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Walras' Law and nonoptimal equilibria in overlapping generations models

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S. Rao Aiyagari

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Abstract

This paper demonstrates a connection between failure of Walras’ Law and nonoptimal equilibria in a quite general overlapping generations model. Consider the following implication of Walras’ Law in finite economies. Suppose that all prices are positive and that all agents are on their budget lines. Then, no matter how the set of goods is partitioned, there cannot be an excess supply (in value terms) for some other set in the partition with excess demand (in value terms) for some other set in the partition. We use the Cass (1972), Benveniste (1976, 1986), Balasko and Shell (1980), and Okuno and Zilcha (1980) price characterization of optimality of equilibria in pure exchange overlapping generations models to show the following link between the above implication of Walras’ Law and optimality of a competitive equilibrium. A competitive equilibrium is nonoptimal if and only if the above implication of Walras’ Law fails in its neighborhood.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Working Papers with number 393.

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Date of creation: 1991
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Publication status: Published in The legacy of Leon Walras (Vol. 2, 2001, pp. 496-514) ; Journal of Mathematical Economics (Vol. 21, No. 4, 1992, pp. 343-361)
Handle: RePEc:fip:fedmwp:393

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, vol. 4(2), pages 200-223, April. [Downloadable!] (restricted)
  2. Shell, Karl, 1971. "Notes on the Economics of Infinity," Journal of Political Economy, University of Chicago Press, vol. 79(5), pages 1002-11, Sept.-Oct. [Downloadable!] (restricted)
  3. Okuno, Masahiro & Zilcha, Itzhak, 1980. "On the Efficiency of a Competitive Equilibrium in Infinite Horizon Monetary Economies," Review of Economic Studies, Blackwell Publishing, vol. 47(4), pages 797-807, July. [Downloadable!] (restricted)
  4. Balasko, Yves & Shell, Karl, 1980. "The overlapping-generations model, I: The case of pure exchange without money," Journal of Economic Theory, Elsevier, vol. 23(3), pages 281-306, December. [Downloadable!] (restricted)
  5. Wilson, Charles A., 1981. "Equilibrium in dynamic models with an infinity of agents," Journal of Economic Theory, Elsevier, vol. 24(1), pages 95-111, February. [Downloadable!] (restricted)
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  1. Mark Pingle & Leigh Tesfatsion, 1993. "``Further Remarks on Walras' Law and Nonoptimal Equilibria''," GE, Growth, Math methods 9312001, EconWPA. [Downloadable!]
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