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.
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Acknowledgements
The author is grateful to Masakazu Fukuzumi and anonymous referees for their invaluable guidance and insightful feedback throughout the development of this study. The author also expresses gratitude to Nicholas C. Yannelis for his helpful comments and for introducing the works by Cornet et al. (2023), Podczeck and Yannelis (2024), and Bhowmik and Yannelis (2024). Any remaining errors are solely the author’s.
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Otsuka, M. The existence of Walrasian equilibrium: infinitely many commodities, measure space of agents, and discontinuous preferences. Econ Theory Bull (2024). https://doi.org/10.1007/s40505-024-00275-9
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DOI: https://doi.org/10.1007/s40505-024-00275-9
Keywords
- Infinite-dimensional commodity space
- Measure space of agents
- Discontinuous preference
- Saturation property
- Continuous inclusion property