Similarly, the integral in the numerator is bounded and since it is divided by σXc it will ap-
proach zero once σXc → ∞. This implies that the entire fraction will approach zero. ∣
4 Discussion
Our results are different to those reported in previous analyses of both reversible catastrophic sys-
tems with instantaneous penalty functions (where it has been argued that increased uncertainty
always leads to an increase in precautionary behavior [32, 33]) and reversible multistate systems
(where it has been argued that threshold uncertainty has little or no effect on precautionary behav-
ior [18, 25]). How can these differences be reconciled?
When the catastrophic event is modeled as an instantaneous penalty, as in Tsur and Zemel’s
[32, 33] studies, an increase in uncertainty corresponds to an increase in the risk of event occur-
rence, and thus always increases precautionary behavior. In a multistate system, uncertainty in
pollutant loadings has a more complicated effect. In particular, large negative shocks in pollutant
loading will reduce the pollutant stock, and may move the system from the undesirable to the de-
sirable state (i.e. a positive utility shock, as the value function is decreasing in X), even when
it may not be economically optimal to do so. As a result, increased uncertainty in the stochastic
component of pollutant loading does not always increase precaution in a multistate reversible sys-
tem. Indeed, for a large enough uncertainty, increasing the variance of the stochastic component
of pollutant loading will always decrease caution, as in this case, the anthropogenic component of
pollutant loading has almost no influence on the probability ofa threshold crossing occurring.
The results of our study are also quite different from those reported in previous studies of
multistate environmental systems [5, 18, 25]. Several of these studies have also suggested that
increased threshold uncertainty always increases the degree of precaution [5, 18]. Whereas we
derive exact analytical solutions to the decisionmaker’s problem, previous studies used numerical
approximations to calculate optimal policies, which may have limited the parameter space con-
sidered and the resolution of observable optimal behavior. Indeed, some of the results presented
in both Carpenter et al. [5] and Ludwig et al. [18] show a nonmonotonic relationship between
uncertainty and precaution analogous to that found in this study. However, because of the coarse
resolution of the numerical approximations used, this nonmonotonicity is either unreported [5] or
reported as a numerical artifact [18]. In light of our analysis, an alternative interpretation is that the
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