Drastic urban growth and redevelopment have given rise to many housing problems. Dynamic analysis of urban residential location is indispensable to tackle them, and provides insights which cannot be gained solely from static models.
This paper focuses on the changes of a durable housing market both in space and with time. In the market, suppliers construct or reconstruct housing inside a city or in an urban fringe whenever profitable, while consumers choose their most-preferred houses taking account of housing quality as well as housing space and distance from the city center. From the conditions of the partial equilibrium, the change of housing quality and density in space and with time and the change of the construction and reconstruction areas with time are examined. Moreover, the assumption that consumers are divided into two groups (a higher-income group and a lower-income group) makes possible the investigation of the change of each residential area with time.
Under several assumptions, the market solutions such as the residential areas and urban renewal areas can be calculated from the set of linear functions of time into space, so patterns of the residential location can be easily obtained by inspecting the straight lines in a time-space diagram.