Consider a market with two horizontally differentiated products and inverse demands given by P_i (q_i, q_j) = a - bq_i - dq_j . Set b = 2=3 and d = 1/3. The system of demands is then given by Q_i (p_i, p_j) = a - 2p_i + p_j . Suppose firm 1 has cost c₁ = 0 and firm 2 has cost c₂ = c (with 7c < 5a). The two firms compete in prices. Compute the firm profits:

1. at the Nash equilibrium of the simultaneous Bertrand game,

2. at the subgame perfect equilibrium of the sequential game

(a) with firm 1 being the leader, and

(b) with firm 2 being the leader.

3. Show that firm 2 always has a second-mover advantage, whereas firm 1 has a first-mover advantage if c is large enough.