Maximal or Minimal Differentiation in a Hotelling Market? A Fresh Perspective

A perplexing problem in spatial modelling—going back to Hotelling’s linear market—is whether firms will cluster together or separate themselves. Maximal differentiation is the prevailing equilibrium when travel costs are quadratic and minimal differentiation results when price competition is limited. The reality for most markets is that the force that draws firms together (maximize demand) and the force that causes them to separate (avoid price competition) are both present. In many cases, this makes the characterization of an equilibrium difficult. The vast majority of research using the Hotelling model is based on the assumption that all potential consumers buy, yet the reality of many markets is that there are some consumers who seriously consider not buying. When allowing for the possibility that some consumers would consider not buying from either firm, we are able to identify equilibrium locations for firms that first choose locations and then prices in a Hotelling market with linear travel costs. Following the discussion above, we consider ranges of consumers’ willingness to pay for the products relative to the outside good such that the market is not necessarily covered for all location choices. The analysis demonstrates the existence of a pure-strategy location equilibrium, supported by a pure-strategy pricing equilibrium, where firms are moderately differentiated and the market is covered.