Microsoft Word - second exam.docx
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QUESTION 1 [40 points]
Suppose that Beth Harmon is considering buying DeepMind Technologies, an artificial intelligence
esearch company that is cu
ently 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 cu
ently developing. She believes that each scenario
is equally likely. Moreover, suppose that (for now, at least) there is nothing Harmon can do to distinguish
etween 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
ejection) 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
ejection) from this offer?
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(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
easoning.
(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
eveal 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.
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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
uy 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 ca
iers. 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 equili
ium to make a prediction, what price is each airline going to
charge? Explain your reasoning.
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(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
usiness 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
emains unchanged. As a result, neither Delta nor JetBlue can serve the whole market alone.
(e) [5 points] Is it a Nash equili
ium for each airline to charge a price of $160 per passenger? Justify
your answer.
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(f) [5 points] Is it a Nash equili
ium for each airline to charge a price of $400 per passenger? Justify
your answer.
Another ca
ier, 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 ca
y 800 passengers on this route each
week. Of course, as we established in class, domestic air ca
iers 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 equili
ium of the pricing game among these airlines. Explain.
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QUESTION 3 [40 points]
A Chinese manufacturer, Fujian Fa
icators, is the supplier to GuavaFamily, a US “manufacturer”
of travel cribs and play pens. Fujian Fa
icators 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
cu
ent 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 a
ives 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 Fa
icators 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 Fa
icators 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 Fa
icators 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 equili
ium.
(b) [6 points] What outcome is collectively prefe
ed to the above-described equili
ium
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?
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Next, suppose that Fujian Fa
icators 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
Fa
icators 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 Fa
icators
again chooses quality and GuavaFamily again chooses how much to buy).
(c) [5 points] Suppose that in the first period, Fujian Fa
icators and GuavaFamily achieve the
outcome identified in part (b). What outcome do you expect in the second period? Why?
(d) [7 points] What equili
ium outcome should be anticipated in the first stage of the two-
stage game? Justify your answer.
Now suppose that Fujian Fa
icators and GuavaFamily enter into a long-run ongoing business
elationship. 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 equili
ium in which Fujian Fa
icators 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 a
angement. (In particular, specify how the two companies should
agree to play the game, and what each would do in case anyone