second midterm solutions 2010 econ

8/11/2019 Second Midterm Solutions 2010 Econ

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BPUB 250: Fall 2010

2ndMidterm

Instructions

1

Work on each question in a separate Bluebook: clearly indicate thequestion number on the Bluebook cover

2

Read over the whole exam, and do the easier questions first.3

Show your work. No credit will be given if work is not shown.4

Make clear which subsection of the exam you are answering!5

Write legibly!6

Write your name and student I.D. number on every Bluebook and onthe first and last page of this exam

YourName:_____________________________________________________

YourI.D. # _______________________________________________________________

Section number:_____________________________________________

DO NOT START UNTIL 6:00 PM

EACH QUESTION IN A SEPARATEBLUEBOOK!


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THIS PAGE INTENTIONALLY BLANK


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Question 1 (20 points)

Steve Employments, the CEO of Pineapple Inc., is developing a new product: a blackturtleneck sweater that incorporates a microphone, ear buds, 4G coverage, an MP3player, GPS, and a health monitoring system. The productcodenamedIHotis ready

to go into production. Unfortunately, Steve knows that his suppliers will eventually sharethe production technology with a competitor: Swansong. Swansong is already developingmarketing materials for their copy-cat product: theMeSweats.

Fortunately for Steve, Pineapple is widely recognized as the leader in new consumer techproducts. Steve will make a decision as to how manyIHotsto produce first and thinksthat Swansong will just accept its secondary position upon entering the industry.

Since the product is outsourced to identical foreign suppliers, the marginal cost ofproduction will be the same for Pineapple and Swansong: $20 per unit. Assume that fixedcosts are zero.

Steve estimates that the overall demand for the indistinguishableIHotsandMeSweatsfollows the function:

1300

2P Q= .

a) (10 points) What should be the production target of Pineapple?

b) (3 points) What will be the likely retail price of the IHot?

Steve realizes that, rather than outsourcing the production ofIHot, he could be producing

it in his Mugertino plants, at an estimated marginal cost of $150 per unit. The advantageof in-house production is that it would not allow any competitors access to theIHottechnology, and Pineapple would be the sole producer in this market.

c) (7 points) Should Steve outsource production or produce the IHot in-house?Briefly discuss.


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Brianna is an iPhone user, whose individual demand for hours of iPhone use is given by q= 40 P, while her opportunity cost of time can be represented by P= 10 + 2q. In thismarket, qrepresents Briannas hours of iPhone use, and Prepresents the amount of

money she would spend for the right to use her phone for an hour or the opportunity costof her time.

Briannas iPhone use affects the people around her on Penns campus: the more she usesher iPhone, the more each hour of texting while walking, talking loudly, game-playing,etc., annoys people around her. These additional costs can be written as MEC(q) = 3q.

a) (3 points) Compute the efficient quantity of Briannas iPhone use.

b) (5 points) Compute Briannas preferred quantity of iPhone use and the totaldeadweight loss at that quantity.

c) (5 points) Suppose Penns administration recognizes the problem in thismarket and charges each user a constant fee of $100 to register her phoneand consequently be permitted to use her phone on campus. How does thisaffect your answers to (b)? Would Brianna pay the fee? Provide appropriatecalculations.

d) (5 points) Now suppose that instead of the policy in (c), Penn assesses eachuser a per-hour fee of $3. How does this affect your answers to (b)? Howmuch revenue would Penn collect from Brianna? Provide appropriatecalculations.

e) (2 points) Describe a policy that yields the efficient quantity of iPhone hoursand generates revenue for Penn. Calculate the revenue Penn collects fromBrianna.


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You own a small company with only two workers:EloiandMorlock. Eloiis hard-working and highly motivated. His utility function is therefore independent of effort and

contingent on his wages: EU W= .Morlock, on the other hand, tends to display

inordinate narcissist tendencies and loathes working hard. IfMorlockdoes not work hard,

his utility function is identical toEloiss: MU (shirking) W= ; however, ifMorlockmust

work hard, he feels as if his wage were reduced by $5,000, and his utility function

therefore becomes ( )MU (working) W 5, 000= .

Union rules force you to pay your workers 50% of the companys gross profits, dividedequally between your workers (25% to Eloi, 25% to Morlock). Eloi will always workhard, and so the chance of experiencing higher profits depends solely on Morlocksattitude. The following table illustrates the probabilities of attaining high gross profits($100,000) or low gross profits ($60,000) as a function ofMorlocks effort:

Probability of Obtaining HighGross Profits ($100,000)

Probability of Obtaining LowGross Profits ($60,000)

MorlockShirks 0.1 0.9Morlock Works Hard 0.7 0.3

a) (2 points) What is the expected wage for each worker if Morlock shirks?

b) (2 points) What is the expected utility of working hard for Morlock, giventhat he obtains wages equal to 25% of profits?

c) (2 points) What is the expected utility of shirking for Morlock?

d) (3 points) What average net profits (after wages) should you expect?

The local union boss, Joe Breccabonni, has realized that you are risk-neutral and onlycare about your expected profits whereas workers are risk-averse. He offers you a deal:you can now pay one or both of your workers a fixed salary if you want to; however, youhave to make sure that the worker would agree to the fixed payment in lieu of his currentsituation (25% profit sharing).

e) (5 points) What is the fixed minimum payment that Eloi will accept in lieu ofhis share in the companys profit?

f) (6 points) How should you structure your wage payments now? What is yourexpected net profit (after all wage disbursements)?


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Hana and Dave play the following simultaneous game:

a) (5 points) Find all Nash equilibria of this game

b) (2 points) Suppose this game is repeated 55 times, what would the Nash

equilibrium or equilibria be? Why?

Now suppose that Hana and Dave have altruistic preferences. Specifically, Hanas and

Daves new utilities are given by

vH(sH,sD)=uH(sH,sD) +yuD(sH,sD), and

vD(sH,sD)=uD(sH,sD) +yuH(sH,sD),

respectively, whereyis a constant and sH, sDrepresent each players strategy.For example, uH(Confess, Confess) = 1, uD(Confess, Confess) = 1, so Hanas utility fromplaying (Confess, Confess) will be vH(Confess, Confess) = 1+ y.

c) (3 points) Draw a payoff matrix that represents this new game.

d) (5 points) Find the range for values ofysuch that the Nash equilibrium or

equilibria of this new game are the same as that or those found in (a).

e) (5 points) Ifylies outside the range found in (d), find all possible Nash

equilibria.

Player D: Dave

Not Confess Confess

Player H:Hana

Not Confess (3,3) (0,5)

Confess (5,0) (1,1)


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Comment on the article snippet from Bloomberg.com below. You can use any argumentrelevant to BPUB 250, but start by focusing on the game-theoretic aspects that underliethe confidence problem that the government of Portugal is facing with investors in the

credit markets. What is the role of the European Central Bank (ECB) in this game?

Please be clear, concise, and persuasive in your analysis. Your response will beevaluated in terms of breadth and quality. Write clearly.

Greek, Portuguese Debt Climbs AmidSpeculation ECB Bought Region's Bonds

By Paul Dobson - Dec 3, 2010 7:47 AM ET

Irish, Greek and Portuguese bonds rose, narrowing the yield difference withbenchmark German bunds, amid speculation the European Central Bank boughtmore assets of high-deficit nations to stem the debt crisis.Bonds from so-called peripheral nations rallied yesterday as traders said that theECB increased purchases of their government bonds. The central bank boughtPortuguese debt as well as Irish bonds today, said two people with knowledge of thedeals who declined to be identified because the transactions are confidential.The ECB may increase purchases of government bonds to ensure the sovereign debtcrisis abates, according to Dirk Schumacher, an economist at Goldman Sachs GroupInc. in Frankfurt.We remain convinced that the political will among policy makers, including theECB, to prevent any systemic event is unquestionable, he wrote in a research reportdated yesterday. We could easily see the ECB stepping up its bond purchasesaggressively if things do not start to normalize.


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a) What should be the production target of Pineapple?

The first step is to find the reaction function of the follower (Swansong) with respectto the leaders decision. Swansongs revenue function is

[ ] 21 1 1 1

Re 300 300 3002 2 2 2

S S S P S S S P S S v P Q Q Q Q Q Q Q Q Q Q

= = = + =

,

and therefore marginal revenue:1

3002

S P SMR Q Q= . At the optimal quantity,

MRS=MC, and so1

300 202

P SQ Q = and the reaction function of Swansong will be:

1280

2

S PQ Q= .

Now, Pineapple should use the anticipated reaction function to make decisions.Pineapples revenues are:

[ ]1 1

Re 300 3002 2

P P P P S Pv P Q Q Q Q Q Q

= = = +

, into which we substitute

Swansongs reaction function:

21 1 1Re 300 280 1602 2 4

P P P P P Pv Q Q Q Q Q

= + =

.

And1

1602

P PMR Q= , which is equated to MC=20 and yields:1

20 1602

PQ= and

280PQ =

, which is the answer.

b) What will be the likely retail price of theIHot?

We need to find the total production in the market and plug into the demand function tofind the price that the market will bear. From the reaction function of Swansong, we

know they will produce:1 1

280 280 280 1402 2

S PQ Q= = = . This implies

[ ] [ ]1 1

300 300 280 140 902 2

P SP Q Q

= + = + =

.

c) Should Steve outsource production or produce theIHotin-house? Brieflydiscuss.

The trade-off is as follows. If you produce in-house you will have a monopoly, but thecosts of production are higher. If you outsource, your secrets will be revealed to a thirdparty, but your costs of production will be lower, and you will remain the market leader.We first need to calculate Pineapples profits under the Stackelberg duopoly.


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90 280 20 280 19,600StackelbergP REV TC = = =

Now if Pineapple were a monopolist, revenues would be

21 1Re 300 3002 2

v P Q Q Q Q Q

= = =

, and so 300MR Q= .

Equating to the new marginal cost of 150, we obtain Q=150.

Now the monopolist price of the IHotis (from demand function):1 150

300 300 2252 2

MonP Q

= = =

and total profits are

225 150 150 150 11, 250StackelbergP REV TC = = = .

It pays off to outsource even if this means that theIHottechnology will eventually betransferred: producing at home is too costly.


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(a) Efficient consumption of iPhones occurs when MSC=MSB.MSC=MSB10+2q+3q=40-q6q=30qeff=5

(b) Brianna will use her phone until MB=MC. (This is not a monopoly, so its totalsurplus we are maximizing, not something akin to profits)40-q=10+2q3q=30

q*=10

DWL=(1/2)MEC(Q*)(Q*-Qeff)=(1/2)(30)(5)=$75.

(c) Briannas total surplus is (1/2)(40-10)(10)=$150, so she will pay any amount under$150 for the right to use her phone. This does not affect the DWL calculation, as thequantity of iPhone use does not change.

(d) 40-q=10+2q+3q*=9This is better, but its still not efficient:

DWL=(1/2)(MSC(9)-MSB(9))(9-5)=$48.Tax revenue=9*3=27.

(e) A per-unit tax equal to the MEC at the efficient quantity will do the trick. TR=qeff*(3qeff)=75.


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Morlock Hazard.

Probability of Obtaining High

Gross Profits ($100,000)

Probability of Obtaining Low

Gross Profits ($60,000)MorlockShirks 0.1 0.9Morlock Works Hard 0.7 0.3

a. (2 points) What is the expected wage for each worker ifMorlockshirks?

W 0.25 (0.1 100,000 0.9 60,000) 0.25 64,000 16,000= + = =

b. (2 points) What is the expected utility of working hard forMorlock, giventhat he obtains wages equal to 25% of profits?

( ) ( )MEU (working) 0.7 0.25 100, 000 5, 000 0.3 0.25 60, 000 5, 000= +

MEU (working) 0.7 25,000 5,000 0.3 15,000 5,000= +

MEU (working) 0.7 141.42 0.3 100 98.994 30 128.994= + = + =

c. (2 points) What is the expected utility of shirking forMorlock?

MEU (shirking) 0.1 25,000 0.9 15,000= +

MEU (shirking) 0.1 158.11 0.9 122.47 126.038= + =

d. (3 points) What average net profits (after wages) should you expect?

The profit-sharing nature of wages makes M MEU (working) EU (shirking)> , and so

Morlock will work. We will obtain 50% of expected profits:E(Net ) 0.5 (0.7 100,000 0.3 60,000) 44,000 = + =

e. (5 points) What is the fixed minimum payment that Eloi will accept in lieu ofhis share in the companys profit?

Since Morlock will work: ( ) ( )EEU 0.7 0.25 100,000 0.3 0.25 60,000= +

EEU 0.7 25, 000 0.3 15, 000 0.7 158.11 0.3 1 22.47 147.4221= + = + =

Elois certainty equivalent is the minimum he is willing to accept in lieu of profit sharing:

( )2

ECE 147.4221 21,733.27= =

f. (6 points) How should you structure your wage payments now? What is yourexpected net profit (after all wage disbursements)?


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Note that you will not want to pay a fixed amount X to Morlock, because in that case

he will certainly shirk: M MU (shirking) X U ( working) X 5, 000= > = . Therefore

you will offer a fixed wage toEloiof 21,733.27 to take advantage of his risk aversionbut keep Morlock incentivized by paying the 25% profit share. Your expected netprofit is:

E(Net ) 0.75 (0.7 100,000 0.3 60,000) 21,733.276 44,266.724 = + = ,which represents an improvement for you.


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1. Hana and Dave play the following simultaneous game:

1) Find all Nash equilibria of this game

(Confess, Confess) is the only Nash equilibrium. Given Dave playing Confess,Hanas best response is to play Confess and given Hana playing Confess,Daves best response is to play Confess as well.

2) Suppose this game is repeated 55 times, what would the Nash equilibrium or

equilibria be? Why?

Hana and Dave will play (Confess, Confess) in the last period. Thus the fact thatthe game is played 55 times does not change the Nash equilibrium in each roundof the game (despite the possibility of reciprocation). Suppose the two playersattempted to collude and both play Not Confess in each period. In the lastperiod, each player would have incentive to cheat, and so get 5 instead of 3. Sothe Nash equilibrium will be played in the last period. This would then be the casefor the 54thperiod, and so on back. So the Nash equilibrium is for Hana toConfess and Dave to Confess in each round of the game.

Now suppose that Hana and Dave have altruistic preferences. Specifically, Hanasand Daves new utilities are given by

vH(sH,sD)=uH(sH,sD) +yuD(sH,sD) andvD(sH,sD)=uD(sH,sD) +yuH(sH,sD),respectively, whereyis a constant andsH,sDrepresent each players strategy.For example, uH(Confess, Confess)=1, uD(Confess, Confess)=1, so Hanas utilityfrom playing (Confess, Confess) will be vH(Confess, Confess)=1+ y.

3) Draw a payoff matrix that represents this new game.

4) Find the range for values ofysuch that the Nash equilibrium or equilibria of

this new game are the same as that or those found in (a).

If the Nash equilibrium of this new game is (Confess, Confess), we need y to be1+y>5y and 3+3y


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Confess), (Confess, Not Confess). If y=1/4, then the Nash equilibria are (NotConfess, Confess), (Confess, Not Confess), (Confess, Confess). If y=2/3, then theNash equilibria are (Not Confess, Confess), (Confess, Not Confess), (NotConfess, Not Confess).

second midterm solutions 2010 econ

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