Existence of a competitive equilibrium when all goods are indivisible |
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| Affiliation: | 1. Université de Paris 1 Panthéon-Sorbonne, 106-112 Boulevard de l’Hôpital, 75647 Paris Cedex 13, France;2. Departamento de Economía, Universidad de Chile, Diagonal Paraguay 257, Torre 26, Santiago, Chile;1. Departamento de Análisis Económico and ERI-CES, University of Valencia, Facultad de Economía, Campus dels Tarongers, 46022 Valencia, Spain;2. D. Mètodes Quantitatius i Teoria Econòmica and Instituto Desarrollo Social y Paz (IUDESP), Universitat d’Alacant, Spain;1. Department of Economics, University of Cologne, Albertus-Magnus Platz, D-50923 Cologne, Germany;2. Vienna Graduate School of Finance and Institute for Advanced Studies, A-1080 Vienna, Austria;1. Department of Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel;2. University of Pennsylvania and Columbia University, Uris Hall, 3022 Broadway, New York, NY 10027, United States;3. Division of Economics, Nanyang Technological University, 14 Nanyang Drive, Singapore 637332, Singapore;4. Sol Snider Entrepreneurial Research Center, Wharton School, University of Pennsylvania, 3733 Spruce Street Philadelphia, PA 19104-6374, United States;1. Paris School of Economics, University Paris 1, CES, 106 boulevard de l’Hopital, 75013, Paris, France;2. University of La Rochelle (MIA), Avenue Michel Crepeau, 47042, La Rochelle, France;3. University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands;1. Washington University in St. Louis, United States;2. MIT, United States |
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| Abstract: | This paper investigates an economy where all consumption goods are indivisible at the individual level, but perfectly divisible at the overall level of the economy. In order to facilitate trading of goods, we introduce a perfectly divisible parameter that does not enter into consumer preferences — fiat money. When consumption goods are indivisible, a Walras equilibrium does not necessarily exist. We introduce the rationing equilibrium concept and prove its existence. Unlike the standard Arrow–Debreu model, fiat money can always have a strictly positive price at the rationing equilibrium. In our set up, if the initial endowment of fiat money is dispersed, then a rationing equilibrium is a Walras equilibrium. This result implies the existence of a dividend equilibrium or a Walras equilibrium with slack. |
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| Keywords: | Competitive equilibrium Indivisible goods |
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