On optimal growth models when the discount factor is near 1 or equal to 1
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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Volume (Year): 2 (2006)
Issue (Month): 1 ()
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- 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).
- Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
- 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.
- Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
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- Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, vol. 59(5), pages 1383-1393, September.
- 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.
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- Venditti, A., 1995. "Strong Concavity Properties of Direct Utility Functions in Multisector Optimal Growth Models," G.R.E.Q.A.M. 95a31, Universite Aix-Marseille III.
- 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.
- 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.
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