Socially-Optimal Locations for Symmetric and Asymmetric Distributions in the Hotelling Duopoly Model

Theoretical models of spatial competition usually assume an uniform consumer distribution. In the real world, firms frequently compete for consumers who are not uniformly located. The equilibrium duopoly locations of several types of commonly used distributions were discussed in Meagher, Teo and Wang (2008). Using the same set of symmetric and asymmetric distributions and specifications from Anderson, Goeree and Ramer (1997), this paper extends Meagher, Teo and Wang (2008) by examining the social-optimum locations. We derive a formula for the social-optimum duopoly locations as one mean-deviation away from the median in the symmetric case. While regulating firm locations are sufficient to optimize welfare for symmetric distributions, additional price regulation is required to ensure social optimality for asymmetric distributions. We also calculate welfare improvements arising from regulation of firm location and show how these vary with the distribution of consumers. The results are significant for urban policy over firm/store locations