Consider the following version of the Hotelling model. There is a city on the interval [0,1], and consumers are uniformly distributed along the interval. There are two firms i = A, B selling identical products with identical cost functions ci(qi) = 1 qi . Firm A is located at point a ? [0, 1], and firm B is located at (1 ? b) ? [0, 1].

Consumers purchase only one unit of the good from one firm. Consumers pay a price pi and also have a quadratic travel cost. Consumer surplus is as follows: