Dynamic stability of an open city with many household classes

This paper analyzes the dynamic stability property of an “open” city with many classes of households. We specify a dynamic adjustment process of household movement into and out of the city in such a way that the number of households in each class increases or decreases over time, according as the utility level households can obtain in the city is higher or lower than a certain utility level attainable elsewhere. Then we prove that a long-run equilibrium is locally stable for positive speeds of adjustment under reasonable assumptions. Some comparative static properties are also explored.