Quality as vertical Product Differentiation There is a continuum of consumers uniformly distributed on the interval [o, 1]. There are two firms denoted by a and B and located at points a and b(o sbs1) from the origin, respectively. Figure 12.2 illustrates the location of the firms on the 0, 1 interval he utility of a consumer located at point x, t E [0, 1] and buying brand i, i=A, B is defined by Pa i=A U()≡{bx-P=B (122) where pA and pB are the price charged by firm A and B, respectively firm a firm B (b-a) Figure 12.2 Vertical differentiation in a modified Hotelling model We seek to define a two-period game where firms choose location in the first period, and choose price in the second period, after locations have been fixed. Before defining the game, let us solve for a Nash-Bertrand equilibrium in prices, assuming fixed locations as illustrated in Figure 12.2Quality as Vertical Product Differentiation