Abstract A maximin program is applied to a policy of sustaining a simple society whose population is dependent on a resource subject to logistic growth. Regular and non-regular paths are characterized. There are continua of both regular and non-regular solutions, the type depending on the initial conditions. A non-regular path involves an intermediate part in which the sustainment constraint is not effective. All solutions are time consistent and Pareto optimal. Because a problem may not be regular, it is not valid to assume that sustainment implies constant utility.