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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.

Suggested Citation

  • Chatterjee, Partha & Shukayev, Malik, 2008. "Note on positive lower bound of capital in the stochastic growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2137-2147, July.
    • Handle: RePEc:eee:dyncon:v:32:y:2008:i:7:p:2137-2147
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    10. Tapan Mitra & Santanu Roy, 2006. "Optimal exploitation of renewable resources under uncertainty and the extinction of species," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 1-23, May.
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    Cited by:

    1. Chatterjee, Partha & Shukayev, Malik, 2012. "A stochastic dynamic model of trade and growth: Convergence and diversification," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 416-432.
    2. 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.
    3. Tapan Mitra & Santanu Roy, 2023. "Stochastic growth, conservation of capital and convergence to a positive steady state," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 311-351, July.
    4. 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.
    5. 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.
    6. Partha Chatterjee & Malik Shukayev, 2006. "Convergence in a Stochastic Dynamic Heckscher-Ohlin Model," Staff Working Papers 06-23, Bank of Canada.
    7. Ali Khan, M. & Zhang, Zhixiang, 2023. "The random two-sector RSS model: On discounted optimal growth without Ramsey-Euler conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    8. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    9. 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.
    10. Mitra, Tapan & Roy, Santanu, 2012. "Sustained positive consumption in a model of stochastic growth: The role of risk aversion," Journal of Economic Theory, Elsevier, vol. 147(2), pages 850-880.

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