Location and Horizontal Differentiation under Duopoly with Marshallian Externalities

A classical differentiated duopoly model is cast in a two regions' framework. An entrant firm, which locates in the other region from the incumbent, comes in and competes with the rival, under markets' segmentation. In the first stage of the game, it has to choose product differentiation. The resulting equilibrium is compared under two different settings: competition in prices (Bertrand) and quantities (Cournot). It is shown that, under both modes of competition, the entrant maximizes product differentiation, producing a completely different good. Afterwards, the Cournot model is extended by assuming that, when firms are located together, they benefit from Marshallian localization economies. First, the minimum cost reduction inducing agglomeration is computed. Second, the implications of a linear spillover function (linking product differentiation to marginal cost reduction) against a quadratic specification, with respect to location and product differentiation, are investigated.