Question

Consider a Cournot model with two firms, firm 1 and firm 2, producing quantities q1 and q2, respectively. Suppose the inverse market demand function is: P = 450 – Q where Q denotes the total quantity supplied on the market. Also, each firm i = 1,2 has a total cost function c(qi) = 30qi. a) What is the Nash equilibrium of this Cournot game ? What is the market prices ? Compute each firm’s profit and the industry profit. b) Consider a Stackelberg model where firm 1 chooses quantity before firm 2. What is the subgame perfect Nash equilbrium in quantities ? Compute each firm’s profit and the industry profit. c) Suppose there is only one firm supplying the market. What is the profit maximizing price and quantity of the monopolist ? Compute each firm’s profit and the industry profit. d) Suppose the market is a perfectly competitive market. What is the price and quantity supplied in equilibrium ? Compute each firm’s profit and the industry profit. e) What do you observe ?

Answer 1