(Total = 30 pts) Two rms, rms 1 and 2, compete in prices in a market for a homogeneous good. The demand curve is given by: D(p) = 40 2p Firm 1 and rm 2 both produce at constant marginal cost. Firm 1's marginal cost equals cl = 2. Firm 2's marginal cost equals C2 = 4. (a) (b) (4 pts) What prices would the two rms charge in a Bertrand equi- librium? Calculate their equilibrium prots. (4 pts) If the rms were able to collude, what price pm would they charge? Calculate their joint prots ''m. Now suppose the pricing game is repeated an innite number of times. Each rm discounts their future prots by a discount factor 6 that lies between 0 and 1. The rms decide to collude and set the collusive price pm every pe- riod (that you derived in question (a)). They agree to split the total prots in half, so that as long as the two rms are cooperating, rm 1 receives 50% of 1mm and rm 2 receives 50% of 7%. The rm decide to adopt a grim trigger strategy to punish any rm that cheats on the agreement. If in any period 15 either rm ever de- viates from the agreed price pm, then both rms will revert back to playing the static Bertrand equilibrium (that you derived in question (a)) in all future periods. (6 pts) What is the discounted present value of prots for (i) rm 1 if it keeps colluding (ii) rm 2 if it keeps colluding