Question

Problem 1: Suppose that the market demand function is given by q-80-2p. All firms in the industry have marginal cost of 10 and no fixed cost. In this problem, the firms compete in quantities. (a) What is the equilibrium price, quantity, consumer surplus, profit (producer surplus) and deadweight loss if there is only one firm in the industry? (b) Now answer the same question if there are two firms in the industry (duopoly). How does your answer compare to the one in (a)? (c) Now go back to (b) and consider what happens when the two firms collude by forming a cartel. That is, they agree on what quantities to produce. For simplicity assume that they both produce the same quantity. Answer (b) under this scenario. (d) Continuing with (c), is firm 1 maximizing its profit at the current output level given the output level of firm 2? If not, in which direction would firm 1 want to change its output level? What about firm 2? What does this imply about stability of cartels when firms choose quantities? Problem 2: Like in Problem 1, suppose that the market demand function is given by q 80-2p. There are two firms in the industry (duopoly) and they compete in quantities. Firm 1 has a constant marginal cost of 10, whereas firm 2 has a constant marginal cost of 20. How much does each firm produce in the Cournot equilibrium? What is the equilibrium price? How to these compare to your answer in part (b) of Problem 1? What is the intuition? Problem 3: Like in Problem 1, suppose that the market demand function is given by q 80-2p. There are two firms in the industry (duopoly). Both firms have a constant marginal cost of 10. In this problem, the firms compete in prices. That is, all the demand s to the firm with a lowe demand is split evenly between them. (a) What is the equilibrium price, quantity, consumer surplus, profit (producer surplus) and deadweight loss in the industry? (b) Now consider what happens when the two firms collude by forming a cartel. That is, they agree on what price to charge. At this price, assume that each firm gets one half of the demand. Answer (a) under this scenario. (c) Continuing with (b), is firm 1 maximizing its profit at the current price given the price charged by firm 2? If no, in which direction would firm 1 want to change its price? What about firm 2? What does this imply about stability of cartels when firms choose prices? r price. In case the two firms charge the same price, the Problem 4: Like in Problem 1, suppose that the market demand function is given by q 80-2p. There are two firms in the industry (duopoly) and they compete in prices. But now firm 1 has a constant marginal cost of 10, whereas firm 2 has a constant marginal cost of 20. How much does each firm produce in the Bertrand equilibrium? What is the equilibrium price? How to these compare to your answer in part (a) of Problem 3? What is the intuition?