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

Eric Nævdal

No 08/2015, Memorandum from Oslo University, Department of Economics

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.

Keywords: Catastrophic risk; fisheries; optimal control; shadow prices (search for similar items in EconPapers)
JEL-codes: C61 Q22 Q54 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2015-03-30
New Economics Papers: this item is included in nep-mic and nep-upt
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