The name is absent

will occur, and optimal loading approaches a target level, Xtarget, of 2 [ 1 — B] (where δ is the
per-period discount rate), which is then also equal to the expected pollutant stock in the next time
period. Conversely, when X_c becomes small, so that additional loading equal to r is present and
transition from the undesirable state to the desirable state is very unlikely, the optimal loading ap-
proaches 2 [ 1 — B] — r, while the expected pollutant stock in the next period once again approaches
the target level. Importantly however, for intermediate values of Xc, the optimal pollutant loading
may be much less than that for both small and large values ofX_c, and as a result the next period’s
expected state variable may be much less than the target level predicted when Xc is either small or
large (Figure 1). The intuition behind these results is as follows: if the threshold is either extremely
low or extremely high then precautionary activity is unwarranted. In the former case, decreasing
loading will not significantly change the probability of transition out of the undesirable state. In the
latter case, additional precaution will decrease the probability of transitioning into the undesirable
state only negligibly. However, if there is a possibility of moving between states in either direc-
tion, then additional precautionary activity carries an expected economic benefit. Note that our
result assumes a reversible process. With an irreversible or hysteretic threshold, the decisionmaker
would presumably have an even larger incentive to avoid crossing a threshold into the undesirable
state. Finally, we have demonstrated that there is a nonmontonic relationship between increasing
uncertainty in the natural system (as represented by the error term vt) and the optimal combined
loading c, i.e. increasing uncertainty can first decrease the optimal loading but will eventually al-
ways increase it. Intuitively, if a manager is absolutely certain that the system is right below the
threshold, then any precautionary reduction is unwarranted. Once uncertainty about the natural
system increases, so does the probability of crossing the threshold, and hence it might be worth-
while to reduce loadings for a reduction in the probability of crossing the threshold. However, if
the uncertainty about the natural system continues to increase, any reduction in loadings implies
only a negligible reduction in the probability of crossing the threshold and hence is too costly.

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