Yuki Takayama

STABLE ECONOMIC AGGLOMERATION PATTERNS IN TWO DIMENSIONS: BEYOND THE SCOPE OF CENTRAL PLACE THEORY

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

Harris and Wilson (1978)’s retail location model is one of the pioneering works in regional sciences on the combination of the “fast” and “slow” dynamic describing spatial pattern formation processes in the economic landscape, which is a current well-established modeling technique. Although proposed some time ago, the comparative static (bifurcation) properties of the model have not yet been sufficiently explored. We employ a simple analytical approach developed by Akamatsu et al. (2012) to reveal previously unknown bifurcation properties of the model in a space with a large number of locations. It is analytically shown that the evolutionary path of spatial structure exhibits a remarkable property, namely “spatial period- doubling cascade,” which we cannot observe in the popular two-location setup. We also discuss strong linkages between the model and the models of “new economic geography” regarding the modeling strategies and their bifurcation properties.

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

Harris and Wilson (1978)’s retail location model is one of the pioneering works in regional sciences on the combination of the “fast” and “slow” dynamic describing spatial pattern formation processes in the economic landscape, which is a current well-established modeling technique. Although proposed some time ago, the comparative static (bifurcation) properties of the model have not yet been sufficiently explored. We employ a simple analytical approach developed by Akamatsu et al. (2012) to reveal previously unknown bifurcation properties of the model in a space with a large number of locations. It is analytically shown that the evolutionary path of spatial structure exhibits a remarkable property, namely “spatial period- doubling cascade,” which we cannot observe in the popular two-location setup. We also discuss strong linkages between the model and the models of “new economic geography” regarding the modeling strategies and their bifurcation properties.