1. Consider the following two-stage game. At time 1, an incumbent firm (Firm 1) chooses its price (p1). At time 2, a potential entrant (Firm 2) decides whether to enter, and if so, chooses its price (p2). If Firm 2 enters, it must pay a fixed cost F<1/4. Market demand is given by Q=1-P, where P is equal to the minimum of p1 and p2. Assume that when both firms set the same price, all the demand goes to Firm 2. Assume all demand goes to the firm with the lower price when the firms' prices differ. The marginal cost of production for both firms is assumed to be zero. (20 marks)
1. Take p1 as given. Conditional on entering, what price will firm 2 set?
2. For what values of p1 will Firm 2 enter?
3. What price will Firm 1 choose at time 1?
2. Assume market demand is given by P=a-Q. Suppose there are two firms (1 and 2) that engage in Cournot competition. Firm 1's marginal cost of production is 1 while firm 2's marginal cost of production is c.
a. Calculate firms' production levels and profits.
b. Calculate the Herfindahl index of market concentration when market shares are measured as production shares. The Herfindahl index is a function of c. When is the Herfindahl index increasing in c? Decreasing in c?
c. Suppose a=14 and c=3. For what discount factors can collusion be sustained in which q1 = 4 and q2 =2?
3. Assume that the inverse demand in an industry is given by P(Q) = 130 - Q and the marginal cost equals 70.
(a) Find the monopolistic quantity, price and profit. (4 marks)
(b) Assume that in the industry there are two firms. Determine the Cournot equilibrium quantities for each firm and the market price. (4 marks)
(c) What are the profit of each firm and the industry profits? (4 marks)
(d) Now, suppose it is a repeated game and the firms would like to collude. Under collusion, each firm produces half of the monopoly output. What is the critical discount factor needed to sustain collusion (i.e., what is the critical discount factor needed to sustain grim trigger strategies)? (4 marks)
(e) Finally, assume that firms compete in prices as in Bertrand competition. Suppose that they collude, what is the critical discount factor to sustain collusion in an infinitely repeated game? (4 marks)
4. Coventry Car is a car manufacturer. Coventry Car has an upstream division that produces car motors. Coventry Car has a downstream division that assembles cars. The demand curve for Coventry Car's cars is given by: Qc =24-Pc where Qc is the quantity of cars it will sell when it sets its price equal to Pc. Each car costs 12 to assemble. Additionally, the total cost for the upstream division of producing motors is Qm2, where Qm is the quantity of motors produced. One motor is needed per car.
(a) Assume that the downstream division's manager maximizes divisional profits in a transfer price system. What is the Net Marginal Revenue of the downstream division?
(b) How should top management optimally set the transfer price (PT) that the downstream division has to pay the upstream division for each motor it sells. How many cars will the downstream division produce? What are Coventry Car's profits?
(c) Assume that due to anti-trust actions, Coventry Car must be split up. The upstream division assumes the new name Warwick Motors, while the downstream division retains the name Coventry Car. How much will Warwick Motors charge Coventry Car for each motor now?
(d) How do the joint profits of Coventry Car and Warwick Motors compare to Coventry Car's profit before the spin-off? Explain (give a reason) for the difference you see (two sentences or less).
(e) Assume once again that the upstream and downstream divisions are a single firm called Coventry Cars. Suppose there is an outside market for motors and the market price of motors is 10. Determine the optimal transfer price and production levels for the upstream and downstream divisions. Will Coventry Cars purchase motors from the outside market or sell motors to the outside market?