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Microsoft Word - second exam.docx 1 QUESTION 1 [40 points] Suppose that Beth Harmon is considering buying DeepMind Technologies, an artificial intelligence research company that is currently a wholly owned subsidiary of Alphabet Inc. Due to antitrust concerns unrelated to DeepMind’s operations, Alphabet is considering selling the company. As it turns out, Harmon is the only potential buyer for DeepMind before it is eventually liquidated. Harmon can make a single take-it-or-leave-it offer to Alphabet, and she judges that there are three possible scenarios for the technology DeepMind is currently developing. She believes that each scenario is equally likely. Moreover, suppose that (for now, at least) there is nothing Harmon can do to distinguish between the three possible scenarios. (in billions) Alphabet’s valuation Harmon’s valuation Cutting-edge technology $2.0 $4.0 Efficient technology $1.2 $1.6 Antiquated technology $0.5 $0.2 You can assume that Alphabet’s management would accept an offer equal to their internal valuation of DeepMind, and that they know what the state of DeepMind’s technology is. (a) [10 points] Suppose Harmon offers a price of $0.5 billion. What is the probability that this offer is accepted? And what are Harmon’s expected profits (taking into account the possibility of rejection) from this offer? (b) [10 points] Suppose Harmon offers a price of $1.2 billion. What is the probability that this offer is accepted? And what are Harmon’s expected profits (taking into account the possibility of rejection) from this offer? 2 (c) [10 points] What price would you advise Harmon to offer, assuming that you have no more information than she does? What would her expected profits be? Be sure to fully explain your reasoning. (d) [10 points] A “consulting firm” offers to conduct some corporate espionage and determine the state of DeepMind’s technology. Suppose that Harmon trusts that the hackers’ information will reveal the true state of DeepMind’s technology, but Harmon has to pay for the information in advance (before learning which state will be revealed). What price would Harmon be willing to pay for this information? Explain. 3 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. 4 (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. 5 (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. 6 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? 7 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