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On choice of technique in the Robinson–Solow–Srinivasan model

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  • M. Ali Khan
  • Tapan Mitra
Abstract
We report results on the optimal “choice of technique” in a model originally formulated by Robinson, Solow and Srinivasan. By viewing this model as a specific instance of the general theory of intertemporal resource allocation associated with Brock, Gale and McKenzie, we resolve long‐standing conjectures in the form of theorems on the existence and price‐support of optimal paths, and on their long‐run behavior. We also examine policies, due to Stiglitz, as a cornerstone for a theory of transition dynamics in this model. We present examples to show that: (i) an optimal program can be periodic; (ii) a Stiglitz' program can be bad; and (iii) a Stiglitz production program can be non‐optimal. We then provide sufficient conditions under which the policies proposed by Stiglitz coincide with optimal behavior.

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  • M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson–Solow–Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110, June.
    • Handle: RePEc:bla:ijethy:v:1:y:2005:i:2:p:83-110
    DOI: 10.1111/j.1742-7363.2005.00007.x
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    Citations

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    Cited by:

    1. Monteiro, Paulo Klinger, 2006. "The set of equilibria of first-price auctions," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 364-372, June.
    2. M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson–Solow–Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110, June.
    3. Khan, M. Ali & Mitra, Tapan, 2005. "On topological chaos in the Robinson-Solow-Srinivasan model," Economics Letters, Elsevier, vol. 88(1), pages 127-133, July.
    4. Kenji Sato & Makoto Yano, 2013. "Optimal ergodic chaos under slow capital depreciation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 57-67, March.
    5. M. Ali Khan & Tapan Mitra, 2007. "Optimal Growth In A Two‐Sector Rss Model Without Discounting: A Geometric Investigation," The Japanese Economic Review, Japanese Economic Association, vol. 58(2), pages 191-225, June.
    6. M. Khan & Alexander Zaslavski, 2007. "On a Uniform Turnpike of the Third Kind in the Robinson-Solow-Srinivasan Model," Journal of Economics, Springer, vol. 92(2), pages 137-166, October.
    7. Khalifa, Sherif, 2011. "Undiscounted optimal growth with consumable capital and labor-intensive consumption goods," Economic Modelling, Elsevier, vol. 28(4), pages 1673-1682, July.
    8. 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.
    9. Metcalf, Christopher J., 2008. "The dynamics of the Stiglitz policy in the RSS model," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 652-661.
    10. Cavalcanti Ferreira, Pedro & Facchini, Giovanni, 2005. "Trade liberalization and industrial concentration: Evidence from Brazil," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(2-3), pages 432-446, May.
    11. Ali Khan, M. & Piazza, Adriana, 2012. "On the Mitra–Wan forestry model: A unified analysis," Journal of Economic Theory, Elsevier, vol. 147(1), pages 230-260.
    12. Tavani, Daniele, 2008. "Optimal Induced Innovation and Growth with Congestion of a Limited Natural Resource," MPRA Paper 11525, University Library of Munich, Germany.
    13. Fujio, Minako & Lei, Yan & Deng, Liuchun & Khan, M. Ali, 2021. "The miniature two-sector model of optimal growth: The neglected case of a capital-intensive investment-good sector," Journal of Economic Behavior & Organization, Elsevier, vol. 186(C), pages 662-671.
    14. Minako Fujio, 2009. "Optimal Transition Dynamics In The Leontief Two‐Sector Growth Model With Durable Capital: The Case Of Capital Intensive Consumption Goods," The Japanese Economic Review, Japanese Economic Association, vol. 60(4), pages 490-511, December.
    15. M. Khan & Alexander Zaslavski, 2010. "On locally optimal programs in the Robinson–Solow–Srinivasan model," Journal of Economics, Springer, vol. 99(1), pages 65-92, February.
    16. Khan, M. Ali, 2016. "On a forest as a commodity and on commodification in the discipline of forestry," Forest Policy and Economics, Elsevier, vol. 72(C), pages 7-17.
    17. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2022. "Continuous unimodal maps in economic dynamics: On easily verifiable conditions for topological chaos," Journal of Economic Theory, Elsevier, vol. 201(C).
    18. Liuchun Deng & Minako Fujio & M. Ali Khan, 2021. "Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 615-639, September.
    19. Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2020. "Exact parametric restrictions for 3-cycles in the RSS model: A complete and comprehensive characterization," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 48-56.
    20. Alexander J. Zaslavski, 2023. "An Optimal Control Problem Related to the RSS Model," Mathematics, MDPI, vol. 11(17), pages 1-14, September.
    21. A. J. Zaslavski, 2010. "Stability of a Turnpike Phenomenon for a Discrete-Time Optimal Control System," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 597-612, June.
    22. Khan, M. Ali & Zaslavski, Alexander J., 2009. "On existence of optimal programs: The RSS model without concavity assumptions on felicities," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 624-633, September.

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O21 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Planning Models; Planning Policy

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