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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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    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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