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The consequences of irreversibility on optimal intertemporal emission policies under uncertainty


  • Thomas Dangl


  • Franz Wirl



This paper investigates how irreversibility affects optimal intertemporal emission policies when negative stock externalities exist. In particular it discusses the effect of irreversible emission, i.e., it concerns the physical issue whether it is possible to recollect pollutants that have been emitted or not. We depict our analysis with the greenhouse effect as a topical example and model the uncertainty with respect to the future evolution of the world’s temperature (i.e., the uncertain factor that determines the costs) as Itô-process with the drift provided by current carbon-dioxide emissions. We show analytically that irreversibility affects the optimal emission policy only if the future impact of today’s emissions is uncertain. Under uncertainty, irreversibility leads to a conservationist policy such that emissions are reduced at any level of environmental concentration of the pollutant. The level where stopping emissions is optimal decreases in the presence of irreversibility. Furthermore, the expected duration of fossil fuel use is derived. A numerical example which is calibrated to roughly reflect the global CO 2 problem illustrates the analytical findings. Copyright Springer-Verlag 2007

Suggested Citation

  • Thomas Dangl & Franz Wirl, 2007. "The consequences of irreversibility on optimal intertemporal emission policies under uncertainty," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 15(2), pages 143-166, June.
  • Handle: RePEc:spr:cejnor:v:15:y:2007:i:2:p:143-166 DOI: 10.1007/s10100-007-0023-1

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    References listed on IDEAS

    1. Mendelsohn, Robert & Nordhaus, William D & Shaw, Daigee, 1994. "The Impact of Global Warming on Agriculture: A Ricardian Analysis," American Economic Review, American Economic Association, vol. 84(4), pages 753-771, September.
    2. Tsur, Yacov & Zemel, Amos, 1996. "Accounting for global warming risks: Resource management under event uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1289-1305.
    3. Pindyck, Robert S, 1980. "Uncertainty and Exhaustible Resource Markets," Journal of Political Economy, University of Chicago Press, vol. 88(6), pages 1203-1225, December.
    4. Wirl, Franz & Dockner, Engelbert, 1995. "Leviathan governments and carbon taxes: Costs and potential benefits," European Economic Review, Elsevier, vol. 39(6), pages 1215-1236, June.
    5. Hoel, Michael & Kverndokk, Snorre, 1996. "Depletion of fossil fuels and the impacts of global warming," Resource and Energy Economics, Elsevier, vol. 18(2), pages 115-136, June.
    6. Birge, John R. & Rosa, Charles H., 1995. "Modeling investment uncertainty in the costs of global CO2 emission policy," European Journal of Operational Research, Elsevier, vol. 83(3), pages 466-488, June.
    7. Gjerde, Jon & Grepperud, Sverre & Kverndokk, Snorre, 1999. "Optimal climate policy under the possibility of a catastrophe," Resource and Energy Economics, Elsevier, vol. 21(3-4), pages 289-317, August.
    8. Peck, Stephen C. & Teisberg, Thomas J., 1993. "Global warming uncertainties and the value of information: an analysis using CETA," Resource and Energy Economics, Elsevier, vol. 15(1), pages 71-97, March.
    9. Tahvonen, Olli, 1994. "Carbon dioxide abatement as a differential game," European Journal of Political Economy, Elsevier, vol. 10(4), pages 685-705, December.
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    11. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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    Cited by:

    1. Marc Gronwald & Janina Ketterer, 2009. "Zur Bewertung von Emissionshandel als Politikinstrument," ifo Schnelldienst, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 62(11), pages 22-25, June.
    2. Chen, Hong & Long, Ruyin & Niu, Wenjing & Feng, Qun & Yang, Ranran, 2014. "How does individual low-carbon consumption behavior occur? – An analysis based on attitude process," Applied Energy, Elsevier, vol. 116(C), pages 376-386.
    3. Marc Gronwald & Janina Ketterer, 2009. "Evaluating Emission Trading as a Policy Tool - Evidence from Conditional Jump Models," CESifo Working Paper Series 2682, CESifo Group Munich.

    More about this item


    Optimal taxation; Optimal resource allocation; Q48; D81; C61;

    JEL classification:

    • Q48 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Government Policy
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis


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