2. Stackelberg Firms 1, 2 and 3 compete in quantities. The inverse market demand is given by p = 400 - (91 + 92 + 93), where q1, 92 and q3 are the quantities produced by firms 1, 2 and 3, respectively. The marginal cost for firm 1 is c1 = 20, and the marginal cost for both firm 2 and firm 3 is 40. The order of play is as follows: Firm 1 first sets a quantity q1. Then, firms 2 and 3 observe qi and simultaneously set 92 and 93. Each firm sets its quantity to maximize its own profits. (a) Let us first consider the optimal action of firm 2. Given a value q1 initially set by firm 1 and a value of q3 set by firm 3, what is the value of q2 that maximizes the profits of firm 2? Hint: Your answer should provide q2 in terms of q1 and q3. (b) Notice that, after firm 1 sets q1, a subgame starts, in which firms 2 and 3 simultaneously set q2 and q3. Given q1, find the values of 92 and q3 that firms 2 and 3 must set in a Subgame Perfect Nash Equilibrium. Hint: Your answer should provide q2 and q3 in terms of q1. (c) Find the value of q1 that firm 1 sets in the Subgame Perfect Nash Equilibrium of this game. What is the equilibrium price? And what are the equilibrium profits of each firm