(b) Let firm I be the one located at point 0 and firm 2 the one located at point L. Let p, be the price of firm / and A, the advertising expenditure of firm / (/ = 1,2). Given p, and p,, let z be the location of the consumers who (if aware of the two products) is indifferent between the two firms. Then z is the solution to p + z =p,+ (1 -z), that is,2. (a) Let A be advertising expenditure and p be the price. Let a = -. Then, ifp + a S E, the profit function is map) = 2a (p-k) -ca if as L =L(p-k) -ca if a> Having p + a > E cannot be profit maximizing, because in that case the consumers at points Ita and L-a prefer not to buy. Hence the effective market is a proper subset of - -a , 7 + a and the firm can increase its profits by keeping p constant and reducing a (revenue and production costs remain the same, while advertising costs decrease). From the above expression it is clear that if a maximizes then it must be that as A second requirement for profit maximization is that the consumers who live at points Zta and L-a pay the reservation price, that is, p+ a =E. In fact, if p + a