The analysis in this paper is related to the literature on optimal management of renewable
resources (see, Clark, 1990) where the objective is to maximize the discounted sum of social welfare
obtained from harvesting a useful biological resource. Particularly relevant to our problem is the analysis
of conservation and extinction of renewable resources on optimal paths. The literature includes models
where the growth function is non-convex (non-convex feasible set for the optimization problem) as well
as models where the utility depends not only on the size of the harvest but also on the total stock size
(see, for example, Olson and Roy, 1996). More generally, the literature on optimal economic growth has
also analyzed related dynamic optimization problems including ones where the feasible set is non-convex
(among others, Majumdar and Mitra, 1982, Dechert and Nishimura, 1983) as well as models where the
utility function depends on both consumption and capital stock (see, for example, Nyarko and Olson,
1991, and the collection of papers in Majumdar, Mitra, and Nishimura, 2000). There is a key distinction
between our analysis and the literatures on economic growth and renewable resources. In the latter, the
physical or biological capital stock contributes to the production of a good that yields positive social
welfare. Hence, conservation of the resource is positively correlated with its growth rate and extinction is
not optimal if the productivity of the resource is higher than the discount rate. With a biological
invasion, the capital stock or size of the invasion contributes in a negative way to social welfare. This
difference turns out to reverse the relationship between biological productivity and incentives to preserve
the invasive species. Under the assumptions of our model, the faster the growth rate of an invasion, the
greater is the incentive to eradicate it.
There has been relatively little work on the dynamic economics of invasive species control.
Early applications of dynamic programming to the problem of pest management are reviewed by
Shoemaker [1981]. These tend to focus on issues such as pesticide resistance and intra-seasonal pest
management. Wilman [1996] and Knowler and Barbier [2000] examine models with an invasive predator
whose prey is harvested for its economic value. Spatial dimensions of pest control strategies are