Optimal dynamic management of the population mix

In this paper we present an optimal control model that addresses a central challenge of modern housing policy: deconcentrating poverty via ‘housing mobility programs’, which move poor families into middle‐class neighborhoods. The tension is that helping poor families is clearly an opportunity, but pursuing these programs too aggressively increases the risk of inducing middle‐class flight. Previous studies in this area of research considered only one state variable representing the middle‐class families; here, we add one more state variable to allow for an explicit consideration of the poor families. While our model is still somewhat stylized given the sophisticated structure of the real world problem, we show that it exhibits complex behavior including multiple equilibria, (strong and weak) DNSS curves, and indifference points for which there exist two different paths approaching one and the same steady state in the long run.