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On Topological Chaos in the Robinson-Solow-Srinivasan Model

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  • Khan, M. Ali

    (Johns Hopkins U)

  • Mitra, Tapan

    (Cornell U)

Abstract

In this paper, we offer an instance of (topologically) chaotic optimal behavior in a twosector model with irreversible investment, originally formulated by Robinson, Solow and Srinivasan. Our result follows from the theory of turbulence in non-linear dynamical systems, and relies only on the existence of a continuous optimal policy function. The fact that there is a unique optimal program from each initial stock when future utilities are discounted by a factor smaller than the labor-capital ratio may be of independent interest.

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Bibliographic Info

Paper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number 04-18.

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Date of creation: Dec 2004
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Handle: RePEc:ecl:corcae:04-18

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References

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  1. Lionel W. McKenzie, 2005. "Classical General Equilibrium Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633302, December.
  2. Khan, M. Ali, 2003. "On choice of technique in the Robinson-Solow-Srinivasan model," Economics Working Papers (Ensaios Economicos da EPGE) 504, FGV/EPGE Escola Brasileira de Economia e Finan├žas, Getulio Vargas Foundation (Brazil).
  3. Dutta, Prajit K. & Mitra, Tapan, 1989. "Maximum theorems for convex structures with an application to the theory of optimal intertemporal allocation," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 77-86, February.
  4. Mitra, Tapan, 1996. "An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models," Journal of Economic Theory, Elsevier, vol. 69(2), pages 281-305, May.
  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.
  6. Nishimura, Kazuo & Yano, Makoto, 1996. "On the Least Upper Bound of Discount Factors That Are Compatible with Optimal Period-Three Cycles," Journal of Economic Theory, Elsevier, vol. 69(2), pages 306-333, May.
  7. Mitra, Tapan, 2001. "A Sufficient Condition for Topological Chaos with an Application to a Model of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 133-152, January.
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Cited by:
  1. Orlando Gomes, 2006. "Local Bifurcations and Global Dynamics in a Solow-type Endogenous Business Cycles Model," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 91-127, May.

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