Existence of equilibria with infinitely many commodities: Banach lattices reconsidered |
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| Institution: | 1. Bar-Ilan University, Ramat-Gan, 5290002, Israel;2. The School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel;3. INSEAD, Boulevard de Constance, 77305, Fontainebleau, France;1. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC;2. Department of Biomedical Engineering, North Carolina State University, Raleigh, NC;3. Department of Orthopaedic Surgery, Wake Forest School of Medicine, Winston-Salem, NC;4. Division of Orthopedic Surgery, Cincinnati Children’s Hospital Medical Center, Cincinnati, OH;1. Department of Orthopedic Surgery, Mayo Clinic, Rochester, MN, United States;2. Shirley Ryan AbilityLab, Chicago, IL, United States |
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| Abstract: | The purpose of this paper is twofold. The first aim is to present an extension of the results on the existence of Walrasian equilibrium to the infinite dimensional setting. The result depends on two crucial assumptions. These are the compactness of the collection of feasible allocations and the non-emptiness of the interior of the production set. The proof is a direct generalization of Bewley's (1972) proof for the L∞ case. The second purpose of this paper is to show that the recent result of Mas-Colell (1986) on the existence of equilibrium for exchange economies on Banach lattices can be obtained through an argument based on the result outlined above. That is, exchange economies on Banach lattices with ‘uniformly proper’ preferences behave as though they were production economies in which the production sets have non-empty interior. |
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