Problem
1. Suppose the demand for beach umbrellas is given by P (Q) = 35 - 5Q Suppose each producer of beach umbrellas has cost function: C(Q) = 5Q There are three firms in the industry, each with a discount factor of = 0.6.
Suppose the firms compete a la Bertrand (by simultaneously setting prices). What will prices and quantities be?
Suppose the firms act as a monopoly cartel, with grim trigger strategies after defection. What is the cartel price? Is the cartel stable?
Suppose that two of the firms merger, what is the effect of this merger both if firms do not collude and if they do collude?
Now suppose there are 3 firms in the industry, as before. Suppose they operate in two cities: city A and city B. Will collusion be sustainable with multi-market contact?
2. Suppose there are N firms in a cartel, and industry demand is: Q = 10 -P 2 Each firm as cost function C(Q) = 4Q. Firms compete in prices (not quantities). Each firm has a discount factor = 0.5. They play grim trigger strategies.
What is the largest number of firms that could be in a stable cartel?
Suppose there are N = 2 firms. Firm 1 has a discount factor of ? = 0.4, firm 2 has a discount factor of ? = 0.8. Which firm will want to defect and why? Explain in words.
Suppose instead of dividing shares up 50/50 between the two cartel members, they allocate a fraction s to firm 1 and 1 ? s to firm 2. Can they do this in a way that makes the cartel stable? Who gets the bigger share?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.