Hotelling Was Right About Snob/Congestion Goods (Asymptotically)

We add congestion/snobbery to the Hotelling model of spatial competition. For any firm locations on opposite sides of the midpoint, a pure strategy price equilibrium exists and is unique if congestion costs are strong enough relative to transportation costs. The maximum distance between firms in any pure strategy symmetric location equilibrium declines toward zero as congestion costs increase relative to transportation costs. For any non-zero minimum distance between firms, high enough congestion costs relative to transportation costs guarantee that the unique pure strategy symmetric location equilibrium involves minimum differentiation. In this sense Hotelling was right about differentiation of snob/congestion goods.