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Abstract

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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Bibliographic Info

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

Contact details of provider:
Postal: Avenue Raymond Dugrand, CS 79606, 34960 Montpellier Cedex 2
Phone: +33-467-158-568
Fax: +33-467-158-467
Web page: http://www.lameta.univ-montp1.fr/
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Find related papers by JEL classification:

• Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
• Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
• C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
• O33 - Economic Development, Technological Change, and Growth - - Technological Change; Research and Development; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

This paper has been announced in the following NEP Reports:

• NEP-ALL-2012-06-05 (All new papers)
• NEP-ENV-2012-06-05 (Environmental Economics)

References

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1. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2011. "Technological vs ecological switch and the environmental Kuznets curve," Working Papers halshs-00633024, HAL.
   
   • Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
2. Fabien Prieur, 2007. "The Environmental Kuznets Curve in a World of Irreversibility," Working Papers 2007.57, Fondazione Eni Enrico Mattei.
   
   • Fabien Prieur, 2009. "The environmental Kuznets curve in a world of irreversibility," Economic Theory, Springer, vol. 40(1), pages 57-90, July.
3. 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).
   
   • Boucekkine, Raouf & Saglam, Cagri & Vall Ee, Thomas, 2004. "Technology Adoption Under Embodiment: A Two-Stage Optimal Control Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 8(02), pages 250-271, April.
   • Raouf, BOUCEKKINE & Cagri, SAGLAM & Thomas, VALLEE, 2002. "Technology adoption under embodiment : A two-stage optimal control approach," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2003007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
4. Fabrizio Zampolli, 2006. "Optimal monetary policy in a regime-switching economy: the response to abrupt shifts in exchange rate dynamics," Bank of England working papers 297, Bank of England.
5. 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.
6. Parente Stephen L., 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth," Journal of Economic Theory, Elsevier, vol. 63(2), pages 346-369, August.
7. 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.
   
   • Valente, Simone, 2011. "Endogenous Growth, Backstop Technology Adoption, And Optimal Jumps," Macroeconomic Dynamics, Cambridge University Press, vol. 15(03), pages 293-325, June.
8. Oded Galor, 2004. "The Demographic Transition and the Emergence of Sustained Economic Growth," GE, Growth, Math methods 0409005, EconWPA.
   
   • Oded Galor, 2005. "The Demographic Transition and the Emergence of Sustained Economic Growth," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 494-504, 04/05.
   • Galor, Oded, 2004. "The Demographic Transition and the Emergence of Sustained Economic Growth," CEPR Discussion Papers 4714, C.E.P.R. Discussion Papers.
   • Oded_Galor, 2004. "The Demographic Transition and the Emergence of Sustained Economic Growth," Working Papers 2004-13, Brown University, Department of Economics.
9. Tahvonen, Olli & Withagen, Cees, 1996. "Optimality of irreversible pollution accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1775-1795.
   
   • Tahvonen, O. & Withagen, C.A.A.M., 1996. "Optimality of irreversible pollution accumulation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3107026, Tilburg University.
10. 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.
11. Fabien Prieur & Mabel Tidball & Cees Withagen, 2012. "Optimal Emission-Extraction Policy in a World of Scarcity and Irreversibility," OxCarre Working Papers 077, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
    
    • 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.
12. 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.
13. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 855-74, November.
14. 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.
    
    • Karp, Larry & Zhang, Jiangfeng, 2008. "Taxes Versus Quantities for a Stock Pollutant with Endogenous Abatement Costs and Asymmetric Information," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt84q0s8tb, Department of Agricultural & Resource Economics, UC Berkeley.
15. Pommeret, Aude & Schubert, Katheline, 2009. "Abatement Technology Adoption Under Uncertainty," Macroeconomic Dynamics, Cambridge University Press, vol. 13(04), pages 493-522, September.
16. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.

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