Three Equivalent Salop Models and Their Normative Representative Consumer

We show that three location models on the Salop circle, involving linear or quadratic transport cost, and asymmetric locations or fixed benefits, are equivalent: they lead to the same demand functions and consumer surplus. The only exception is the case of asymmetric locations with an even number of firms, which has one less degree of freedom. These models are also fully equivalent to a normative representative consumer whose indirect utility is given by the standard Salop consumer surplus. This result provides a further unification of location and representative consumer models