| Sumario: | A central objective of modern US housing policy is deconcentrating poverty through "housing mobility programs" that move poor families into middle class neighborhoods. Pursuing these policies too aggressively risks inducing middle class flight, but being too cautious squanders the opportunity to help more poor families. This paper presents a stylized dynamicoptimization model that captures this tension. With base-caseparameter values, cost considerations limit mobility programs before flight becomes excessive. However, for modest departures reflecting stronger flight tendencies and/or weaker destination neighborhoods, other outcomes emerge. In particular, we find state-dependence and multiple equilibria, including both de-populated and oversized outcomes. For certain sets of parameters there exists a Skiba point that separates initial conditions for which the optimal strategy leads to substantial flight and depopulation from those for which the optimal strategy retains or even expands the middle class population. These results suggest the value of estimating middle-class neighborhoods' "carrying capacity" for absorbing mobility program placements and further modeling of dynamic response.housing policy, multiple equilibria, negative externality, optimal control, segregation, separation, Skiba point
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