An Urban Economic Model over a Continuous Plane with Spatial Characteristic Vector Field - Asymmetric Land Use Pattern and Internalizing Transportation Networks -

Among others Beckmann (1952) firstly introduced the concept of a two dimensional continuous space into economics. This great step had unfortunately not shown further expansion in economics. Through several papers related to Beckmann’s initiation, Beckmann and Puu (1985) at last reached a systematic treatment of the continuous spatial economics. Although their achievement is fascinated by employing a partial differential equations approach, Beckmann’s original philosophy, that is, the gradient law has still been inherited. Beckmann and Puu’s book (1985) aims to study formation of urban configuration in a two dimensional continuous space, focusing on flows of commodities. However, consideration of households and firms location is not necessarily sufficient, resulting in reconsideration from a new urban economics point of view. Differing from Beckmann and Puu’s studies, Miyata (2010) introduces bid rent functions (Fujita (1989)), which are familiar in the new urban economics, for land of households and firms, and then he studies how the results of Beckmann and Puu are rigorously modified by using the theory of partial differential equations. However Miyata (2010) deals with a symmetric equilibrium which seems to be a little unrealistic. This article extends the author’s previous study introducing spatial characteristic vector field in the model which stands for heterogeneity in geographical conditions in a city, and try to show asymmetry in land use pattern and endogenous formation of transportation networks in a two dimensional continuous space.