This article studies the competition between an electronic commerce firm and a traditional shop, that set respectively a uniform delivered price and a mill price. Furthermore, they face different geographical constraints: the proximity of consumers in the case of the traditional shop, and logistic costs in the case of the on line retailer that takes in charge home delivery. The aim of this paper is to assess the impact of the introduction of an electronic commerce firm on the level of competition and to understand the different advantages of these two kinds of firms.