Three firms operate in a market with inverse demand given by P (Q) = a - Q, where Q = q1 + q2 + q3 and qi is the quantity produced by firm i. Each firm has a constant marginal cost of production, c, and no fixed cost. The firms choose their quantities as follows:

(a) firm 1 chooses q1 0 first; firm 2 observes q1 and then chooses q2 0; finally, firm 3 observes both q1 and q2, and then chooses q3. What is the subgame-perfect outcome in this setting (find the formulas: q1, q2, and q3)?

(b) firm 1 chooses q1 0 first; firms 2 and 3 observe q1 and then simultaneously

choose q2 and q3, respectively. What is the subgame-perfect outcome in this setting

(find the formulas: q1, q2, and q3)?