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Walras' Law and nonoptimal equilibria in overlapping generations models

  • S. Rao Aiyagari

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
Date of revision:
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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  1. Burke, Jonathan L., 1987. "Inactive transfer policies and efficiency in general overlapping-generations economies," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 201-222, June.
  2. repec:oup:restud:v:47:y:1980:i:4:p:797-807 is not listed on IDEAS
  3. 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.
  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.
  5. 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.
  6. 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.
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