The dynamics of a population and a resource are investigated in a maximin model based on Brander and Taylor’s stylization of Easter Island, in order to consider the sustainability of the society represented. There are continua of both regular and non-regular maximin solutions, the type depending on the initial conditions. A non-regular maximin steady state corresponds with the steady state in Brander and Taylor’s model. All solutions are time consistent and Pareto optimal. For the regular paths, a partial analytic characterization and a simulation are provided. The non-regular paths involve two regular sections and one degenerate solution in which the maximin constraint is not effective. The high degree of mathematical subtlety of the solution to this ostensibly simple problem calls into question the likelihood of a planner’s being able to devise and follow a program of efficient, sustained development.