The existence of Walrasian equilibrium: infinitely many commodities, measure space of agents, and discontinuous preferences

Motoki Otsuka ()
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Motoki Otsuka: Graduate School of University of Tsukuba

Economic Theory Bulletin, 2024, vol. 12, issue 2, No 1, 119-140

Abstract: Abstract This study establishes two equilibrium existence results for large economies with infinitely many commodities. The novel results allow for nontransitive, incomplete, discontinuous, and price-dependent preferences and do not require an interiority condition on initial endowments. The first result is an existence result when the positive cone of the commodity space has a nonempty interior. The second result is an existence result under a nonsatiation condition, including the case of the empty interior of the positive cone. The second result covers infinite-dimensional commodity spaces which could not be covered before due to the interiority condition, such as the space of square integrable functions. Specifically, we employ a saturated measure space of agents to appeal to the convexifying effect of aggregation. The notion of the continuous inclusion property introduced for finite-agent economies is applied to large economies, enabling us to dispense with the continuity assumption regarding preferences. In addition, we provide examples of Walrasian equilibrium and infinite-dimensional commodity spaces newly covered by our results.

Keywords: Infinite-dimensional commodity space; Measure space of agents; Discontinuous preference; Saturation property; Continuous inclusion property (search for similar items in EconPapers)
JEL-codes: C02 C62 D51 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s40505-024-00275-9

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