As we know, natural environment is a very important element for social development. We must face and deal with it properly. Since the industrial revolution, the economic system was achieved by mass production, mass consumption, and mass disposal of wastes in the past. In order to attain a sustainable society, we must realign our present urban system. Compact city is one solution to attain a sustainable urban system. From this viewpoint, the authors have already published papers [13] and [18] which consider the concept of a compact city [6] and [10] that have been reexamined mainly in European counties and the United States. In these papers, some simulations show a possibility of formation of a compact city. However, there is a shortcoming that the natural environment, which is important in the environmental symbiosis oriented city, is not incorporated. Therefore, this article aims to take into account the natural environment as an endogenous public good and to develop a new dynamic urban model. About the theoretical analysis of a dynamic model, one can find some contributions in the urban economics literature. Palivos and Wang [15] developed an endogenous dynamic urban model and they derived the optimal population by incorporating human capital into the dynamic mono-centric urban framework. Black and Henderson [3] further extended a dynamic urban model into a dynamic system of cities which involves two types of cities with human capital accumulation. In this paper, we construct a dynamic urban model internalizing the natural environment. This model is characterized as a social optimization problem. And we also simulate and analyze the possibility of formation of a compact city with natural environment.

JEL Classification : R11, Q20