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Dynamic Optimization with a Non-Convex Technology: The Case of a Linear Objective Function

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  • Mukul Majumdar
  • Tapan Mitra

Abstract

The paper studies the problem of optimal intertemporal allocation in an aggregative model with a non-convex technology set and a discounted sum of consumptions as the objective function. The study demonstrates the existence of a threshold initial stock such that the long-run behaviour of optimal programmes depends critically on whether the initial stock is, above or below the threshold. This is in contrast with the standard turnpike theory of convex models in which the long-run behaviour of optimal programmes is independent of the initial stock.

Suggested Citation

  • Mukul Majumdar & Tapan Mitra, 1983. "Dynamic Optimization with a Non-Convex Technology: The Case of a Linear Objective Function," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 143-151.
    • Handle: RePEc:oup:restud:v:50:y:1983:i:1:p:143-151.
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    File URL: http://hdl.handle.net/10.2307/2296961
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    Cited by:

    1. Stefano Bosi & Thai Ha-Hui, 2023. "A multidimensional, nonconvex model of optimal growth," Documents de recherche 23-07, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    2. Dawid, Herbert & Kopel, Michael, 1997. "On the Economically Optimal Exploitation of a Renewable Resource: The Case of a Convex Environment and a Convex Return Function," Journal of Economic Theory, Elsevier, vol. 76(2), pages 272-297, October.
    3. Ha-Huy, Thai & Tran, Nhat Thien, 2020. "A simple characterisation for sustained growth," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 141-147.
    4. N. Hung & C. Le Van & P. Michel, 2009. "Non-convex aggregate technology and optimal economic growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 457-471, September.
    5. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    6. Gregory Cox, 2018. "Almost Sure Uniqueness of a Global Minimum Without Convexity," Papers 1803.02415, arXiv.org, revised Feb 2019.
    7. Rabah Amir, 1985. "A Characterization of Globally Optimal Paths in the Non-Classical Growth Model," Cowles Foundation Discussion Papers 754, Cowles Foundation for Research in Economics, Yale University.
    8. 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.
    9. Banerjee, Kuntal & Mitra, Tapan, 2010. "Equivalence of utilitarian maximal and weakly maximal programs," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 279-292, May.
    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.
    11. Dilip Mookherjee & Debraj Ray, 2003. "Persistent Inequality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 369-393.
    12. Ha-Huy, Thai & Tran, Nhat-Thien, 2019. "A simple characterization for sustained growth," MPRA Paper 94576, University Library of Munich, Germany.
    13. Serena Brianzoni & Cristiana Mammana & Elisabetta Michetti, 2012. "Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function," Working Papers 70-2012, Macerata University, Department of Finance and Economic Sciences, revised Sep 2015.
    14. Koji Kotani & Makoto Kakinaka & Hiroyuki Matsuda, 2006. "Dynamic Economic Analysis on Invasive Species Management: Some Policy Implications of Catchability," Working Papers EMS_2006_16, Research Institute, International University of Japan.
    15. Rabi Bhattacharya & Mukul Majumdar, 2010. "Random iterates of monotone maps," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 185-192, March.
    16. Michetti, Elisabetta, 2015. "Complex attractors and basins in a growth model with nonconcave production function and logistic population growth rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 215-232.
    17. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2015. "Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function," Discussion Paper Series DP2015-39, Research Institute for Economics & Business Administration, Kobe University.

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