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Skiba Points for Small Discount Rates

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  • F. O. O. Wagener

    (University of Amsterdam)

Abstract

The present article uses perturbation techniques to approximate the value function of an economic minimization problem for small values of the discount rate. This can be used to obtain the approximate location of the Skiba states in the problem; these are states for which there are two distinct optimal state trajectories, converging to different optimal steady states. It is shown that the sets of these indifference thresholds are locally smooth manifolds. For a simple example, all relevant quantities are computed explicitly. Moreover, the approximation can be used to obtain parameter-dependent approximations to the indifference manifolds.

Suggested Citation

  • F. O. O. Wagener, 2006. "Skiba Points for Small Discount Rates," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 261-277, February.
    • Handle: RePEc:spr:joptap:v:128:y:2006:i:2:d:10.1007_s10957-006-9028-5
    DOI: 10.1007/s10957-006-9028-5
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    Cited by:

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    3. Grass, D., 2012. "Numerical computation of the optimal vector field: Exemplified by a fishery model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1626-1658.
    4. Thierry Bréchet & Natali Hritonenko & Yuri Yatsenko, 2013. "Adaptation and Mitigation in Long-term Climate Policy," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 55(2), pages 217-243, June.
    5. Antoci, Angelo & Galeotti, Marcello & Russu, Paolo, 2011. "Poverty trap and global indeterminacy in a growth model with open-access natural resources," Journal of Economic Theory, Elsevier, vol. 146(2), pages 569-591, March.
    6. 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.
    7. Brechet, Thierry & HRITONENKO, Natali & YATSENKO, Yuri, 2010. "Adaptation and mitigation in long-term climate policies," LIDAM Discussion Papers CORE 2010065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.
    9. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2015. "Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function," Discussion Paper Series DP2015-39, Research Institute for Economics & Business Administration, Kobe University.

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