the threshold will be crossed and hence precautionary reductions in loading have a payoff from
lowering that probability. If the uncertainty continues to grow, the decisionmaker will eventually
feel he/she has no knowledge at all and precautionary reductions will be too costly compared to
the negligible reduction in the probability that the threshold is crossed. These results are different
to previous results from analyses of both reversible multistate systems and reversible catastrophic
systems with instantaneous penalty functions, where it has been argued that increased threshold
uncertainty always leads to an increase in precautionary behavior [5, 18, 32, 33], or that the thresh-
old and associated uncertainty have no effect on precautionary behavior [25].
Several strands of economic research are relevant to the problem of optimal resource manage-
ment when catastrophic events can occur. The most common way of modeling catastrophes in
the economic literature is to consider catastrophic events as penalty functions with an associated
hazard rate. The state of the resource - and hence optimal economic behavior - may or may not
influence the probability of event occurrence. By using survival probability as a state variable,
the optimization problem can then be treated as a deterministic control problem. In general, an
irreversible catastrophe is viewed as instantaneously and permanently reducing social welfare to
zero (e.g. [9]), whereas a reversible catastrophe is modeled as imposing an instantaneous penalty
equal to the sum of damages from the catastrophes and healing costs for the resource (e.g. [32, 33]).
When catastrophic, irreversible thresholds exist, economic studies suggest that some precau-
tionary reduction in economic activity may be desirable. Examples of irreversible thresholds that
have been studied by economists include species extinction, collapse of thermohaline circulation
[17], disintegration of the West Antarctic ice sheet [24], and aquifer salinization [31, 33]. Many
of these studies find that increasing uncertainty decreases the amount of managers’ precaution.
Clarke and Reed [9] show that an exogenous increase in the risk of catastrophe can increase or
decrease the degree of precaution undertaken by resource managers behaving optimally. Tsur and
Zemel [32, 33] argue that such nonmonoticity in behavior as a function of increasing risk is a
characteristic of irreversible catastrophes, resulting from the tradeoff as pollution levels increase
between increasing hazard rate and a decreasing penalty function (because the value function is
decreasing in pollution level). Conversely, Tsur and Zemel argue that for reversible events with an
instantaneous penalty function, increasing pollution increases both the hazard rate and the penalty,
so that exogenous increases in the risk ofa catastrophe always increase the degree of precaution.
Finally, Tsur and Zemel [33] show that in the absence of exogenous uncertainty in pollution, when
the only uncertainty is in the location of the threshold, increasing uncertainty always makes the