Suppose two firms supply the market for computer chips and their products are perfect substitutes. The firms choose what quantity to produce independently, i.e. compete as Cournot. The market inverse demand is described by p = 120-20Q, Q measured in millions of chips, p measured in dollars. Each firm has a constant marginal cost of $20.
a. What is the one-period Cournot-Nash equilibrium output and price?
b. What is the output of each firm if they collude to produce the monopoly output?
c. Show that each firm has an incentive to cheat on the collusion.
d. Suppose that interaction between the two firms is repeated infinitely. Show that the collusive outcome which you derived in part (b) can be sustained when the discount factor R > 0.529.