Three firms compete in the style of Bertrand

Three firms compete in the style of Bertrand. All firms have the same cost function: TC(q) = 89. They produce differentiated products that are substitutes. The demand system is given by the following equations: = Demand for Firm 1: q1 = 95 – 20p1 + 10p2 + 5p3. Demand for Firm 2: q2 = 95 – 20p2 + 10p1 + 5p3. Demand for Firm 3: q3 = 100 – 20p3 + 5p1 + 5p2. = = A. Please compute the Nash equilibrium prices. B. Now suppose firm 1 and firm 2 merge and become a single firm. Firm 3 and the merged firm compete in the style of Bertrand. Now, p1 and p2 are chosen to maximize the total profits of firm 1 and firm 2. Compute the Nash equilibrium prices now.