significant control. In addition, the results show the importance of the initial invasion size in determining
the optimal policy. Propositions 1 or 2 may apply when the invasion is small while Proposition 7 may
simultaneously apply when the invasion is large. In such cases the optimal policy is path dependent and
there is an economic rationale for eradication if the invasion is small, but not if the invasion is large.
The paper also illustrates the information that is needed to evaluate the economic efficiency of
invasive species control. Estimates of the costs of control, damages from an invasion, and the invasion
growth rate are required. These may be difficult to assess, particularly in the early stages of an invasion.
Yet this is precisely the time when prompt action can reduce future consequences.
There are a number of important issues related to invasive species problems that are not
addressed in this paper. There are many circumstances where prevention may be the best control.
Similarly, our model does not consider the possibility of re-invasion. Clearly, the value of eradicating an
invasive species will depend on the likelihood that a new invasion might occur. Finally, many invasive
species problems involve private actions where individuals do not consider the consequences for social
welfare. The design of policies that mitigate the conflicts between private incentives and social welfare
is another interesting aspect of invasive species problems.
Appendix.
Proof of Lemma 1. The cost functions C and D are bounded continuous functions on their relevant
domains. Define the operator ΓV(y) = inf C(a,y) + D(x) + δV(f(x)) subject to y = x + a. By the
contraction mapping theorem maps the set of bounded continuous functions into itself. Hence, V is
continuous. We now show that V maps non-decreasing functions into non-decreasing functions.
Suppose V is non-decreasing. Let x and x' be optimal from y and y', respectively where y < y'. Suppose
x' < y. Then x' is feasible from y and ΓV(y) = C(y-x,y) + D(x) + δV(f(x)) ≤ C(y-x',y) + D(x') + δV(f(x'))
≤ C(y'-x',y') + D(x') + δV(f(x')) = ΓV(y'), where the first inequality is due to optimality while the second
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