1. Two firms are operating as a cartel using a grim trigger strategy. Thestage game is Bertrand pricing; firms have constant marginal costs equal to c= 4, and they sell a homogenous, perfectly substitutable output. Demand is given by D(p) = 12p, and the collusive arrangement has it that they split the market evenly.

However, today (at t= 0) there is a one-time demand shock, and demand is given by 3 D(p).

Firms know that this is a one-time shock, and put zero probability on it ever happening again.

1. How does the monopoly price today compare to the monopoly pricein every other period? What about monopoly profits?
2. For what values of , the discount factor, will the grim trigger strategy be a SPNE?
3. Suppose that is too low by some small amount. What can they do to preserve the collusive arrangement? Motivate your argument using the monopoly profits you derived in part (a).