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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 cheats.)

8

(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.

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 cheats.)

8

(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.

Answered Same DayMay 02, 2021

a)

Harmon’s expected profit taking into account of possibility of rejection from this offer is =1/3*200000000-1/3*1600000000-1/3*4000000000

=...

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