Competitive equilibria in general choice spaces |
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| Affiliation: | 1. Department of Botany, Hansraj College, University of Delhi, Delhi 110007, India;2. J C Bose Centre for Plant Genomics, Hansraj College, University of Delhi, Delhi 110007, India;3. Molecular Biology Research Lab, Department of Zoology, Deshbandhu College, University of Delhi, Kalkaji, New Delhi 110019, India;4. Delhi School of Climate Change and Sustainability, Institution of Eminence, Maharishi Karnad Bhawan, University of Delhi, Delhi 110007, India;1. School of Mathematical Sciences, Tongji University, Shanghai 200092, China;2. College of Information Technology, Shanghai Ocean University, Shanghai 201306, China;3. Department of Mathematics and Physics, Anyang Institute of Technology, Anyang 455000, China;4. Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105, United States |
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| Abstract: | This paper primarily demonstrates the existence of Arrow-Debreu equilibria in a general class of topological vector spaces of commodity bundles. Two conditions based on production possibilities, preferences, and the topological nature of bounded sets are shown to substitute, in any locally convex space, for the advantages of the Euclidean topology. Examples fulfilling these conditions are supplied. The approach is that of Bewley, demonstrating equilibria on finite dimensional sub-economies and establishing a net of these equilibria that converges to an equilibrium on the whole commodity space. An example of equilibrium with a storage technology is given. An auxiliary result concerns the price support of efficient allocations. |
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