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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
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167268116300828
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    Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

    Volume (Year): 132 (2016)
    Issue (Month): PB ()
    Pages: 153-160

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    Handle: RePEc:eee:jeborg:v:132:y:2016:i:pb:p:153-160
    DOI: 10.1016/j.jebo.2016.04.021
    Contact details of provider: Web page: http://www.elsevier.com/locate/jebo

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    1. 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.
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    8. 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.
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    10. 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.
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