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Equilibrium existence in an overlapping generations model with altruistic preferences

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  • S. Rao Aiyagari
Abstract
We prove the existence of a competitive equilibrium in an overlapping generations model in which each generation has a preference ordering over its own and its descendents? consumptions. The model is one of pure exchange with many goods in each period and two period lived generations. The bequest from one generation to the next is required to be non-negative and is endogenous. In equilibrium, some sequences of agents of successive generations may be continually ?linked? by positive bequests and act as infinitely lived agents. Other sequences of agents may not be so linked and therefore behave as sequences of finite lived agents. We give three examples which illustrate the following points: (i) multiple equilibria may exist some of which resemble those of standard overlapping generations models, whereas in others some sequences of agents behave as if infinitely lived, (ii) multiple steady states of the above two types may exist in which the latter are unstable and the former are stable, and (iii) if agents have preferences given by discounted sums of utilities with different discount rates, then not all sequences of generations can be continually linked and hence behave as infinitely lived agents.

Suggested Citation

  • S. Rao Aiyagari, 1987. "Equilibrium existence in an overlapping generations model with altruistic preferences," Working Papers 356, Federal Reserve Bank of Minneapolis.
    • Handle: RePEc:fip:fedmwp:356
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    Cited by:

    1. Eckstein, Zvi & Zilcha, Itzhak, 1994. "The effects of compulsory schooling on growth, income distribution and welfare," Journal of Public Economics, Elsevier, vol. 54(3), pages 339-359, July.
    2. Óscar Arce & David López-Salido, 2011. "Housing Bubbles," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(1), pages 212-241, January.
    3. Smetters, Kent, 1999. "Ricardian equivalence: long-run Leviathan," Journal of Public Economics, Elsevier, vol. 73(3), pages 395-421, September.
    4. Nobuhiro Kiyotaki, 2008. "Comment on "Aggregate Implications of Credit Market Imperfections"," NBER Chapters, in: NBER Macroeconomics Annual 2007, Volume 22, pages 71-77, National Bureau of Economic Research, Inc.
    5. Dutta, Jayasri & Michel, Philippe, 1998. "The Distribution of Wealth with Imperfect Altruism," Journal of Economic Theory, Elsevier, vol. 82(2), pages 379-404, October.
    6. Philippe Michel & Pierre Pestieau, 1998. "Fiscal Policy in a Growth Model with Both Altruistic and Nonaltruistic Agents," Southern Economic Journal, John Wiley & Sons, vol. 64(3), pages 682-697, January.
    7. Aiyagari, S. Rao, 1992. "Co-existence of a representative agent type equilibrium with a non-representative agent type equilibrium," Journal of Economic Theory, Elsevier, vol. 57(1), pages 230-236.
    8. Roberto Ricciuti, 2003. "Assessing Ricardian Equivalence," Journal of Economic Surveys, Wiley Blackwell, vol. 17(1), pages 55-78, February.
    9. Lakshmi Raut, 2006. "Two-sided altruism, Lindahl equilibrium, and Pareto optimality in overlapping generations models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(3), pages 729-736, April.
    10. Nourry, Carine & Venditti, Alain, 2001. "Determinacy of Equilibrium in an Overlapping Generations Model with Heterogeneous Agents," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 230-255, January.

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