On the continuity of the Walras correspondence in distributional economies with an infinite-dimensional commodity space," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 61-69.

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