associated with an arbitrarily small invasion. It is possible that the condition for immediate eradication
may be satisfied for large y and not for small y. That is, immediate eradication may be optimal for a
large invasion even if it is not optimal for a smaller invasion. Since Propositions 1 and 4 are not
mutually exclusive there can exist circumstances where: eradication of small invasions is optimal,
eradication is not optimal for medium size invasions, and eradication is optimal for large invasions.
These results on the economics of eradication have the following implications. First, eradication
is more likely to be an optimal policy for invasions that have a higher discounted growth rate than it is for
invasions that grow slowly. This might seem counter-intuitive, but it is because the benefits from control
today are higher when an invasion expands rapidly. In addition, the benefits from control today are
magnified further into the future when the discount rate is lower. Second, for some invasions economic
considerations may favor eradication when the invasion is small, but not when the invasion is large. In
such cases a rapid response may be necessary for eradication to justified. Finally, in the special case
where the marginal costs of control at a=0 are insignificant, the criteria for eradication in Propositions 1,
2 and 4 essentially involve static benefit cost considerations that balance current marginal costs and
damages. This is a consequence of the fact that Ca(0,y) = 0 and Ca(a,y) + Cy(a,y) ≥ 0 imply
i∏f0sasf(x),x Ca(a,f(x)) + Cy(a,f(x)) = 0. Hence, the lower bound on future marginal social costs is relatively
weak when marginal control costs are insignificant.
5. The Economics of Noneradication.
In this section we characterize the economic and biological environments under eradication is not
optimal. Under these circumstances the optimal policy either involves no intervention, or suppression in
order to reduce damages. Our first result rules out immediate eradication as an optimal strategy.
Proposition 5.a. If Dx(0) + δCa(0,0)fx(0) < Ca(y,y) then X(y) > 0.
17
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