Dynamic optimization with a nonconvex technology: Determination of critical stocks (Q1071634)

It is well-known that, in the presence of a nonconvex production technology, economically optimal policies for management of biologically renewable resources depend on the position of the initial resource stock relative to a certain critical stock. If the initial stock is less than this critical volume, an extinction policy is optimal, and if the initial stock is greater than the critical volume, a regeneration policy is optimal. The present paper considers the problem of determining the volume of the critical stock in a continuous time framework with irreversible investment. Its sensitivity to policy parameters such as the interest rate is also investigated. A simple example illustrates the results.