Dynamic Instability of a Mixed City in the Presence of Neighborhood Externalities
构建了一个包含两组居民（如黑人与白人）的开放城市长期动态模型，分析邻里外部性（组间负外部性和组内正外部性）如何影响混合城市的稳定性，发现当不考虑交通成本时混合均衡总是不稳定，而单中心城市中交通成本可能通过空间隔离产生稳定效应。
It has been often asked whether a city, currently accommodating a variety of economic, social, and racial groups, will continue to be a city or will become exclusively occupied by a single group, particularly poor blacks, with all other groups moving out of the city in the long run. In order to answer this question properly, it seems essential to develop a long-run dynamic model of a city with emphasis on socioeconomic factors like neighborhood externalities within or among various groups of residents as well as spatial factors like the individual choice of residential space and location. It might be safely said that in the literature the only theoretical work which employs a long-run dynamic approach to this kind of problem is a paper on dynamic models of segregation by Thomas Schelling (197 1).' Although his socioeconomic analysis has revealed some of the dynamic properties of a racially mixed area with neighborhood externalities, his model itself is quite unsatisfactory from the economic point of view, since it lacks individual utility functions and thereby disregards the aspect of the individual choice of space and location within the city.2 As a result, he failed to analyze the effect of spatial segregation within the city on the long-run nature of the residential composition of the city. In this paper I develop a long-run dynamic model of an open city which accommodates two groups of households (for example, blacks and whites, rich and poor, young and old) with their utility functions depending on a consumption good and residential space. I also assume two kinds of neighborhood externalities. The first is called intergroup externalities; that is, the utility level of a typical household in one group is adversely affected by an increase in the number of households in the other group living in the city. The second is called intragroup externalities; that is, the utility level of a typical household in one group is positively affected by an increase in the size of its own group in in the city. First, I define a equilibrium as a long-run equilibrium which allows the two groups to coexist in the city in the long run, and then introduce a dynamic adjustment process of household movement into and out of the city. It is proved that the mixed-city equilibrium is always unstable in the presence of negative intergroup externalities and/or positive intragroup externalities, if residential land is perfectly homogeneous and there is no differential transport cost incurred within the city. It turns out, however, that in the case of a monocentric city with positive transport cost, the mixed-city equilibrium may be stable or unstable depending on the degree of neighborhood externalities because of the stabilizing effect of spatial segregation between the two groups within the city.