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

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Author Info
Cuong Le Van () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
Lisa Morhaim (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
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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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00096034_v1.

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Date of creation: Mar 2006
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Publication status: Published, International Journal of Economic Theory, 2006, 2, 1, 55-76
Handle: RePEc:hal:cesptp:halshs-00096034_v1

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Keywords: Optimal growth; discount factor; value function; policy function; differentiability; turnpike.;

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-93, September. [Downloadable!] (restricted)
  2. 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.
  3. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-20, April. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Constructing the Optimal Solutions to the Undiscounted Continuous-Time Infinite Horizon Optimization Problems," Quantitative Finance Papers 0803.4046, arXiv.org. [Downloadable!]
  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," Quantitative Finance Papers 0803.4050, arXiv.org. [Downloadable!]
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