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Optimal Control in Space and Time and the Management of Environmental Resources

Author

Listed:
  • William Brock
  • Anastasios Xepapadeas
  • Athanasios Yannacopoulos

Abstract

We present methods and tools that can be used to study dynamic environmental resource management in a spatial setting, to explore spatially dependent regulation, and to understand pattern formation.In particular we present the maximum principle and its use in the context of the emerging frontier of applications of optimal control of diffusive transport processes to environmental and resource economics. We show how optimal spatiotemporal control induces pattern formation, and how deep uncertainty with a spatial structure can be handled with spatial robust control methods. Finally we show how models with diffusive transport can be extended to allow for long-range effects and more general transport mechanisms.

Suggested Citation

  • William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," DEOS Working Papers 1402, Athens University of Economics and Business.
  • Handle: RePEc:aue:wpaper:1402
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    References listed on IDEAS

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    1. Kyriakopoulou, Efthymia & Xepapadeas, Anastasios, 2013. "Environmental policy, first nature advantage and the emergence of economic clusters," Regional Science and Urban Economics, Elsevier, vol. 43(1), pages 101-116.
    2. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
    3. Smith, Martin D. & Sanchirico, James N. & Wilen, James E., 2009. "The economics of spatial-dynamic processes: Applications to renewable resources," Journal of Environmental Economics and Management, Elsevier, vol. 57(1), pages 104-121, January.
    4. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(01), pages 20-45, February.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics," AMSE Working Papers 1334, Aix-Marseille School of Economics, Marseille, France, revised 05 Jun 2013.
    7. Brock, William & Xepapadeas, Anastasios, 2010. "Pattern formation, spatial externalities and regulation in coupled economic-ecological systems," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 149-164, March.
    8. Desmet, Klaus & Rossi-Hansberg, Esteban, 2015. "On the spatial economic impact of global warming," Journal of Urban Economics, Elsevier, vol. 88(C), pages 16-37.
    9. James E. Wilen, 2007. "Economics of Spatial-Dynamic Processes," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(5), pages 1134-1144.
    10. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    11. Catarina Roseta-Palma & Anastasios Xepapadeas, 2004. "Robust Control in Water Management," Journal of Risk and Uncertainty, Springer, vol. 29(1), pages 21-34, July.
    12. Benteng Zou & Carmen Camacho, 2004. "The spatial Solow model," Economics Bulletin, AccessEcon, vol. 18(2), pages 1-11.
    13. Brito, Paulo, 2011. "Global endogenous growth and distributional dynamics," MPRA Paper 41653, University Library of Munich, Germany.
    14. John Hassler & Per Krusell, 2012. "Economics And Climate Change: Integrated Assessment In A Multi-Region World," Journal of the European Economic Association, European Economic Association, vol. 10(5), pages 974-1000, October.
    15. Brock, William A. & Engström, Gustav & Grass, Dieter & Xepapadeas, Anastasios, 2013. "Energy balance climate models and general equilibrium optimal mitigation policies," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2371-2396.
    16. Hansen, Lars Peter & Sargent, Thomas J., 2003. "Robust control of forward-looking models," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 581-604, April.
    17. Xabadia, M. Àngels & Goetz, Renan U. & Zilberman, David, 2004. "Spatially and Intertemporally Efficient Management of Waterlogging," Working Papers of the Department of Economics, University of Girona 9, Department of Economics, University of Girona.
    18. Athanassoglou, Stergios & Xepapadeas, Anastasios, 2012. "Pollution control with uncertain stock dynamics: When, and how, to be precautious," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 304-320.
    19. Giannis Vardas & Anastasios Xepapadeas, 2010. "Model Uncertainty, Ambiguity and the Precautionary Principle: Implications for Biodiversity Management," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 45(3), pages 379-404, March.
    20. Camacho, Carmen & Zou, Benteng & Briani, Maya, 2008. "On the dynamics of capital accumulation across space," European Journal of Operational Research, Elsevier, vol. 186(2), pages 451-465, April.
    21. Goetz, Renan U. & Zilberman, David, 2000. "The dynamics of spatial pollution: The case of phosphorus runoff from agricultural land," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 143-163, January.
    22. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    23. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    24. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1087-1122, September.
    25. Klaus Desmet & Esteban Rossi-Hansberg, 2010. "On Spatial Dynamics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 43-63.
    26. Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
    27. Magill, Michael J. P., 1977. "Some new results on the local stability of the process of capital accumulation," Journal of Economic Theory, Elsevier, vol. 15(1), pages 174-210, June.
    28. Papageorgiou, Yorgo Y & Smith, Terrence R, 1983. "Agglomeration as Local Instability of Spatially Uniform Steady-States," Econometrica, Econometric Society, vol. 51(4), pages 1109-1119, July.
    29. repec:cor:louvrp:-2449 is not listed on IDEAS
    30. Maenhout, Pascal J., 2006. "Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium," Journal of Economic Theory, Elsevier, vol. 128(1), pages 136-163, May.
    31. Takao Asano, 2010. "Precautionary Principle and the Optimal Timing of Environmental Policy Under Ambiguity," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 47(2), pages 173-196, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Giorgio Fabbri, 2014. "Ecological Barriers and Convergence: A Note on Geometry in Spatial Growth Models," Documents de recherche 14-05, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    2. Anastasios Xepapadeas & Athanasios Yannacopoulos, 2015. "Spatial Resource Management under Pollution Externalities," DEOS Working Papers 1516, Athens University of Economics and Business.
    3. Fabbri, G. & Faggian, S. & Freni, G., 2018. "Spatial resource wars: A two region example," Working Papers 2018-04, Grenoble Applied Economics Laboratory (GAEL).
    4. Javier de Frutos & Guiomar Martín-Herrán, 2016. "Pollution control in a multiregional setting: a differential game with spatially distributed controls," Gecomplexity Discussion Paper Series 201601, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2016.

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    Keywords

    Diffusion; optimal control; pattern formation; robust control; hot spots; spatial externalities;

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