Horizontal and Vertical Differentiation in the Circular City

We study price, quality, and location competition between two firms on a circular market when consumers differ both horizontally and vertically. Firms choose locations on a circle, qualities from a bounded but costless set, and prices, while consumers have heterogeneous valuations for quality. Transportation costs are quadratic, and the market is fully covered. We show that two distinct equilibrium regimes arise. In a vertical regime, firms maximally differentiate in quality, one choosing the highest feasible quality and the other the lowest. Prices and market shares are pinned down by the vertical differentiation mechanism, and---because of the symmetry of the circle---locations are irrelevant as long as an interior vertical sorting condition holds. In a horizontal regime, firms choose identical (maximal) quality levels and instead differentiate spatially, locating at antipodal points on the circle. We provide exact conditions under which each regime constitutes an equilibrium and characterize the parameter regions where one regime dominates the other. The analysis highlights how vertical differentiation can insulate firms from spatial competition and rationalize co-location, while sufficiently strong transportation costs restore the standard incentive for maximal spatial differentiation. JEL Codes: D4, L13