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Catastrophes and Expected Marginal Utility – How The Value Of The Last Fish In A Lake Is Infinity And Why We Shouldn't Care (Much)

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  • Nævdal, Eric

    (The Ragnar Frisch Centre for Economic Research)

Abstract

Catastrophic risk is currently a hotly debated topic. This paper contributes to this debate by showing two results. First it shown that the value function in dynamic optimization can have an infinite derivative at some point even if the model specification has functional forms that are finite and without infinite derivatives. In the process it is shown that standard phase diagrams used in optimal control theory contain more information than generally recognized. Second we show that even if the value function has an infinite derivative at some point, it is not correct that this point should be avoided in finite time at almost any cost. The results are illustrated in a simple linear-quadratic fisheries model, but proven for a more general class of growth functions.

Suggested Citation

  • Nævdal, Eric, 2015. "Catastrophes and Expected Marginal Utility – How The Value Of The Last Fish In A Lake Is Infinity And Why We Shouldn't Care (Much)," Memorandum 08/2015, Oslo University, Department of Economics.
    • Handle: RePEc:hhs:osloec:2015_008
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    References listed on IDEAS

    as
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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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