TITLE:
Socially-Optimal Locations of Duopoly Firms with Non-Uniform Consumer Densities
AUTHORS:
Kieron J. Meagher, Ernie G. S. Teo, Taojun Xie
KEYWORDS:
Socially Optimal Firm Locations, Distributions, Spatial Competition, Duopoly
JOURNAL NAME:
Theoretical Economics Letters,
Vol.4 No.6,
June
16,
2014
ABSTRACT: Advances in the theoretical literature have
extended the Hotelling model of spatial competition from a uniform distribution
of consumers to the family of log-concave distributions. While a closed form
has been found for the equilibrium locations for symmetric log-concave
distributions, the literature contains no closed form solution for the socially
optimal locations. We provide a closed form solution for the socially optimal
locations: one mean-deviation away from the median. We also derive a formula
for the excess differentiation ratio which complements the bounds previously
derived in the literature, and establish the invariance of this ratio to a form
of mean preserving spread. The equilibrium duopoly locations of several types
of commonly used distributions were discussed in [1]. This paper provides the
closed form solutions for the socially optimal locations to the same set of
distributions. We calculate welfare improvements arising from regulation of
firm location and show how these vary with the distribution of consumers. While
regulating firm locations is sufficient to optimize welfare for symmetric
distributions, additional price regulation is required to ensure social
optimality for asymmetric distributions. These results are significant for
urban policy over firm/store locations.