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Catastrophes and ex post shadow prices—How the value of the last fish in a lake is infinity and why we should not care (much)

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  • Nævdal, Eric

Abstract

Catastrophic risk is currently a hotly debated topic. This paper contributes to this debate by showing two results. First, it is shown that for a certain class of optimal control problems, the derivative of the value function with respect to the initial state may approach infinity as the state variable goes to zero, even when the first-order partial derivatives of the integrand and transition functions are finite. In the process, it is shown that standard phase diagrams used in optimal control theory contain more information than generally recognized and that the value function itself may be easily illustrated in these diagrams. Second, we show that even if the value function has an infinite derivative at some point, it is not correct to avoid this point in finite time at almost any cost. The results are illustrated in a simple linear-quadratic fisheries model and proven for a more general class of growth functions.

Suggested Citation

  • Nævdal, Eric, 2016. "Catastrophes and ex post shadow prices—How the value of the last fish in a lake is infinity and why we should not care (much)," Journal of Economic Behavior & Organization, Elsevier, vol. 132(PB), pages 153-160.
    • Handle: RePEc:eee:jeborg:v:132:y:2016:i:pb:p:153-160
    DOI: 10.1016/j.jebo.2016.04.021
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    1. de Zeeuw, Aart & Zemel, Amos, 2012. "Regime shifts and uncertainty in pollution control," Journal of Economic Dynamics and Control, Elsevier, vol. 36(7), pages 939-950.
    2. Polasky, Stephen & de Zeeuw, Aart & Wagener, Florian, 2011. "Optimal management with potential regime shifts," Journal of Environmental Economics and Management, Elsevier, vol. 62(2), pages 229-240, September.
    3. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    4. Robert S. Pindyck, 2011. "Fat Tails, Thin Tails, and Climate Change Policy," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(2), pages 258-274, Summer.
    5. Takashi Kamihigashi, 2006. "Almost sure convergence to zero in stochastic growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 231-237, September.
    6. Hartl, Richard F., 1987. "A simple proof of the monotonicity of the state trajectories in autonomous control problems," Journal of Economic Theory, Elsevier, vol. 41(1), pages 211-215, February.
    7. Martin L. Weitzman, 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 1-19, February.
    8. Naevdal, Eric, 2006. "Dynamic optimisation in the presence of threshold effects when the location of the threshold is uncertain - with an application to a possible disintegration of the Western Antarctic Ice Sheet," Journal of Economic Dynamics and Control, Elsevier, vol. 30(7), pages 1131-1158, July.
    9. -, 2009. "The economics of climate change," Sede Subregional de la CEPAL para el Caribe (Estudios e Investigaciones) 38679, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    10. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    11. William D. Nordhaus, 2011. "The Economics of Tail Events with an Application to Climate Change," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(2), pages 240-257, Summer.
    12. Mirman, Leonard J & Zilcha, Itzhak, 1976. "Unbounded Shadow Prices for Optimal Stochastic Growth Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 121-132, February.
    13. Clark, Colin W. & Munro, Gordon R., 1975. "The economics of fishing and modern capital theory: A simplified approach," Journal of Environmental Economics and Management, Elsevier, vol. 2(2), pages 92-106, December.
    14. Clarke, Harry R. & Reed, William J., 1994. "Consumption/pollution tradeoffs in an environment vulnerable to pollution-related catastrophic collapse," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 991-1010, September.
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    More about this item

    Keywords

    Catastrophic risk; Fisheries; Optimal control; Shadow prices;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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