The locations of firms on intersecting roadways

With Bertrand-Nash mill-price competition, travel costs proportional to distance squared, and three firms on an interval, the equilibrium locations of the peripheral firms are further from the center than is socially optimal. If there is a central intersection, with four (or more) finite roadway segments radiating outward from the center (a small city spread along two intersecting roadways), and with one firm at the center and one on each radial segment, then the equilibrium locations of the peripheral firms are closer to the center than is socially optimal. Extensions include competition with spatial price discrimination, a more complicated system of intersecting roadways, and more than one firm on each roadway segment.