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Recursive utility and optimal growth with bounded or unbounded returns

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  • LE VAN, Cuong
  • VAILAKIS, Yiannis

Abstract

In this paper we propose a unifying approach to the study of recursive economic problems. Postulating an aggregator function as the fundamental expression of tastes, we explore conditions under which a utility function can be constructed. We also modify the usual dynamic programming arguments to include this class of models. We show that Bellman's equation still holds, so many results known for the additively separable case can be generalized for this general description of preferences. Our approach is general, allowing for both bounded and unbounded (above/below) returns. Many recursive economic models, including the standard examples studied in the literature, are particular cases of our setting.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2002055.

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Date of creation: 00 Oct 2002
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Handle: RePEc:cor:louvco:2002055

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Keywords: recursive utility; dynamic programming; Bellman equation; unbounded returns;

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References

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  1. LE VAN, Cuong & MORHAIM, Lisa, 2001. "Optimal growth models with bounded or unbounded returns: a unifying approach," CORE Discussion Papers 2001034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, vol. 32(1), pages 139-171, February.
  3. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
  4. Dana, Rose-Anne & Van, Cuong Le, 1991. "Optimal growth and Pareto optimality," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 155-180.
  5. Duran, Jorge, 2001. "Discounting long run average growth in stochastic dynamic programs," CEPREMAP Working Papers (Couverture Orange) 0101, CEPREMAP.
  6. Streufert, Peter A, 1990. "Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 79-97, January.
  7. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
  8. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
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Cited by:
  1. repec:hal:wpaper:hal-00294828 is not listed on IDEAS
  2. Matkowski, Janusz & Nowak, Andrzej S., 2008. "On Discounted Dynamic Programming with Unbounded Returns," MPRA Paper 12215, University Library of Munich, Germany.
  3. Jaśkiewicz, Anna & Matkowski, Janusz & Nowak, Andrzej S., 2011. "On Variable Discounting in Dynamic Programming: Applications to Resource Extraction and Other Economic Models," MPRA Paper 31069, University Library of Munich, Germany, revised 24 May 2011.
  4. Cuong Le Van & Lisa Morhaim & Yiannis Vailakis, 2008. "Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation," Discussion Papers 0803, Exeter University, Department of Economics.
  5. Mohamed Mabrouk, 2005. "Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations," GE, Growth, Math methods 0511007, EconWPA.
  6. Mohamed Mabrouk, 2005. "Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth I: Consensual optimality," GE, Growth, Math methods 0510013, EconWPA.
  7. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.

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