customer who is indifferent between the two stores. First note that if store a attracts customer x, it"also attracts all customers at x> going beyond customers's distances from both sellers increase at the same rate. So we know that if there is an indifferent customer at x, he is situated between x and or this customer t〔 )+p=t(x-×)+p so that Pb"Pa s t(2x -xa-*b) Therefore, 2EI (P1p)+t(x+×1) (3) Since store a keeps all customers between 0 and x, equation (3)is the demand curve for a so long as he does not set his price so far above b's that he looses even customer 0. The payoff of store a will then be ma=(Pa-c)2t(Pb-Pa Store a will choose p so as to maximise its profits The first order condition gives =0 2E|(Pb2)+ 2 2pa"Pb=c+t(xa+b) The demand facing store b is 1-x and by following the same procedure we find that the first order condition for store b is t〔2-x 5 Solving the two first order conditions (4) and (5) for the two prices gives