I model a central city where citizens differ by income, and housing confers benefits on neighbors. Zoning separates citizens into neighborhoods by income. This maximizes total surplus and facilitates redistributing gains to a majoritarian governing coalition of citizens, which changes from rich to poor as the city grows. Non-members of the coalition may form suburbs. These theoretical results are supported by empirical facts compiled by Schnore and Varley (1955). It is difficult to justify stratified zoning on Paretian grounds, even when a municipal government can redistribute income. If stratified zoning is not a Pareto improvement before gains are redistributed, it will not be afterward under majority rule. Gains in total surplus increase as the distribution of income becomes less equal, which helps explain why neighborhood stratification has outpaced stratification of income in U.S cities in recent decades, as documented by Booza et al (2006) and Sampson (2016).

我对一个中心城市建模，在该城市中，公民的收入有所不同，而住房则为邻居带来利益。区划将居民按收入划分为社区。这将使总盈余最大化，并有助于将收益重新分配给由多数派统治的公民联盟，随着城市的发展，这种联盟从富人变成穷人。非联盟成员可以组成郊区。这些理论结果得到了Schnore和Varley（1955）汇编的经验事实的支持。即使在市政府可以重新分配收入的情况下，也很难证明基于Paretian理由的分层分区是合理的。如果在重新分配收益之前，分层分区不是Pareto改进，那么根据多数制规则，分层分区将不会在以后。随着收入分配的不平等，总盈余增加，