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Note on positive lower bound of capital in the stochastic growth model

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  • Chatterjee, Partha
  • Shukayev, Malik

Abstract

In the context of the classical stochastic growth model, we provide a simple proof that the optimal capital sequence is strictly bounded away from zero whenever the initial capital is strictly positive. We assume that the utility function is bounded below and the shocks affecting output are bounded. However, the proof does not require an interval shock space, thus, admitting both discrete and continuous shocks. Further, we allow for finite marginal product at zero capital. Finally, we use our result to show that any optimal capital sequence converges globally to a unique invariant distribution, which is bounded away from zero.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 32 (2008)
Issue (Month): 7 (July)
Pages: 2137-2147

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Handle: RePEc:eee:dyncon:v:32:y:2008:i:7:p:2137-2147

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Web page: http://www.elsevier.com/locate/jedc

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  1. Donaldson, John B. & Mehra, Rajnish, 1983. "Stochastic growth with correlated production shocks," Journal of Economic Theory, Elsevier, vol. 29(2), pages 282-312, April.
  2. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  3. Tapan Mitra & Santanu Roy, 2006. "Optimal exploitation of renewable resources under uncertainty and the extinction of species," Economic Theory, Springer, vol. 28(1), pages 1-23, 05.
  4. Stefan baumgärtner, 2004. "The Inada Conditions for Material Resource Inputs Reconsidered," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 29(3), pages 307-322, November.
  5. Mirman, Leonard J & Zilcha, Itzhak, 1976. "Unbounded Shadow Prices for Optimal Stochastic Growth Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 121-32, February.
  6. Rolf Fare & Daniel Primont, 2002. "Inada Conditions and the Law of Diminishing Returns," International Journal of Business and Economics, College of Business, and College of Finance, Feng Chia University, Taichung, Taiwan, vol. 1(1), pages 1-8, April.
  7. Partha Chatterjee & Malik Shukayev, 2006. "Convergence in a Stochastic Dynamic Heckscher-Ohlin Model," Working Papers 06-23, Bank of Canada.
  8. Takashi Kamihigashi, 2003. "Almost Sure Convergence to Zero in Stochastic Growth Models," Discussion Paper Series 140, Research Institute for Economics & Business Administration, Kobe University.
  9. Olson, Lars J., 1989. "Stochastic growth with irreversible investment," Journal of Economic Theory, Elsevier, vol. 47(1), pages 101-129, February.
  10. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
  11. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November.
  12. Nishimura, Kazuo & Stachurski, John, 2005. "Stability of stochastic optimal growth models: a new approach," Journal of Economic Theory, Elsevier, vol. 122(1), pages 100-118, May.
  13. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
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Citations

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Cited by:
  1. Mitra, Tapan & Privileggi, Fabio, 2009. "On Lipschitz continuity of the iterated function system in a stochastic optimal growth model," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 185-198, January.
  2. Partha Chatterjee & Malik Shukayev, 2008. "A Stochastic Dynamic Model of Trade and Growth: Convergence and Diversification," DEGIT Conference Papers c013_034, DEGIT, Dynamics, Economic Growth, and International Trade.
  3. Takashi Kamihigashi & John Stachurski, 2011. "Stability of Stationary Distributions in Monotone Economies," ANU Working Papers in Economics and Econometrics 2011-561, Australian National University, College of Business and Economics, School of Economics.
  4. Mitra, Tapan & Roy, Santanu, 2010. "Sustained Positive Consumption in a Model of Stochastic Growth: The Role of Risk Aversion," Working Papers 10-03, Cornell University, Center for Analytic Economics.
  5. Kam, Timothy & Lee, Junsang, 2014. "On stationary recursive equilibria and nondegenerate state spaces: The Huggett model," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 156-159.
  6. Partha Chatterjee & Malik Shukayev, 2006. "Convergence in a Stochastic Dynamic Heckscher-Ohlin Model," Working Papers 06-23, Bank of Canada.
  7. Takashi Kamihigashi & John Stachurski, 2011. "Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2011-32, Research Institute for Economics & Business Administration, Kobe University.

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