Suppose there are two firms competing in a market. Both firms have the cost function c(x) = 10x/2 while the demand function is given by x(p) = 100 - 0.1p.

(a) Suppose firm 1 decides its quantity first and firm 2 follows after observing x1. Find the profit maximizing quantity and price for this Stackelberg competition. (15 marks)

(b) Now suppose that the firms are playing the quantity game repeatedly and does not now when the game will end. Find the discount factor that will ensure cooperation is sustainable given firms are playing a grim trigger strategy. (15 marks)