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Sustained positive consumption in a model of stochastic growth: The role of risk aversion

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  • Mitra, Tapan
  • Roy, Santanu

Abstract

In a stochastic economy, long run consumption and output may not be bounded away from zero even when productivity is arbitrarily high near zero and uncertainty is arbitrarily small. In the one-sector stochastic optimal growth model with i.i.d. production shocks, we characterize the nature of preferences that lead to this phenomenon for a stochastic Cobb–Douglas technology. For the general version of the model, we outline sufficient conditions under which the economy expands its capital stock near zero and long run consumption is bounded away from zero with certainty. Our conditions highlight the important role played by risk aversion for small consumption levels.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 2 ()
Pages: 850-880

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:2:p:850-880

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Stochastic growth; Sustained consumption; Extinction; Risk aversion;

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References

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  1. 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.
  2. 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.
  3. Danyang Xie, 2002. "Power Risk Aversion Utility Functions," International Finance 0207006, EconWPA.
  4. Takashi Kamihigashi, 2003. "Almost Sure Convergence to Zero in Stochastic Growth Models," Discussion Paper Series 140, Research Institute for Economics & Business Administration, Kobe University.
  5. Boylan, Edward S., 1979. "On the avoidance of extinction in one-sector growth models," Journal of Economic Theory, Elsevier, vol. 20(2), pages 276-279, April.
  6. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
  7. Mirman, Leonard J. & Zilcha, Itzhak, 1977. "Characterizing optimal policies in a one-sector model of economic growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 14(2), pages 389-401, April.
  8. 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.
  9. Olson, Lars J. & Roy, Santanu, 2000. "Dynamic Efficiency of Conservation of Renewable Resources under Uncertainty," Journal of Economic Theory, Elsevier, vol. 95(2), pages 186-214, December.
  10. Mitra, Tapan & Roy, Santanu, 2007. "On the possibility of extinction in a class of Markov processes in economics," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 842-854, September.
  11. Mendelssohn, Roy & Sobel, Matthew J., 1980. "Capital accumulation and the optimization of renewable resource models," Journal of Economic Theory, Elsevier, vol. 23(2), pages 243-260, October.
  12. 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.
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Cited by:
  1. Herbst, Anthony F. & Wu, Joseph S.K. & Ho, Chi Pui, 2012. "Relationship between risk attitude and economic recovery in optimal growth theory," Global Finance Journal, Elsevier, vol. 23(3), pages 141-150.
  2. Acemoglu, Daron, 2012. "Introduction to economic growth," Journal of Economic Theory, Elsevier, vol. 147(2), pages 545-550.

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