What describes a city characterized by a small population and limited social mobility?

A city characterized by a small population and limited social mobility is best described as a preindustrial city. Preindustrial cities often arise in agrarian societies where the population is generally lower, and social structures are more rigid and stratified based on tradition, class, and land ownership rather than on individual achievement or opportunity. This lack of mobility means that individuals are often born into their social class and have limited means to change their status.

In contrast, postindustrial cities tend to have larger populations, enhanced social mobility, and are characterized by service-oriented economies and technology-driven industries. Urban cities typically encompass a wide range of social dynamics and do not necessarily have the specific characteristics of limited mobility. Metropolitan cities can refer to large urban areas that include various social classes and communities, often exhibiting greater social mobility due to economic opportunities present in such environments. Thus, the features of a preindustrial city distinctly align with the characteristics described in the question.