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Growth in the Robinson-Solow-Srinivasan model: Undiscounted optimal policy with a strictly concave welfare function

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  • Ali Khan, M.
  • Mitra, Tapan

Abstract

In a special case of a model due to Robinson, Solow and Srinivasan, we characterize the optimal policy function (OPF) for undiscounted optimal growth with a strictly concave felicity function. This characterization is based on an equivalence of optimal and minimum value-loss programs that allows an extension of the principal results of dynamic programming. We establish monotonicity properties of the OPF, and obtain sharper characterizations when restrictions on the marginal rate of transformation are supplemented by sufficient conditions on the "degree of concavity" of the felicity function. We show that important similarities and intriguing differences emerge between the linear and strictly concave cases as the marginal rate of transformation moves through its range of possible values.

Suggested Citation

  • Ali Khan, M. & Mitra, Tapan, 2008. "Growth in the Robinson-Solow-Srinivasan model: Undiscounted optimal policy with a strictly concave welfare function," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 707-732, July.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:7-8:p:707-732
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    1. William A. Brock & Mukul Majumdar, 2015. "On Characterizing Optimal Competitive Programs in Terms of Decentralizable Conditions," World Scientific Book Chapters, in: Mukul Majumdar (ed.), Decentralization in Infinite Horizon Economies, chapter 3, pages 46-57, World Scientific Publishing Co. Pte. Ltd..
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    3. M. Khan & Tapan Mitra, 2006. "Undiscounted optimal growth in the two-sector Robinson-Solow-Srinivasan model: a synthesis of the value-loss approach and dynamic programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 341-362, October.
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    9. Roy Radner, 1961. "Prices and the Turnpike: III. Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 98-104.
    10. Robinson, Joan, 1969. "A Model for Accumulation Proposed by J. E. Stiglitz," Economic Journal, Royal Economic Society, vol. 79(314), pages 412-413, June.
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    Cited by:

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    2. M. Ali Khan & Adriana Piazza, 2010. "On uniform convergence of undiscounted optimal programs in the Mitra–Wan forestry model: The strictly concave case," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 57-76, March.
    3. Ali Khan, M. & Zhang, Zhixiang, 2023. "The random two-sector RSS model: On discounted optimal growth without Ramsey-Euler conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).

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