This paper focuses on the analysis of price equilibrium in a two-stage game within the linear-city model of spatial competition. Assuming a convex linear-quadratic transport cost function the study computes locations on the unit line for which price equilibrium exists. By introducing a decisive change of variable to allow for symmetry in the profit functions of both firms, the study allocates the exact regions of location pairs where price equilibrium exists. Therefore, it completes the analysis on equilibrium existence for convex linear-quadratic transport costs functions.
JEL classification: C72, D43