EXISTENCE OF EQUILIBRIUM-CONFIGURATIONS OF COMPETITIVE FIRMS ON AN INFINITE 2-DIMENSIONAL SPACE

This paper analytically examines the existence of equilibrium configurations of competitive firms on an infinite two-dimensional space. It is shown that the Löschian configuration (a regular-hexagonal lattice) and a square lattice are in global equilibrium; the Löschian configuration is in the strongest global equilibrium among the regular lattices (in this sense, spatial competition leads to the social optimum); and the so-called back-to-back configuration is not in equilibrium. These results are in marked contrast to those obtained from a one-dimensional model, implying that spatial equilibrium configurations in a two-dimensional space should not be inferred only from one-dimensional models frequently employed in spatial economics. © 1991.