Spatial price discrimination in the unidirectional Hotelling model with elastic demand

The unidirectional Hotelling model is extended to allow for elastic demand functions. A two-stage Bertrand-type model and a two-stage Cournot-type model are considered. If firms choose location and then set prices, agglomeration never arises; instead, if firms choose location and then set quantities, agglomeration arises at one endpoint of the segment when the transportation costs are low enough. Instead, when the transportation costs are high enough, a dispersed equilibrium arises in Cournot. The equilibrium distance between the firms is lower in Cournot than in Bertrand. When the transportation costs are high (low) the Bertrand equilibrium is welfare superior (inferior) to the Cournot equilibrium.