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Characterization of the turnpike property of optimal paths in the aggregative model of intertemporal allocation

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  • Tapan Mitra

Abstract

The present paper provides a complete characterization of the turnpike property of optimal paths in the (reduced form) aggregative model of intertemporal allocation. The characterization allows one to identify precisely the bifurcation point between globally stable and cyclical long‐run optimal behavior. The complete characterization result is used to evaluate several sufficient conditions for global asymptotic stability of optimal paths that have been proposed in the published literature. It is also used to examine sufficient conditions for the emergence of competitive equilibrium cycles in two‐sector models.

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  • Tapan Mitra, 2005. "Characterization of the turnpike property of optimal paths in the aggregative model of intertemporal allocation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(4), pages 247-275, December.
    • Handle: RePEc:bla:ijethy:v:1:y:2005:i:4:p:247-275
    DOI: 10.1111/j.1742-7363.2005.00016.x
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    1. Cass, David & Shell, Karl, 1976. "The structure and stability of competitive dynamical systems," Journal of Economic Theory, Elsevier, vol. 12(1), pages 31-70, February.
    2. Mitra, Tapan & Nishimura, Kazuo, 2001. "Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 256-293, January.
    3. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    4. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
    5. Tyrrell Rockafellar, R., 1976. "Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate," Journal of Economic Theory, Elsevier, vol. 12(1), pages 71-113, February.
    6. Jess Benhabib & Kazuo Nishimura, 2012. "Competitive Equilibrium Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 75-96, Springer.
    7. McKenzie, Lionel W., 1982. "A primal route to the Turnpike and Liapounov stability," Journal of Economic Theory, Elsevier, vol. 27(1), pages 194-209, June.
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    Cited by:

    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. Ali Khan, M. & Piazza, Adriana, 2011. "Optimal cyclicity and chaos in the 2-sector RSS model: An anything-goes construction," Journal of Economic Behavior & Organization, Elsevier, vol. 80(3), pages 397-417.

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    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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