Consider a duopoly in which inverse demand is given by P = 160 - q1 - q2, where P is the price, q1 is the output produced and sold by firm 1 and q2 is the output produced and sold by firm 2. The firms compete by simultaneously setting quantities. Both firms have a constant marginal cost of 10. There are no fixed costs.

(a) [6 marks] Derive the reaction functions of the two firms and illustrate them on a graph.

(b) [7 marks] Calculate the equilibrium quantity of each firm, the equilibrium price in the market and the profit of each firm.

(c) [6 marks] Suppose instead that the firms were to form a cartel, act as an effective monopoly and share the monopoly profit equally between them. Calculate the overall output in the market and the profit of each firm. Would total welfare (i.e. profit plus consumer surplus) in the market rise or fall? Explain.

(d) [6 marks] Explain why the collusive agreement in (c) is not sustainable when firms interact only once or for a finite number of periods.