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Non-convex Aggregate Technology and Optimal Economic Growth

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  • Nguyen Manh Hung

    ()
    (Université de Laval - Universite Laval (Quebec) - Canada)

  • Cuong Le Van

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Philippe Michel

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - École des Hautes Études en Sciences Sociales (EHESS) - CNRS : UMR6579)

Abstract

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state equilibrium toward which the convergence of the optimal paths is monotone and asymptotic. When the discount rate is in some intermediate range, we find sufficient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, the optimal paths converge to one single appropriate equilibrium steady state. This state might be a poverty trap with low per capita capital, which acts as the extinction state encountered in earlier studies focused on S-shapes production functions. Second, we consider the case of linear utility and provide sufficient conditions to have either unique or two steady states when the discount rate is in some intermediate range . In the latter case, we give conditions under which the above critical value might not exist, and the economy attains one steady state infinite time, then stays at the other steady state afterward.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00267100.

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Date of creation: Sep 2009
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Publication status: Published, Economic Theory, 2009, 40, 457-471
Handle: RePEc:hal:cesptp:halshs-00267100

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Keywords: Non-convex agreggative technology - optimal economic growth - steady state;

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References

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  1. Dana, Rose-Anne & Le Van, Cuong, 2003. "Dynamic Programming in Economics," Economics Papers from University Paris Dauphine 123456789/13605, Paris Dauphine University.
  2. Takashi Kamihigashi & Santanu Roy, 2004. "Dynamic Optimization with a Nonsmooth, Nonconvex Technology: The Case of a Linear Objective Function," Discussion Paper Series, Research Institute for Economics & Business Administration, Kobe University 161, Research Institute for Economics & Business Administration, Kobe University.
  3. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  4. 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, Elsevier, vol. 31(2), pages 332-354, December.
  5. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, Elsevier, vol. 85(1), pages 24-51, March.
  6. Takashi Kamihigashi & Santanu Roy, 2003. "A Nonsmooth, Nonconvex Model of Optimal Growth," Discussion Paper Series, Research Institute for Economics & Business Administration, Kobe University 158, Research Institute for Economics & Business Administration, Kobe University.
  7. Majumdar, Mukul & Mitra, Tapan, 1983. "Dynamic Optimization with a Non-Convex Technology: The Case of a Linear Objective Function," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 50(1), pages 143-51, January.
  8. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, Econometric Society, vol. 46(3), pages 527-39, May.
  9. Dana, Rose-Anne & Le Van, Cuong, 2003. "Dynamic Programming in Economics," Economics Papers from University Paris Dauphine 123456789/416, Paris Dauphine University.
  10. Mukul Majumdar & Manfred Nermuth, 1982. "Dynamic Optimization in Non-Convex Models with Irreversible Investment: Monotonicity and Turnpike Results (Now published in Zeitschrift für National-Ökonomie (Journal of National Economics), vol.42,," STICERD - Theoretical Economics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE 40, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  11. Majumdar, Mukul & Mitra, Tapan, 1982. "Intertemporal allocation with a non-convex technology: The aggregative framework," Journal of Economic Theory, Elsevier, Elsevier, vol. 27(1), pages 101-136, June.
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Cited by:
  1. Cuong Le Van & Cagri Saglam & Agah Turan, 2014. "Optimal Growth Strategy Under Dynamic Threshold," Working Papers, Department of Research, Ipag Business School 2014-123, Department of Research, Ipag Business School.
  2. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2011. "Monotonicity and Continuity of the Critical Capital Stock in the Dechert-Nishimura Model," Discussion Paper Series, Research Institute for Economics & Business Administration, Kobe University DP2011-20, Research Institute for Economics & Business Administration, Kobe University, revised Sep 2011.

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