Spatial Competition with an Outside Good and Distributed Reservation Prices

In this paper, we analyze spatial competition within the framework of a Hotelling model with quadratic transportation costs and an outside option. The new feature of our approach is that consumers are uniformly distributed not only along the Hotelling line but also with regard to reservation prices. It turns out that in this particular model, duopolists always locate their shops exactly at the first and third quartile of the consumer distribution – i.e., at the socially optimal locations. Moreover, with uniformly distributed reservation prices, less than seventy percent of the consumers buy the good, and profits are less than fifteen percent of those in the standard model without an outside option. Received February 7, 2001; revised version received March 27, 2002 Published online: November 11, 2002