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Equilibria of large production economies with interdependent preferences: A role for the infinite dimensional Fatou’s lemma

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  • Otsuka, Motoki

Abstract

This study establishes the existence of Walrasian equilibrium for large production economies with infinitely many commodities and interdependent preferences. The interdependence is formulated so that each agent’s preference depends on the average demand among agents. Preferences are allowed to be price-dependent and need not be represented by a utility function. This result generalizes previous existence results for large economies with infinitely many commodities. We employ a saturated measure space of agents to apply the infinite dimensional Fatou’s lemma, Lyapunov convexity theorem and regularity properties (convexity, norm/weak compactness, and preservation of norm/weak upper hemicontinuity) of the Bochner integration of correspondences. We use a subsequence formulation of the infinite dimensional Fatou’s lemma in the limiting argument.

Suggested Citation

  • Otsuka, Motoki, 2026. "Equilibria of large production economies with interdependent preferences: A role for the infinite dimensional Fatou’s lemma," Journal of Mathematical Economics, Elsevier, vol. 124(C).
    • Handle: RePEc:eee:mateco:v:124:y:2026:i:c:s0304406826000339
    DOI: 10.1016/j.jmateco.2026.103245
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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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