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Walras and dividends equilibrium with possibly satiated consumers

  • Allouch, Nizar
  • Le Van, Cuong

The main contribution of the paper is to provide a weaker nonsatiation assumption than the one commonly used in the literature to ensure the existence of competitive equilibrium. Our assumption allows for satiation points inside the set of individually feasible consumptions, provided that the consumer has satiation points available to him outside this set. As a result, we show the concept of equilibrium with dividends [see Aumann, R.J., Drèze, J.H., 1986. Values of markets with satiation or fixed prices. Econometrica 54, 1271-1318; Mas-Collel, A., 1992. Equilibrium theory with possibly satiated preferences. In: Majumdar, M. (Ed.), Equilibrium and Dynamics: Proceedings of the Essays in Honour of David Gale. MacMillan, London, pp. 201-213] is pertinent only when the set of satiation points is included in the set of individually feasible consumptions. Our economic motivation stems from the fact that in decentralized markets, increasing the incomes of consumers through dividends, if it is possible, is costly since it involves the intervention of a social planner. Then, we show, in particular, how in securities markets our weak nonsatiation assumption is satisfied by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403-1418] assumption.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 9-10 (September)
Pages: 907-918

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Handle: RePEc:eee:mateco:v:44:y:2008:i:9-10:p:907-918
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. LE VAN, Cuong & BA MINH, Nguyen, 2004. "No-arbitrage condition and existence of equilibrium with dividends," CORE Discussion Papers 2004034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Kajii, Atsushi, 1996. "How to discard non-satiation and free-disposal with paper money," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 75-84.
  3. Allouch, Nizar & Le Van, Cuong & Page, Jr. Frank H., 2001. "The geometry of arbitrage and the existence of competitive equilibrium," The Warwick Economics Research Paper Series (TWERPS) 598, University of Warwick, Department of Economics.
  4. Aumann, R.J. & Dreze, J.H., 1984. "Values of markets with satiation or fixed prices," CORE Discussion Papers 1984033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Cornet, Bernard & Topuzu, Mihaela & Yildiz, Aysegul, 2003. "Equilibrium theory with a measure space of possibly satiated consumers," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 175-196, June.
  6. Dana, Rose-Anne & Le Van, Cuong & Magnien, François, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Economics Papers from University Paris Dauphine 123456789/6228, Paris Dauphine University.
  7. Makarov, V. L., 1981. "Some results on general assumptions about the existence of economic equilibrium," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 87-99, March.
  8. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "A necessary and sufficient condition for the compactness of individually rational and feasible outcomes and the existence of an equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 153-162, August.
  9. Alexander Konovalov, 2005. "The core of an economy with satiation," Economic Theory, Springer, vol. 25(3), pages 711-719, 04.
  10. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
  11. Dreze, Jacques H. & Muller, Heinz, 1980. "Optimality properties of rationing schemes," Journal of Economic Theory, Elsevier, vol. 23(2), pages 131-149, October.
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