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Instabilities in Concave, Dynamic, Economic Optimization

Author

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  • G. Feichtinger

    (Vienna University of Technology)

  • F. Wirl

    (Otto von Guericke University Magdeburg)

Abstract

An important and numerous literature argues that nonconcavity (often convexity with respect to the state) of the Hamiltonian leads to multiple steady states, instability, and a threshold. This threshold property provides a powerful paradigm to explain history dependency and hysteresis. This paper shows that economically relevant properties (in particular, multiple steady states and thresholds) are possible in strict concave models too. Two corresponding necessary conditions with intuitive economic interpretation are derived.

Suggested Citation

  • G. Feichtinger & F. Wirl, 2000. "Instabilities in Concave, Dynamic, Economic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 275-286, November.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:2:d:10.1023_a:1026408814862
    DOI: 10.1023/A:1026408814862
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    References listed on IDEAS

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    8. Feichtinger, Gustav & Novak, Andreas & Wirl, Franz, 1994. "Limit cycles in intertemporal adjustment models : Theory and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 18(2), pages 353-380, March.
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    Cited by:

    1. Jonathan P. Caulkins & Gustav Feichtinger & Josef Haunschmied & Gernot Tragler, 2006. "Quality Cycles and the Strategic Manipulation of Value," Operations Research, INFORMS, vol. 54(4), pages 666-677, August.
    2. G. Feichtinger & A. Steindl, 2006. "DNS Curves in a Production/Inventory Model," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 295-308, February.
    3. Wirl, Franz & Feichtinger, Gustav, 2006. "History versus expectations: Increasing returns or social influence?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 35(5), pages 877-888, October.
    4. Caulkins, Jonathan P. & Feichtinger, Gustav & Johnson, Michael & Tragler, Gernot & Yegorov, Yuri, 2005. "Skiba thresholds in a model of controlled migration," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 490-508, August.
    5. Wirl, Franz, 2004. "Thresholds in concave renewable resource models," Ecological Economics, Elsevier, vol. 48(2), pages 259-267, February.
    6. Dieter Grass & Gernot Tragler, 2010. "Optimal dynamic management of the population mix," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 539-551, December.
    7. Dockner, Engelbert J. & Nishimura, Kazuo, 2005. "Capital accumulation games with a non-concave production function," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 408-420, August.
    8. S.A. Reshmin & A.M. Tarasyev & C. Watanabe, 2002. "Optimal Trajectories of the Innovation Process and Their Matching with Econometric Data," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 639-655, March.
    9. B. K. Ane & A. M. Tarasyev & C. Watanabe, 2007. "Construction of Nonlinear Stabilizer for Trajectories of Economic Growth," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 303-320, August.
    10. Gavrila, C. & Feichtinger, G. & Tragler, G. & Hartl, R.F. & Kort, P.M., 2005. "History-dependence in a rational addiction model," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 273-293, May.

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