Racetrack Economy: Introduction to Group-Theoretic Analysis

This chapter demonstrates how to use group-theoretic bifurcation analysis in studying pattern formation in economic agglomerations. We consider a racetrack economy, comprising identical places spread evenly on the circumference of a circle. The dihedral group describes the regular-polygon symmetry of this economy, and its subgroup expresses the symmetry of a bifurcating solution. We address the mechanism of direct bifurcation from the uniform population distribution in this economy by using the results of a group-theoretic analysis. Chapter 9 deals with the secondary and further bifurcations and presents the numerical analysis of economic geography models. This chapter is a prelude to the group-theoretic analysis of larger groups in Chap. 4 for a square lattice, Chap. 5 for a hexagonal lattice, and Chap. 14 for an equidistant economy. This chapter is a foundation for studying a long-narrow economy in Chap. 12 and a square lattice in Chap. 13 based on racetrack economy analogy.