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

  • Chatterjee, Partha
  • Shukayev, Malik

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. Takashi Kamihigashi, 2003. "Almost Sure Convergence to Zero in Stochastic Growth Models," Discussion Paper Series 140, Research Institute for Economics & Business Administration, Kobe University.
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  8. 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.
  9. Olson, Lars J., 1989. "Stochastic growth with irreversible investment," Journal of Economic Theory, Elsevier, vol. 47(1), pages 101-129, February.
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