Trigger strategy

1. Suppose there are two firms in the market. If they cooperate, they can make $400 each per year in economic profit. If they both compete, they make $200 per year. If one competes and one tries to cooperate, the “competer” makes $800 and the cooperator makes $50. The yearly interest rate is r.
Suppose firm 1 plays a “trigger strategy” of cooperating until it observes the other firm competing, and then competing ever afterward. In this case, for what values r would firm 2 prefer playing a trigger strategy to competing in every period?
2. There are two firms in a market that produce an identical good, both with marginal cost MC=10. Fixed costs are zero for both firms. Suppose inverse demand for a product is P = 130 – Q.
a) If the firms set the monopoly price and split the monopoly quantity. What quantities do they choose and what profit do they receive?
b) Suppose they set quantities simultaneously. That is, suppose the firms play a Cournot game. What quantities do they choose and what profit do they receive?
c) Suppose firm 1 knows that firm 2 will play the quantity it chooses in (a). What quantity should firm 1 pick? (Hint: use the best response function you derive in (b)). What are profits for each firm?
d) Suppose the firms meet infinitely often. They can save money at interest rate r. Suppose both firms play trigger strategies. That is, suppose firm 2’s strategy is to play the collusive quantity every period (the quantity derived in (a)) unless it observes firm 1 cheat, in which case firm 2 switches to playing the competitive quantity (the quantity derived in (b)). If firm 2 plays this way, what interest rate is necessary for a trigger strategy to be preferable for firm 1, as compared to cheating in the first period (playing the quantity in (c)) and playing the competitive quantity (as in (b)) afterward.