The name is absent

invasion against the discounted sum of current and future damages associated with that increment of the
invasion. When the costs of control depend on the size of the invasion, the stream of future damages
must be adjusted to account for the influence of the invasion size on future control costs.

Figure 1 illustrates the tradeoffs involved in the dynamic cost-benefit analysis. Points along the
horizontal axis represent feasible amounts of control, ranging between 0 and y_t. As control increases, so
do marginal control costs. At the same time, more control lowers the current and future marginal
damages caused by the invasion. The point a_t⁰ represents the static optimum that equates marginal
control costs with current marginal damages. The point a_t^* is the dynamic optimum that equates marginal
control costs with current marginal damages plus the marginal effect of the invasion on future damages
and costs. Given that it is less costly to reduce the size of the invasion to x from y than it is from y' > y
(assumption A3), the dynamic optimum always involves at least as much control as the static optimum
and at* ≥ at⁰.

4. The Economics of Eradication

In this section, we consider the conditions under which it makes sense to eradicate an invasive
species. The term eradication can have two meanings. In general it applies when the species is
eradicated in the long run and the invasion is controlled in a manner that reduces its size to zero in the
limit. It can also have a narrower meaning in cases where the species is fully exterminated in the current
period. Eradication in the general sense includes both immediate eradication and the possibility that the
species is fully eliminated within a finite number of periods.

It is intuitively clear that a first step towards eradication is a reduction in the size of invasion. We
begin by giving a result about when it is economic for the current control to do so.

Proposition 1. Suppose that for y₀ = y > 0, the invasion is currently controlled from all y' e [y, f(y)]

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