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Existence and Calculation of Optimal Equilibria on Overlapping Generations Economies

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  • Leandro Lyra Braga Dognini

Abstract

A well-known feature of overlapping generations economies is that the First Welfare Theorem fails and equilibrium may be inefficient. The Cass (1972) criterion furnishes a necessary and sufficient condition for efficiency, but does not address the matter of existence of efficient equilibria, and Cass, Okuno, and Zilcha (1979) provide nonexistence examples. I develop an algorithm based on successive approximations of a nonstationary, consumption-loan, prone to savings, overlapping generations economy with finite-lived heterogeneous agents to find elements of its set of equilibria as the limit of nested compact sets. These compact sets are the result of a backward calculation through equilibrium equations that departs from the set of Pareto optimal equilibria of well-behaved tail economies. The equilibria calculated through this algorithm satisfy the Cass (1972) criterion and are used to derive the existence results on efficient equilibria.

Suggested Citation

  • Leandro Lyra Braga Dognini, 2025. "Existence and Calculation of Optimal Equilibria on Overlapping Generations Economies," Papers 2509.19019, arXiv.org.
    • Handle: RePEc:arx:papers:2509.19019
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    References listed on IDEAS

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    1. Benveniste, Lawrence M & Cass, David, 1986. "On the Existence of Optimal Stationary Equilibria with a Fixed Supply of Fiat Money: I. The Case of a Single Consumer," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 402-417, April.
    2. David Cass & Menahem E. Yaari, 1966. "A Re-examination of the Pure Consumption Loans Model," Journal of Political Economy, University of Chicago Press, vol. 74(4), pages 353-353.
    3. Rao Aiyagari, S. & Peled, Dan, 1991. "Dominant root characterization of Pareto optimality and the existence of optimal equilibria in stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 54(1), pages 69-83, June.
    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. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
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