Please provide pricing for attached assignment
Firms and Markets (Spring 2021) Simon W. Bowmaker This exam is designed to test your understanding of the concepts covered in the course. Take some time to read the questions carefully. · Please check that you have 9 pages in your copy of the exam. There are three questions in all. · Be sure to answer what is asked in each question. Your answers may be typed or hand-written. · This is an open-book exam and calculators are permitted. · Show your work and explain your reasoning! To get full credit, it is not sufficient to answer correctly but without explaining your solution. Similarly, you can get partial credit if your reasoning is correct, but you make a mistake in your calculations. · The exam is worth 120 points. · You may discuss the possible answers with anyone else in the class (but not with anyone who is not a member of the class). But you must decide on your own answers and use your own words in writing your answers to the questions. · Please upload your completed exam by 9 am on Saturday, April 24. · Finally, please read and then sign the following statement: I understand that the honor code applies: I will not lie, cheat, or steal to gain an academic advantage, or tolerate those who do. _______________________________________ Name QUESTION 1 [40 points] Suppose that Warren Buffett is considering buying Mysterious Practices, Inc. (MPI). Due to financial distress unrelated to MPI’s operations, MPI’s current ownership has fallen on hard times and is considering selling the company. As it turns out, Buffett is the only potential buyer for MPI before it is eventually liquidated. Buffett can make a single take-it-or-leave-it offer to MPI, and he judges that there are four possible scenarios for the technology MPI is currently using. Each scenario is equally likely. Moreover, suppose that (for now, at least) there is nothing Buffett can do to distinguish between the four possible scenarios. (in billions) Buffett’s valuation Current owner’s valuation Cutting-edge technology $3.0 $2.0 Efficient technology $2.0 $1.5 Average technology $1.5 $1.0 Antiquated technology $0.5 $0.2 You can assume that MPI’s current owners would accept an offer equal to their valuation, and that they know what the state of their technology is. (a) [5 points] Suppose Buffett offers a price of $1 billion. What is the probability that this offer is accepted? And what are Buffett’s expected profits (taking into account the possibility of rejection) from this offer? (b) [5 points] Suppose Buffett offers a price of $2 billion. What is the probability that this offer is accepted? And what are Buffett’s expected profits (taking into account the possibility of rejection) from this offer? (c) [15 points] What price would you advise Buffett to offer, assuming that you have no more information than he does? What would his profits be? Be sure to fully explain your reasoning. (d) [15 points] A consulting firm offers to determine the state of MPI’s technology. Suppose that Buffett trusts that the consultant’s information will reveal the true state of MPI’s technology, but Buffett has to pay for the information in advance (before learning which state will be revealed). What price would Buffett be willing to pay for this information? Explain. QUESTION 2 [40 points] JetBlue and Delta are the only two major airlines with regularly scheduled service between New York and Nantucket. There are 900 potential passengers every week, each of whom is willing to pay up to $400 for a ticket. Since the two airlines provide an essentially identical (bad) service, customers simply prefer to buy from the cheaper one. (If they charge the same price, then they will split the market equally.) Each airline can transport at most 1200 passengers each week. You can safely assume that each airline spends literal peanuts (i.e., zero) serving passengers; however, each passenger displaces air cargo that is worth $160 in profits to the carriers. Suppose that each airline takes a short-run perspective and only wants to maximize each week’s profits, and that neither one would consider shutting down the route in the foreseeable future. (a) [3 points] What is the appropriate economic model to study price competition in this market? (b) [7 points] If you use Nash equilibrium to make a prediction, what price is each airline going to charge? Explain your reasoning. (c) [4 points] Give two possible practical means by which the airlines could earn more than predicted in (b). (d) [8 points] If construction-related traffic congestion at LaGuardia airport makes Delta’s cargo business less attractive to shippers while JetBlue’s JFK-based operations remain unaffected, how will your prediction in (b) change? Explain. From now on, focus on the baseline setting where both airlines face the same tradeoff between passengers and cargo: each passenger displaces cargo worth $160 in profits. However, suppose that the market size has doubled and there are now 1800 potential customers, but each airline’s capacity of 1200 passengers remains unchanged. As a result, neither Delta nor JetBlue can serve the whole market alone. (e) [5 points] Is it a Nash equilibrium for each airline to charge a price of $160 per passenger? Justify your answer. (f) [5 points] Is it a Nash equilibrium for each airline to charge a price of $400 per passenger? Justify your answer. Another carrier, American Airlines, also begins serving the New York to Nantucket route. Because their fleet has suffered from the grounding of the 737MAX, it can only carry 800 passengers on this route each week. Of course, as we established in class, domestic air carriers in the US are all equally bad, so passengers still prefer to buy the cheapest ticket possible (splitting the market equally between any airlines charging the same price), and American’s cargo business is no more or less profitable than Delta’s or JetBlue’s. (g) [8 points] What is the Nash equilibrium of the pricing game among these airlines. Explain. QUESTION 3 [40 points] A Chinese manufacturer, Fujian Fabricators, is the supplier to GuavaFamily, a US “manufacturer” of travel cribs and play pens. Fujian Fabricators can supply either high-quality cribs or low-quality cribs. GuavaFamily must decide whether to buy one million or two million cribs from its supplier’s current production run. All cribs in a given production run are of the same quality. GuavaFamily cannot tell the quality of the cribs when it decides how many to buy, but does discover the quality once the shipment arrives and is opened. (The nonrefundable payment must be made before the cribs are shipped.) If GuavaFamily buys 2 million units, its profits are $30 million if quality is high, and zero if quality is low. When it buys 1 million units, its profits are $20 million if quality is high, and $10 million if quality is low. If Fujian Fabricators sells 2 million units, then it earns a profit of $40 million if it makes low-quality cribs, but $15 million if it supplies high-quality cribs. If Fujian Fabricators sells 1 million units, its profits are $10 million if it makes low-quality cribs, but zero if it makes high-quality cribs. (a) [8 points] Suppose the two companies interact only once, and they make their decisions simultaneously (i.e., Fujian Fabricators decides on quality before knowing how large an order it will receive, and GuavaFamily must decide how many units to order before learning their quality). Describe the game in matrix form and find the Nash equilibrium. (b) [6 points] What outcome is collectively preferred to the above-described equilibrium outcome? Explain why this better outcome cannot be achieved in a one-shot simultaneous move game. In particular, who has an incentive to deviate from that outcome? Next, suppose that Fujian Fabricators and GuavaFamily interact and play this game for exactly two production runs (and then their relationship ends forever). In other words, in the first period, Fujian Fabricators chooses the quality of cribs they will deliver while (simultaneously) GuavaFamily chooses the size of its order. Then, in the second period, the game is repeated (Fujian Fabricators again chooses quality and GuavaFamily again chooses how much to buy). (c) [5 points] Suppose that in the first period, Fujian Fabricators and GuavaFamily achieve the outcome identified in part (b). What outcome do you expect in the second period? Why? (d) [7 points] What equilibrium outcome should be anticipated in the first stage of the two-stage game? Justify your answer. Now suppose that Fujian Fabricators and GuavaFamily enter into a long-run ongoing business relationship. We can model such an ongoing relationship as an infinitely repeated game in which the two firms play the one-shot game of part (a) in every period. We aim to study the possibility of a cooperative equilibrium in which Fujian Fabricators makes high-quality cribs in every period, and GuavaFamily buys 2 million units in every period. (e) [6 points] Describe clearly (in words) possible strategies of each player that could sustain such a cooperative arrangement. (In particular, specify how the two companies should agree to play the game, and what each would do in case anyone cheats.) (f) [8 points] Suppose that there is a production run every month, and that the monthly interest rate is r. Find the conditions under which the cooperative agreement can be sustained. Interpret the economic intuition of these conditions. 2