Potential and Spatial Structure of Population

The goal of this work is to suggest a mechanism explaining different spatial patterns of residential locations. The basic idea is counterbalance of centripetal and centrifugal forces. This paper complements the previous author's works in this area. This article addresses the following questions: a) agglomeration potential, b) optimal city size, c) equilibrium agricultural density, d) influence of agglomeration on land rent. Both relative location and size distribution of cities and residential patterns in agricultural areas represent interesting objects of study. There exist two main forces, centripetal (agglomeration) and centrifugal (congestion) that shape urban areas. The origin of agglomeration forces is in scale economies, while congestion forces represent a cumulative negative externality from such agglomeration. Following the stylized facts about different production technologies, it is assumed that agricultural technology creates dispersion force (through intensive land use), while industrial technology creates agglomeration force. It is possible to find the optimal city size assuming some scale economies in production counterbalanced by commuting costs. Location heterogeneity is balanced across residents via location rent to bring identical utility. There might be two possibilities: finite optimal size (for low scale economies) and infinitely large city (for high scale economies). The rural community of farmers is also considered. Here the average distance to neighbor (as a proxy to market access) is balanced with the benefits from land ownership. The optimal rural population density is the point maximizing this potential. Finally, the spatial equilibrium is constructed. It consists of discrete cities of optimal size attracting certain fraction of the population and the continuous farmland between them. The concept of potential for agro-industrial cluster is also introduced. It is assumed that rural resident has an access to scale economies in production of a city via commuting, and also has land slot for agricultural activity. There exists equilibrium land rent giving agents identical utility.