Stable Economic Agglomeration Patterns in Two Dimensions: Beyond the Scope of Central Place Theory

Abstract

This paper elucidates which agglomeration patterns exist in two‐dimensional economic space and how such patterns appear stably. Hexagonal lattices, that with and that without a boundary, are advanced, respectively, as practical and theoretical spatial platforms of economic activities. Agglomeration patterns on these lattices include hexagons in central place theory, but also encompass megalopolis and racetrack‐shaped decentralization. As the transport cost decreases, stable economic agglomeration undergoes the formation of the smallest hexagon and transition to patterns with larger market areas, often undergoing downtown decay but finally leading to a megalopolis. Formulas for break points are provided in an economic geography model.

Harris and Wilson (1978) Model Revisited: The Spatial Period‐doubling Cascade in an Urban Retail Model

“…The underlying mechanism for this striking result, however, had not been fully explained due to lack of analytical equipment. Recent studies by Ikeda, Murota, and Akamatsu (2012), Ikeda et al (2014), and Ikeda et al (2016) reveal that two-dimensional NEG models admit hexagonal spatial configurations as stable equilibria. Judging from the strong linkage between NEG models and the HW model, it is likely that we can rigorously explain Clarke and Wilson (1985)'s numerical results for the HW model; such an explanation will be a materialization of Harris (1985)'s idea, where he hints the applicability of the HW model, which is an intraurban model, to an interregional context so that we can explain central place systems.…”

Beyond urban form: How Masahisa Fujita shapes us

“…Most notably, as demonstrated by, Ikeda et al . (, , ) it is now possible to formally predict the bifurcation path of stable equilibria in many‐region models by utilizing a combination of group‐theoretic and computational bifurcation theory (e.g., Ikeda et al . ()).…”

City formation with complex landscapes

“…Using this grid and US census data, they attempt to “fit” the historical emergence of cities in this region. More recently, Ikeda, Murota, and Takayama () use computer‐based simulations to study which agglomeration patterns can stably exist in a two‐dimensional space.…”

“…Using this grid and US census data, they attempt to "fit" the historical emergence of cities in this region. More recently, Ikeda, Murota, and Takayama (2017) use computer-based simulations to study which agglomeration patterns can stably exist in a two-dimensional space. Krugman (1996), as noted in the earlier quote, explicitly considers the issue of inhomogeneous landscapes in an NEG model.…”