4. Watson 22.2 B. Cournot Repeated Consider the basic Cournot competition. Suppose their are two firms who are competing on producing ice cream. The market demand curve is P = 20-Q1 Q2. Where Qi is the quantity that firm 1 produces and Q2 is the quantity that firm 2 produces. Suppose this game is repeated infinitely with discount factor 5. (a) Find the stage game Nash equilibrium (b) Calculate the Profits of each firm in the stage game Nash equilibrium (c) Suppose the firm colluded to produce the monopoly amount and split the profits evenly. Calculate the monopoly quantity and each firms shared profits. (Hint: In monopoly case suppose their is only one firm who sets both quantities to find max profit. (d) Find what is needed to support the grim trigger strategy of collud- ing unless deviation in which firms play the Nash equilibrium forever. (e) Graphically represent the set of average payoffs that are possible for a high enough delta (Folk Theorem).