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Optimal Regime Switching and Threshold Effects: Theory and Application to a Resource Extraction Problem under Irreversibility

  • Raouf Boucekkine
  • Aude Pommeret
  • Fabien Prieur

We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features ecological-like regimes relying on given threshold values for given state variables. We propose a general optimal control framework allowing to derive the first-order optimality conditions and in particular to characterize the geometry of the shadow prices at optimal switching times (if any). We apply this new optimal control material to address the problem of the optimal management of natural resources under ecological irreversibility, and with the possibility to switch to a backstop technology.

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File URL: http://www.lameta.univ-montp1.fr/Documents/DR2012-14.pdf
File Function: First version, 2012
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Paper provided by LAMETA, Universtiy of Montpellier in its series Working Papers with number 12-14.

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Length: 40 pages
Date of creation: May 2012
Date of revision: May 2012
Handle: RePEc:lam:wpaper:12-14
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Web page: http://www.lameta.univ-montp1.fr/

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  1. BOUCEKKINE, RAOUF & SAGLAM , Cagri & VALLÉE, Thomas, 2003. "Technology adoption under embodiment: a two-stage optimal control approach," CORE Discussion Papers 2003055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. repec:cor:louvrp:2335 is not listed on IDEAS
  3. Oded Galor, 2004. "The Demographic Transition and the Emergence of Sustained Economic Growth," GE, Growth, Math methods 0409005, EconWPA.
  4. Fabien Prieur & Mabel Tidball & Cees A. Withagen, 2011. "Optimal Emission-Extraction Policy in a World of Scarcity and Irreversibility," CESifo Working Paper Series 3512, CESifo Group Munich.
  5. Larry Karp & Jiangfeng Zhang, 2012. "Taxes versus quantities for a stock pollutant with endogenous abatement costs and asymmetric information," Economic Theory, Springer, vol. 49(2), pages 371-409, February.
  6. Simone Valente, 2009. "Endogenous Growth, Backstop Technology Adoption and Optimal Jumps," CER-ETH Economics working paper series 09/104, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  7. Makris, Miltiadis, 2001. "Necessary conditions for infinite-horizon discounted two-stage optimal control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1935-1950, December.
  8. Tahvonen, Olli & Withagen, Cees, 1996. "Optimality of irreversible pollution accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1775-1795.
  9. repec:ner:tilbur:urn:nbn:nl:ui:12-3107026 is not listed on IDEAS
  10. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
  11. Tomiyama, Ken, 1985. "Two-stage optimal control problems and optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 9(3), pages 317-337, November.
  12. Fabien Prieur, 2007. "The Environmental Kuznets Curve in a World of Irreversibility," Working Papers 2007.57, Fondazione Eni Enrico Mattei.
  13. Pommeret, Aude & Schubert, Katheline, 2009. "Abatement Technology Adoption Under Uncertainty," Macroeconomic Dynamics, Cambridge University Press, vol. 13(04), pages 493-522, September.
  14. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 855-74, November.
  15. Zampolli, Fabrizio, 2006. "Optimal monetary policy in a regime-switching economy: The response to abrupt shifts in exchange rate dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1527-1567.
  16. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2011. "Technological vs ecological switch and the environmental Kuznets curve," Working Papers halshs-00633024, HAL.
  17. BOUCEKKINE, Raouf & KRAWCZYK, Jacek B. & VALLEE, Thomas, . "Environmental quality versus economic performance: a dynamic game approach," CORE Discussion Papers RP -2335, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. Parente Stephen L., 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth," Journal of Economic Theory, Elsevier, vol. 63(2), pages 346-369, August.
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