Problem 4 (Bertrand Stage game). Suppose two firms compete in micro-chip industry. The market demand curve of Q = 5 1/10P. Each period firm 1 charges price p1 chips and firm 2 charges price p2 chips. Both firms have a constant marginal cost of $20 per chip. Suppose the same industry exists for an infinite number of periods, the discount factor for profits is =0.8.

1. What are the static Nash equilibrium strategies for this market? That is, what is the NE if the game is played once? What are profits for a single period in this case?

2. Suppose the two firms agree to maximize joint profits rather than individual profits and share the proceeds equally(collusion). What price does each firm agree to charge? What are firms profits for a single period?

3. Suppose the firms have agreed to maximize joint profits, but while firm 2 charges the price according to the agreement, firm 1 decides to cheat and maximize individual profits instead. What price firm 1 should charge? What are profits for each firm?