BADM 505 - FIRM ANALYSIS AND STRATEGY PROBLEM SET FIVE QUESTIONS 1. Attila Inc. wants to take over CAM Inc., Michael Cichello's and Jeffrey Macher's recycled ice cream market. Cichello and Macher each own two shares of C&M Inc. (for a total of four shares). The market price of each share is currently $20,000. Attila plans to purchase all the shares of the firm. By bringing in new Georgetown MiM-educated management, Attila Inc. is certain he can raise the market value to $36,000 per share. Attila offers to pay $40,000 each for the first two shares tendered, but only $20,000 each for the next two shares. If Cichello and Macher simultaneously tender all their shares, they will evenly split $120,000. If neither tenders, they can jointly eventually sell the company for $144,000 (its expected present value under the new Georgetown MiM-educated management). Draw the game that Cichello and Macher find themselves in normal form. Does Cichello or Macher have a dominant strategy? What is the Nash equilibrium? Why Is Atilla smiling? . You are considering entering the market for the SmokeRunner, an innovative type of running shoe. One shoe in each pair has a cigarette holder built in and a long tube that connects to the runner's mouth. This allows one to exercise, while simultaneously enjoying the clean, sweet taste of nicotine. No one is in this market yet, and there is only one other firm other than you that could potentially compete. If only one firm enters, it enjoys profits of $100 million per year (needless to say, SmokeRunners"" are likely to be a huge hit). If both firms enter, each will lose $10 million. A firm that does not enter earns zero (50) profit. What should you do? If the other firm acts like you do, what will happen? Is there anything that you could do to improve the outcome? 3. Two firms produce identical products at zero cost, and they compete by setting price. if each firm charges a low price, then both firms earn profits of $5. If each firm charges a high price, then both firms earn profits of $15. If one firm charges a high price and the other firm charges a low price, the firm that charges the lower price earns profits of $60 and the firm that charges the higher price earns zero profits. a. Write this game in normal form and find the Nash equilibria. b. Suppose this pricing game is infinitely repeated. Can the players sustain the "collusive outcome" of high prices as a Nash equilibrium if the discount rate is 50 percent? C. At what discount rate will the firms "agree" to cooperate? 4. Two firms are engaged in Bertrand competition. There are 10,000 people in the population, each of whom is willing to pay at most $10 for at most one unit of the good. Currently, both firms can produce as many units as they want to for $5 each. a. What is the equilibrium in this market? What are the firms' profits? b. Suppose that one firm can adopt a new technology that allows it to produce as many units as it wants to for 53 each. What is the equilibrium now? How much would this firm be willing to pay for the new technology? C. Suppose that the new technology mentioned in part b. is available to both firms. The cost to a firm of purchasing this technology is $10,000. The game is now played in two stages. First, the firms simultaneously decide whether to adopt the new technology or not. Then, in the second stage, the firms set prices simultaneously. Assume that each firm knows whether or not its rival acquired the new technology when choosing its prices. What is (are) the Nash equilibrium (equilibria] of this game? (HINT: You can solve this problem by drawing a single normal-form game that incorporates both the first and second period payoffs.)5. Assume that there are only two firms in the market for breeding and selling weasels and only two species of weasel (badgers and wolverines) are bred. Firm Badger breeds and sells only badgers; Firm Wolverine breeds and sells only wolverines. Assume that these firms are in competition for those consumers who desire badgers or weasels as pets, and assume that both firms compete strictly on price. Firm Badger faces demand of q, (P.) = 1000 -20P, + 20P, and total cost of TC,(q,) = 1045- Firm Wolverine faces a symmetric demand of qw(P) = 1000 - 20P + 20Pg and has total costs of TCw (qw) = 104w- a. Find each firm's Bertrand best response (reaction] function. b. Solve for the Bertrand Nash equilibrium. c. Find each firm's profit. 6. Bugs Bunny is the sole proprietor of high-end carrot cake in Brooklyn, NY (the Flatbush section), The daily demand for carrot cake in Brooklyn, NY is Op(P) - 45-P, where Q. is the number of carrot cakes demanded per day and P is the price per carrot cake. Bugs Bunny can make carrot cakes at a constant marginal cost of MCas = 3 per carrot cake. He incurs fixed costs of 100 per day. a. How many carrot cakes does Bugs Bunny make per day? b. What is the price charged? What is the profit per day? c. Daffy Duck is considering entering the Flatbush carrot cake market. Daffy Duck has the exact same cost structure as Bugs Bunny. Daffy Duck and Bugs Bunny know each other's cost structures with certainty. Assume that Bugs Bunny and Daffy Duck will compete as Cournot oligopolists if Daffy Duck enters. If Daffy Duck enters, how many carrot cakes are made by Bugs Bunny and Daffy Duck per day? d. What would be the price per carrot cake? What would be the profit for Bugs Bunny and Daffy Duck? How much would Bugs Bunny be willing to pay Daffy Duck per day to stay out of the carrot cake market