Consider the price competition model with product differentiation in the class of week 11 . This exercise extends the model further incorporating a (simple) vertical product differentiation. Consumers are uniformly distributed over [0,1] unit interval with mass 1 . A consumer located on x and buys the product of firm i receives the indirect utility: vitlixpi. Note that in the horizontal differentiation model in the class, we assumed v1=v2=v. We assume that the market is fully covered; i.e., all consumers buy one unit of product either from firm 1 or firm 2 who are located on 0 and 1 , respectively. (a) Write down the indifferent consumer x^ 's location as a function of v1,v2,p1,p2. (b) What are the demand functions, q1(p1,p2),q2(p1,p2), for each firm? (c) Find the Nash equilibrium of this game and compute the equilibrium prices, and profits. Explain the results concisely. Consider the price competition model with product differentiation in the class of week 11 . This exercise extends the model further incorporating a (simple) vertical product differentiation. Consumers are uniformly distributed over [0,1] unit interval with mass 1 . A consumer located on x and buys the product of firm i receives the indirect utility: vitlixpi. Note that in the horizontal differentiation model in the class, we assumed v1=v2=v. We assume that the market is fully covered; i.e., all consumers buy one unit of product either from firm 1 or firm 2 who are located on 0 and 1 , respectively. (a) Write down the indifferent consumer x^ 's location as a function of v1,v2,p1,p2. (b) What are the demand functions, q1(p1,p2),q2(p1,p2), for each firm? (c) Find the Nash equilibrium of this game and compute the equilibrium prices, and profits. Explain the results concisely