This paper analytically investigates the validity of Eaton and Lipsey's (1976) conjecture that there exist more than one equilibrium configurations in an infinite two-dimensional market. The competition considered here is under the assumptions of (i) an infinite two-dimensional market, (ii) fixed and identical mill price for all firms, (iii) evenly spreading consumers endowed with inelastic demand functions, (iv) firm's zero conjectural variation. etc.
It is scrutinized whether or not several configurations of the firms in a two-dimensional market are in Nash equilibrium, and among which regular hexagonal configuration and regular square configuration are proved to be in equilibrium.
Comparison between equilibrium configurations of one-dimensional and two-dimensional markets shows that they are qualitatively different in terms of “strength of equilibrium” and “social optimality”.
