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A Nonsmooth, Nonconvex Model of Optimal Growth

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Author Info
Takashi Kamihigashi (Research Institute for Economics and Business Administration, Kobe University)
Santanu Roy (Department of Economics, Southern Methodist University)

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Abstract

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We provide sufficient conditions for boundedness, extinction (convergence to zero), survival (boundedness away from zero), and unbounded growth. These conditions reveal that boundedness and survival are symmetrical phenomena, so are extinction and unbounded growth. Since many of the conditions are only local, it is possible that extinction occurs from small capital stocks, while unbounded growth occurs from large capital stocks. Despite such nonclassical results and nonclassical features such as nonconvexity and discontinuity, the model behaves much like a classical one as the discount factor approaches unity. In particular, we show that in most cases, if the discount factor is close to one, any optimal path from a given initial capital stock converges to a small neighborhood of what we define as the golden rule capital stock. If this stock is not finite, i.e., if sustainable consumption is maximized atinfinity, then as the discount factor approaches one, unbounded growth at least almost occurs.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp139.pdf
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Publisher Info
Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 139.

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Length: 46 pages
Date of creation: Aug 2003
Date of revision:
Handle: RePEc:kob:dpaper:139

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Keywords: Nonconvex; nonsmooth; and discontinuous technology; optimal growth; unbounded growth; extinction; neighborhood turnpike.;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Joshi, Sumit, 1997. "Turnpike Theorems in Nonconvex Nonstationary Environments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 225-48, February.
  2. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March. [Downloadable!] (restricted)
  3. Jones, Larry E & Manuelli, Rodolfo E, 1990. "A Convex Model of Equilibrium Growth: Theory and Policy Implications," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 1008-38, October. [Downloadable!] (restricted)
  4. Guerrero-Luchtenberg, C.L., 2000. "A uniform neighborhood turnpike theorem and applications," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 329-357, November. [Downloadable!] (restricted)
  5. Montrucchio, Luigi, 1995. "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer, vol. 5(3), pages 371-82, May.
  6. Azariadis, Costas & Drazen, Allan, 1990. "Threshold Externalities in Economic Development," The Quarterly Journal of Economics, MIT Press, vol. 105(2), pages 501-26, May. [Downloadable!] (restricted)
  7. de Hek, Paul & Roy, Santanu, 2001. "On Sustained Growth under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 801-13, August.
  8. Larry E. Jones & Rodolfo E. Manuelli, 1994. "The Sources of Growth," Macroeconomics 9411002, EconWPA, revised 05 Mar 1999. [Downloadable!]
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  9. Dolmas, Jim, 1996. "Endogenous Growth in Multisector Ramsey Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 403-21, May.
  10. Takashi Kamihigashi & Santanu Roy, 2003. "A Nonsmooth, Nonconvex Model of Optimal Growth," Discussion Paper Series 158, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
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  11. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December. [Downloadable!] (restricted)
  12. Kaganovich, Michael, 1998. "Sustained endogenous growth with decreasing returns and heterogeneous capital," Journal of Economic Dynamics and Control, Elsevier, vol. 22(10), pages 1575-1603, August. [Downloadable!] (restricted)
  13. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August. [Downloadable!] (restricted)
  14. Montrucchio, Luigi, 1994. "The neighbourhood turnpike property for continuous-time optimal growth models," Ricerche Economiche, Elsevier, vol. 48(3), pages 213-224, September. [Downloadable!] (restricted)
  15. Takashi Kamihigashi & Santanu Roy, 2005. "Dynamic optimization with a nonsmooth, nonconvex technology: The case of a linear objective function," Discussion Paper Series 175, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
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  16. Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February. [Downloadable!] (restricted)
  17. Olson, Lars J. & Roy, Santanu, 1996. "On Conservation of Renewable Resources with Stock-Dependent Return and Nonconcave Production," Journal of Economic Theory, Elsevier, vol. 70(1), pages 133-157, July. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Nguyen Manh Hung & Cuong Le Van & Philippe Michel, 2008. "Non-convex Aggregate Technology and Optimal Economic Growth," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00267100_v1, HAL. [Downloadable!]
    Other versions:
  2. Takashi Kamihigashi & Santanu Roy, 2005. "A nonsmooth, nonconvex model of optimal growth," Discussion Paper Series 173, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
    Other versions:
  3. Olivier Bruno & Cuong Le Van & Benoit Masquin, 2008. "When Does a Developing Country Use New Technologies?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00101361_v2, HAL. [Downloadable!]
  4. Takashi Kamihigashi, 2006. "Stochastic Optimal Growth with Bounded or Unbounded Utility and with Bounded or Unbounded Shocks," Discussion Paper Series 189, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
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