onsider the following oligopolistic market. In the first stage, Firm 1 chooses quantity 1q1. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose 2q2 and 3q3, respectively.

Market demand is given by ()=100p(Q)=100Q, and =1+2+3Q=q1+q2+q3. Firm 1's costs are 1(1)=11c1(q1)=1q1, firm 2's costs are2(2)=12c2(q2)=1q2 and firm 3's costs are3(3)=13c3(q3)=1q3.

Starting from the end of the game, you can express Firm 2's best response function in terms of 1q1 and 3q3, and you can similarly express Firm 3's best response function in terms of 1q1 and 2q2. Using these, answer the following questions.

a) (0.5 point) If Firm 1 chooses 1=12q1=12, what quantity will Firm 2 choose?

Answer for part 1

b) (0.5 point) If Firm 1 chooses 1=100q1=100, what quantity will Firm 2 choose?

Answer for part 2

c) (1 point) In the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity?

Answer for part 3

d) (0.5 point) In the subgame perfect Nash equilibrium of this game, firm 2 and firm 3 each produce what quantity?

Answer for part 4