3. (16pts) (Stackelberg Duopoly) Two firms produce identical products. Each has the same constant average cost of $10 per unit of output. Market price P=902(q1+q2). Both firms choose outputs to compete. (a) (5pts) Find the subgame perfect equilibrium outcome of the Stackelberg Duopoly game with Firm 1 moving first. First, solve for the follower's (Firm 2's) best response function. Then solve for the leader's optimal strategy. (b) (4pts) Find the Nash equilibrium of the Cournot duopoly under the same assumptions on costs and demand. (c) (3pts) Compare the two equilibria. Discuss the differences as to which firm earns more profit in which case. (d) (4pts) Suppose again firm 1 chooses output first and firm 2 chooses output second. But now before firm 1 makes a decision, firm 2 makes a claim that it would produce the Cournot equilibrium level of output regardless of what output q1 firm 1 chooses first. If firm 1 believes firm 2's claim, then what is the best output q1 for firm 1 to choose first? Compared with standard Stackelberge equilibrium in part (a), verify if firm 2 will earn more profit in this case. What might be the challenge for firm 2 to achieve this outcome? 3. (16pts) (Stackelberg Duopoly) Two firms produce identical products. Each has the same constant average cost of $10 per unit of output. Market price P=902(q1+q2). Both firms choose outputs to compete. (a) (5pts) Find the subgame perfect equilibrium outcome of the Stackelberg Duopoly game with Firm 1 moving first. First, solve for the follower's (Firm 2's) best response function. Then solve for the leader's optimal strategy. (b) (4pts) Find the Nash equilibrium of the Cournot duopoly under the same assumptions on costs and demand. (c) (3pts) Compare the two equilibria. Discuss the differences as to which firm earns more profit in which case. (d) (4pts) Suppose again firm 1 chooses output first and firm 2 chooses output second. But now before firm 1 makes a decision, firm 2 makes a claim that it would produce the Cournot equilibrium level of output regardless of what output q1 firm 1 chooses first. If firm 1 believes firm 2's claim, then what is the best output q1 for firm 1 to choose first? Compared with standard Stackelberge equilibrium in part (a), verify if firm 2 will earn more profit in this case. What might be the challenge for firm 2 to achieve this outcome