Partial Agglomeration or Dispersion in Spatial Cournot Competition

Abstract

We revisit Pal (1998) and Matsushima (2001a), which present different equilibrium locations respectively. We consider nonlinear transport costs and show that Pal's result (dispersion) is more robust than Matsushima's (partial agglomeration). Pal's result holds true for any transport cost function, while Matsushima's does not hold true under strong concavity or convexity of the transport cost function. If we consider sequential move of location, Pal's result holds for any transport costs. On the other hand, Matsushima's does not hold except for the linear transport costs. We also discuss welfare and show that non-linearity of the transport cost function yields rich welfare implications.

Sequential mergers under general symmetric product differentiation with four firms

“…The model in our paper can be extended to more than four (even) firms, but the differentiation levels cannot be as general as in the current paper without making the analysis intractable. Four-firm, four-market model is also considered in the spatial connotation in Matsumura, Ohkawa, and Shimizu (2005). 2.…”

Spatial Cournot competition and transportation costs in a circular city

“…As mentioned earlier, Matsumura et al (2005) discussed general transport cost functions in a spatial Cournot competition model with four firms (a four-market setting), and showed that Pal's results (equidistance) are more robust than Matsushima's conclusions (partial agglomeration). Proposition 1 does not show such a property because the linear-quadratic transport cost function cannot capture extremely concave functions.…”

“…Matsumura et al (2005) discussed nonlinear transport cost in a four-market model with four firms. In their model, possible locations are only four, so it excluded the possibility of a continuum of equilibria.…”

Models of spatial competition: A critical review

“…An interesting result is that in the case of an even number of firms, all equilibrium situations yield equal profits and equal consumer surpluses. Matsumura et al (2005) extend the previous framework by assuming non-linear transportation costs. However, the paper considers the existence of four isolated markets in the city rather than a continuum of consumers.…”