Handout 15 Oligopoly – Collusion and Price Leadership Models This handout contains exercises of - Collusion Model - Price Leadership Model Things you should know - Why would collusion be unsuccessful? - How to solve the price leadership model? Exercises Question 1 (Collusion) Suppose there are two firms – A and B – entering into a collusion agreement to restrict the quantity sold. The demand curve of this good is given by P = 100 – Q, where Q is the total quantity in the market. Each unit of good costs AC = MC = 20. A single monopolist would maximize its profits of $1600 at Q = 40 units at price P = $60. 1. It is initially agreed that each firm will produce 20 units. Suppose firm A is contemplating cheating by producing 10 more units, what would be its profits compared to firm B? Collusion Firm A Cheats Q P Profit Q P Profit Firm A 20 units $60 $800 Firm A 30 units $50 Firm B 20 units $60 $800 Firm B 20 units $50 2. What do you expect to happen next after Firm A cheats? When would this cheating ends? Question 2 (Price Leadership Model) Suppose the market demand is P = 100 – Q, the supply curve of small firms is P = 20 + Q, the marginal cost of dominant firm is MC = AC = 30. After each step, exhibit your curves or solutions graphically. 0. Find the price where market demand and supply curve of small firms intersect. 1. Find the equations of demand and marginal revenue for dominant firm. 2. What is the quantity the dominant firm produces? At what price would this dominant firm lead into this market? 3. What is the quantity the small firms produce? At what price would the small firms sell? 4. What is the total quantity sold in this market? Verify your answer. 5. (Bonus) What if the dominant firm has the marginal cost of MC = 10? Question 3 (Price Leadership Model) There is one dominant firm and several smaller firms in the market for a particular good. The small firms supply curve is P = 10 + Q. The dominant faces a residual demand of P = 50 – 0.5Q. 1. Find the market demand curve. 2. If small firms produce 30 units, what is the price that the leader has set? What is the quantity that the leader has produced? 3. Assuming constant marginal cost by the leader firm, what is marginal cost? Question 4 (Price Leadership Model) There is one dominant firm and several smaller firms in the market for a particular good. The residual demand is P = 60 – 0.5Q, the market demand is P = 100 – Q. Suppose the small firms will not operate at price below $20, and that price is currently $40. 1. What is the marginal cost of the dominant firm if it has constant marginal cost? 2. What is the equation for the small firms supply? 1