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Pareto optimality in continuous-time OLG economies

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  • Molina-Abraldes, Antonio
  • Pintos-Clapés, Juan

Abstract

The aim of this paper is the achievement of a complete characterization of the Pareto optimality of competitive equilibria for deterministic, pure exchange, continuous-time economies with a countable number of overlapping generations, where each consumer's life-span consists in a bounded interval of time. For such an environment, we obtain separate sufficient and necessary conditions for Pareto optimality in the form of the Cass' criterion, that is, in terms of the equilibrium prices. However, these conditions are not equivalent in general. Therefore, in order to get that equivalence we are compelled to impose certain restrictions, either on consumers' lifetimes, assuming that all of them have the same longevity, or on the dynamic behaviour of relative intertemporal equilibrium prices. In both cases, we are able to derive a single condition that is sufficient and necessary for efficiency, thus achieving full characterizations.

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Bibliographic Info

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

Volume (Year): 44 (2008)
Issue (Month): 9-10 (September)
Pages: 933-950

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Handle: RePEc:eee:mateco:v:44:y:2008:i:9-10:p:933-950

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Web page: http://www.elsevier.com/locate/jmateco

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References

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  1. Subir Chattopadhyay & Piero Gottardi, 1999. "Stochastic OLG Models, Market Structure, and Optimality," Working Papers 99-12, Brown University, Department of Economics.
  2. 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.
  3. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 66, pages 467.
  4. 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.
  5. Olivier J. Blanchard, 1984. "Debt, Deficits and Finite Horizons," NBER Working Papers 1389, National Bureau of Economic Research, Inc.
  6. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 70(2), pages 631-662, March.
  7. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, Elsevier, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
  8. Okuno, Masahiro & Zilcha, Itzhak, 1980. "On the Efficiency of a Competitive Equilibrium in Infinite Horizon Monetary Economies," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 47(4), pages 797-807, July.
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  10. Benveniste, Lawrence M., 1976. "A complete characterization of efficiency for a general capital accumulation model," Journal of Economic Theory, Elsevier, vol. 12(2), pages 325-337, April.
  11. DEMICHELIS, Stefano & POLEMARCHAKIS, Heracles, 2000. "Life-span and the determinacy of equilibrium in economies of overlapping generations," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2000034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Majumdar, Mukul, 1972. "Some general theorems on efficiency prices with an infinite-dimensional commodity space," Journal of Economic Theory, Elsevier, vol. 5(1), pages 1-13, August.
  13. Molina-Abraldes, Antonio & Pintos-Clapes, Juan, 2003. "A complete characterization of Pareto optimality for general OLG economies," Journal of Economic Theory, Elsevier, vol. 113(2), pages 235-252, December.
  14. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, December.
  15. Balasko, Yves & Cass, David & Shell, Karl, 1980. "Existence of competitive equilibrium in a general overlapping-generations model," Journal of Economic Theory, Elsevier, vol. 23(3), pages 307-322, December.
  16. Burke, Jonathan L., 1996. "Equilibrium for Overlapping Generations in Continuous Time," Journal of Economic Theory, Elsevier, vol. 70(2), pages 364-390, August.
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Cited by:
  1. Feigenbaum, James & Gahramanov, Emin & Tang, Xueli, 2013. "Is it really good to annuitize?," Journal of Economic Behavior & Organization, Elsevier, vol. 93(C), pages 116-140.

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