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)
Link to article:
Authors:
Nævdal, Eric
Year:
2016
Reference:
Journal of Economic Behavior and Organization
Vol 132, 153-160Summary
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.
JEL:
C61; Q22; Q54
Keywords:
Catastrophic risk; Fisheries; Optimal control; Shadow prices
Project:
Oppdragsgiver: Norges forskningsrådOppdragsgivers prosjektnr.: 196199
Frisch prosjekt: 3172 - Managing Thresholds and Uncertainty in Resource Economics