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On optimal growth models when the discount factor is near 1 or equal to 1

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  • Cuong Le Van
  • Lisa Morhaim

Abstract

The aim of this paper is to fill the gap between intertemporal growth models when the discount factor beta is close to one and when it equals one.We show that the value function and the policy function are continuous with respect both to the discount factor and the initial stock of capitalx0. We prove that the optimal policy g(x0) is differentiable and that Dg(x0) is continuous with respect to (beta, x0). As a by-product, a globalturnpike result is proved.
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  • Cuong Le Van & Lisa Morhaim, 2006. "On optimal growth models when the discount factor is near 1 or equal to 1," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(1), pages 55-76.
  • Handle: RePEc:bla:ijethy:v:2:y:2006:i:1:p:55-76
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    References listed on IDEAS

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    1. Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-1393, September.
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    3. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    4. Santos, M.S., 1989. "Differentiability And Comparative Analysis In Discrete-Time Infinite-Horizon Optimization Problems," UFAE and IAE Working Papers 127-89, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    5. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
    6. Venditti, Alain, 1997. "Strong Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Journal of Economic Theory, Elsevier, vol. 74(2), pages 349-367, June.
    7. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
    8. Santos, Manuel S., 1994. "Smooth dynamics and computation in models of economic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 18(3-4), pages 879-895.
    9. Montrucchio, Luigi, 1998. "Thompson metric, contraction property and differentiability of policy functions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 449-466, January.
    10. Makoto Yano, 1998. "On the Dual Stability of a von Neumann Facet and the Inefficacy of Temporary Fiscal Policy," Econometrica, Econometric Society, vol. 66(2), pages 427-452, March.
    11. McKenzie, Lionel W., 2005. "Optimal economic growth, turnpike theorems and comparative dynamics," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 2, volume 3, chapter 26, pages 1281-1355 Elsevier.
    12. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
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    Cited by:

    1. Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Constructing the Optimal Solutions to the Undiscounted Continuous-Time Infinite Horizon Optimization Problems," Papers 0803.4046, arXiv.org.
    2. Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Limit of the Solutions for the Finite Horizon Problems as the Optimal Solution to the Infinite Horizon Optimization Problems," Papers 0803.4050, arXiv.org.
    3. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    4. Emmanuel Thibault, 2008. "Dynamic efficiency and intergenerational altruism," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 679-687, July.

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