Bertrand and Cournot in the unidirectional Hotelling model

The unidirectional Hotelling model where consumers can buy only from firms located on their right (left) is extended to allow for elastic demand functions. A Bertrand-type model and a 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 transportation costs are low enough. Equilibrium distance between firms is lower in Cournot than Bertrand under the whole parameters’ set. We also study the impact of firms’ location on perfect collusion sustainability. We show that when consumers can buy only from firms located on their right (left), the incentive to deviate of each firm decreases the more the firm is located to the right (left) and the more the rival is located to the left (right).