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Why Politics Makes Strange Bedfellows: Dynamic Model with DNS Curves

Author

Listed:
  • J. P. Caulkins

    (Carnegie Mellon University)

  • R. F. Hartl

    (University of Vienna)

  • G. Tragler

    (Vienna University of Technology)

  • G. Feichtinger

    (Vienna University of Technology)

Abstract

We analyze a two-dimensional system of political behavior which has three equilibria in the uncontrolled version. After adding a control variable, two more equilibria occur and Skiba curves (also called DNS curves) can be analyzed. In this model, it is possible to derive under what conditions each of the different equilibria is a saddle point, a node, or a focus. In particular, for certain parameter ranges, all five equilibria have real eigenvalues. In this case, the Skiba curves can be computed in a more straightforward way than usual. The curves spiral outward, so any ray extending from the origin crosses these curves arbitrarily many times, as it alternately crosses regions for which it is optimal to approach each of the three equilibria.

Suggested Citation

  • J. P. Caulkins & R. F. Hartl & G. Tragler & G. Feichtinger, 2001. "Why Politics Makes Strange Bedfellows: Dynamic Model with DNS Curves," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 237-254, November.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1011925332503
    DOI: 10.1023/A:1011925332503
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    References listed on IDEAS

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    1. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    2. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    3. Gustav Feichtinger & Peter M. Kort & Richard F. Hartl & Franz Wirl, 2001. "The Dynamics of a Simple Relative Adjustment Cost Framework," German Economic Review, Verein für Socialpolitik, vol. 2(3), pages 255-268, August.
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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. Bruno Buonomo & Alberto d’Onofrio, 2013. "Modeling the Influence of Public’s Memory on the Corruption–Popularity Dilemma in Politics," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 554-575, August.
    3. Akao, Ken-Ichi & Kamihigashi, Takashi & Nishimura, Kazuo, 2011. "Monotonicity and continuity of the critical capital stock in the Dechert–Nishimura model," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 677-682.
    4. Akao, Ken-Ichi & Kamihigashi, Takashi & Nishimura, Kazuo, 2025. "Critical capital stock in a continuous-time growth model with a convex-concave production function," Journal of Mathematical Economics, Elsevier, vol. 119(C).

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