Market Scale and Agglomeration in a Spatial Cournot Model of Product Differentiation

This paper analyzes the equilibrium of optimal production locations for two firms engaging in quantity competition under different degree of product differentiation and demand size. The main findings in this paper, which are different from the conventional findings in the literature that quantity completion always leads to central market agglomeration under the prerequisites of homogeneous product and full market coverage, are the followings. (1) Central market agglomeration is guaranteed under traditional "full market coverage" assumption, since the implicit demand size behind the assumption is so large that the demand effect, which attracts firms to agglomerate at the central market, would dominate the strategic effect, which tends to separate firms into different location. (2) Under the revised full-market-coverage, we prove that to reach the central agglomeration equilibrium requires only a smaller demand size than the conventional. In addition and importantly, when demand size shrinks to the level below the threshold, both separation and central-agglomeration are the equilibria, however, only the former equilibrium of separation is stable; and the smaller the demand size and/or the lower the degree of product differentiation between the two goods, the farther the two firms’ production locations will separate.