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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 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, β, and the initial stock of capital, x0. We prove that the optimal policy gβ(x0) is differentiable and that Dgβ(x0) is continuous with respect to (β, x0). As a by‐product, a global turnpike 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, March.
    • Handle: RePEc:bla:ijethy:v:2:y:2006:i:1:p:55-76
    DOI: 10.1111/j.1365-2966.2006.0024.x
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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. Ha-Huy, Thai, 2022. "A tale of two Rawlsian criteria," Mathematical Social Sciences, Elsevier, vol. 118(C), pages 30-35.
    3. Jean-Michel Grandmont, 2013. "Tribute to Cuong Le Van," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 5-10, March.
    4. 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.
    5. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    6. 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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