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Optimal growth models with bounded or unbounded returns: a unifying approach

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  • LE VAN, Cuong
  • MORHAIM, Lisa

Abstract

In this paper we propose a unifying approach to study optimal growth models with bounded or unbounded returns (above/below). We prove existence of optimal solutions. We prove also, without using contraction method, that the Value function is the unique solution to the Bellman equation in some classes of functions. The value function can be obtained by the usual algorithm defined by the operator provided by the Bellman equation. The well-known results, and those in Alvarez and Stokey (1998) can be obtained from this paper.

Suggested Citation

  • LE VAN, Cuong & MORHAIM, Lisa, 2001. "Optimal growth models with bounded or unbounded returns: a unifying approach," LIDAM Discussion Papers CORE 2001034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2001034
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    References listed on IDEAS

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    1. Dana, Rose-Anne & Van, Cuong Le, 1991. "Optimal growth and Pareto optimality," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 155-180.
    2. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
    3. Boud, John III, 1990. "Recursive utility and the Ramsey problem," Journal of Economic Theory, Elsevier, vol. 50(2), pages 326-345, April.
    4. Jorge DurÂn, 2000. "On dynamic programming with unbounded returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 339-352.
    5. Streufert, Peter A., 1992. "An abstract topological approach to dynamic programming," Journal of Mathematical Economics, Elsevier, vol. 21(1), pages 59-88.
    6. Becker, Robert A & Boyd, John H, III & Foias, Ciprian, 1991. "The Existence of Ramsey Equilibrium," Econometrica, Econometric Society, vol. 59(2), pages 441-460, March.
    7. Peter A. Streufert, 1990. "Stationary Recursive Utility and Dynamic Programming under the Assumption of Biconvergence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 79-97.
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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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