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On the non-existence of optimal programs in the Robinson-Solow-Srinivasan (RSS) model

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  • Khan, M. Ali
  • Piazza, Adriana

Abstract

We show that in the 2-sector RSS model, there is no optimal program for any initial stock when the felicity function is linear and the marginal rate [xi] equals unity. This settles a conjecture, unresolved since 2005.

Suggested Citation

  • Khan, M. Ali & Piazza, Adriana, 2010. "On the non-existence of optimal programs in the Robinson-Solow-Srinivasan (RSS) model," Economics Letters, Elsevier, vol. 109(2), pages 94-98, November.
    • Handle: RePEc:eee:ecolet:v:109:y:2010:i:2:p:94-98
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    4. Kazuo Nishimura & Makoto Yano, 2012. "Non-linear Dynamics and Chaos in Optimal Growth: An Example," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 127-150, Springer.
    5. Robert M. Solow, 1962. "Substitution and Fixed Proportions in the Theory of Capital," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(3), pages 207-218.
    6. M. Ali Khan & Alexander J. Zaslavski, 2009. "On Locally Optimal Programs in The RSS (Robinson-Solow-Srinivasan) Model," Discussion Papers Series 396, School of Economics, University of Queensland, Australia.
    7. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 275-280.
    8. McKenzie, Lionel W., 2005. "Optimal economic growth, turnpike theorems and comparative dynamics," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 2, volume 3, chapter 26, pages 1281-1355, Elsevier.
    9. Hiroshi Atsumi, 1965. "Neoclassical Growth and the Efficient Program of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 127-136.
    10. 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.
    11. Metcalf, Christopher J., 2008. "The dynamics of the Stiglitz policy in the RSS model," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 652-661.
    12. 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.
    13. Lionel W. McKenzie, 2005. "Classical General Equilibrium Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633302, December.
    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.
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    Cited by:

    1. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2015. "On the Mitra–Wan forest management problem in continuous time," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1001-1040.
    2. Giorgio Fabbri & Silvia Faggian & Giuseppe Freni, 2016. "Non-Existence of Optimal Programs in Continuous Time," AMSE Working Papers 1630, Aix-Marseille School of Economics, France.
    3. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2017. "Non-existence of optimal programs for undiscounted growth models in continuous time," Economics Letters, Elsevier, vol. 152(C), pages 57-61.

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