bepp250 final testbank

8/10/2019 BEPP250 Final Testbank

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BPUB 250Final Examination Spring 2006

Name:

Please write your name at the top of the exam and hand this sheet in with your blue book(s). Youmust show your work to receive full or partial credit. Partial credit is available, so you shouldattempt to answer all of the questions, even if you are not sure of the answer. This exam is wortha total of 100 points. You have two hours to complete the exam. Good luck!

1) (20 points) Two candidates, Ed and Lynn, are running against one another in thePennsylvania Gubernatorial race. Initially, each expects to get half the votes. Ed has settledon using one of two campaign strategies: run positive ads or run negative ads. Lynn has three

possible strategies: run positive ads, run negative ads, or run no ads at all. Because there areonly two candidates, any increase in the percentage of voters choosing Ed equals a loss in the

percentage of voters choosing Lynn. If Ed runs negative ads, he will gain 8 percentage pointsif Lynn runs positive ads, 1 percentage point if Lynn runs negative ads, and 7 points if Lynnruns no ads. If Ed runs positive ads, he will lose 5 percentage points if Lynn runs positive ads,he will lose 2 points if Lynn runs negative ads and he will gain 10 points if Lynn runs no adsat all.

a. (4 points) Show the payoff matrix for this game. b. (4 points) Does either candidate have a dominant strategy?c. (5 points) Define Nash equilibrium. Which if any of the pairs of pure strategies (i.e. one

for each candidate) constitute a Nash equilibrium?d. (7 points) Lynn decides not to run negative ads and to randomize between positive and no

advertising: on some days Lynn will run positive ads, on some days he will not run anyads at all. What is Lynns equilibrium randomizing strategy?

2) (20 points) Mark owns a small biotechnology company. His utility function is given by

U = 0.5,

where is the companys annual profit. Mark is considering whether his company shouldinvest in bringing a new drug to market. If the drug is a huge success in the market, theannual profit will be $2.5 billion. If the drug is less successful the profit will be $36 million.Mark assesses the probability that the drug is a huge success to be 0.25.

a. (6 points) Find both expected profits and expected utility from developing the drug. b. (8 points) Pfizer comes along and offers to buy the rights to market the drug and earn

whatever profits the drug yields. What is the minimum amount of payment that Markwould accept to sell the right to market the drug?

c. (6 points) Assume Pfizer offered the minimum amount required for Mark to sell therights as identified in the previous problem. However, before they start the transaction, amarket research company approaches Mark and tells him that they can predict whetherthe profits will be $2.5 billion or $36 million with certainty. The market researchcompany is willing to sign a confidentiality agreement so that Pfizer will never learn ofthis service. How much is Mark willing to pay the company for its service?

(Page 1 of 2)


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3) (30 points) The production of paper produces a negative externality (water pollution). Themarginal cost to society of this externality is MC S = Q. The paper supply curve based on the

private marginal cost is MC P = 3Q. The inverse demand curve faced by the paper producer is P (Q) = 30 Q.

a. (5 points) How much output would the company produce in an (unregulated) perfectlycompetitive equilibrium?

b. (7 points) What level of production corresponds to the socially optimal output?c. (6 points) Make a picture illustrating this market, labeling all important features.d. (6 points) How much dead weight loss does the companys output choice in part (a)

generate?e. (6 points) What specific tax could the government impose on the competitive equilibrium

to restrict output to the socially optimal level?

4) (30 points) The Flourtown Golf Club, the only golf club in the area, serves two towns,Flourtown ( F ) and Wyndmoor ( W ). The club charges a price of P per round of golf.

Each of the 100 residents of Flourtown has demand for rounds of golf of: Q F = 100 P,Each of the 50 residents of Wyndmoor has demand of: Q W = 80 2P.

The club incurs total costs of 21 10

( )2200 11

TC Q Q Q , where Q is total rounds across all

residents of Flourtown and Wyndmoor.

Assume initially that the club CANNOT price discriminate between the residents of eachtown.

a. (13 points) What price does it charge per round of golf? How many rounds do theresidents from the two towns purchase together? What is the clubs marginal cost for thenumber of rounds of golf that it sells?

Now assume that the club CAN price discriminate between the residents of each town.

b. (7 points) What price does the club charge Flourtown residents? What price does itcharge Wyndmoor residents? What is the clubs total profit?

c. (10 points) Instead of the simple per-round fee, the club decides to charge a membershipfee and a per-round fee. It decides to set the per-round fee based on marginal cost pricingof the total number of rounds sold. What per-round fee does the club charge? Whatmembership fee does the club charge to each resident of the two towns if it discriminates

between the residents of each town ( i.e. the membership fees can potentially bedifferent)?

Have a great summer!

(Page 2 of 2)


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BPUB 250 Final Exam AnswersSpring 2006

Question 1

a) The payoff matrix is given by:

LynnPositive Negative None

Negative (58,42) (51,49) (57,43)EdPositive (45,55) (48,52) (60,40)

b) The players do not have dominant strategies. For Ed, running negative ads is bestwhen Lynn is running positive or negative ads, but running positive ads is better whenLynn is running no ads at all. Lynns best strategy is to run negative ads when Ed runs

negative ads, but positive ads when Ed is running positive ads.

c) The only pure strategy equilibrium is (Negative, Negative), as indicated in thematrix. Neither candidate has an incentive to deviate given what the other is doing.

d) The key for finding mixed strategies is to randomize so that the opponent hasequal payoffs across his strategies.

The new payoff matrix is:

Lynn Positive None

Negative (58,42) (57,43)EdPositive (45,55) (60,40)

Assume p 1 is the probability that Lynn will run positive ads and 1-p 1 is the probabilitythat he will run no ads.

1 1Ed's expected payoff from negative ads: ( ) .58 .57(1 ) E E p p

1 1Ed's expected payoff from positive ads: ( ) .45 .60(1 ) E E p p )()( E E E E

16/31 p

(We can similarly solve for Eds mixed strategy. The solution is p 1 = 15/16.)

Question 2

a) Expected profits: M E 652)36)(75.0()2500)(25.0()(


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Expected utility:

17)36)(75.0()2500)(25.0()( u E

b) This question asks about the certainty equivalent of the gamble. From a) weknow the expected utility is 17. Then

17 289

He will be indifferent between a (certain) offer of 289 million and taking the gamble.

c) Before purchasing the information, the value of marketing the drug is now $2.5 billion with probability 0.25 (Pfizers offer is rejected) or $289 M (drug turns out to be a bust and Pfizers offer is accepted).

M E 75.841)289)(75.0()2500)(25.0()(

25.25)289)(75.0()2500)(25.0()(

u E

The certainty equivalent for this second gamble with information is25.25 2 = 637.56

This means that knowing the information will increase the certainty equivalent from289M to 637.56M. Therefore he is willing to pay up to the difference between the two,or 348.56M.

Question 3

a) Without regulation, the firm will just consider its own cost. For profitmaximization,MC p = P3Q = 30 QQ = 7.5P = 22.5

b) From societys point of view, total marginal cost should be considered.MC Total = MC p + MC s = 3Q + Q=>3Q + Q = 30 QQ = 6

P = 24


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c)

MC p(tax)

Q

MC total

taxDWL

22.5

24

P

MC p

MC s

6 7.5

d) DWL = (7.5 6) (30 22.5) / 2 = 5.625

e) A constant per-unit tax is easiest to implement. We want the tax to shift the producers marginal cost curve up to entail the socially optimal equilibrium quantity.

(MC p + tax) = 30-Q where Q = 6

tax = $6 per unit

(Other, more complicated tax schemes could also work.)

Question 4

a) We first derive the total demand curve.QF = 100(100-P) = 10000 100PQW = 50(80-2P) = 4000 100P

QT = 10000 100P if P>=40 (when Ws demand = 0)QT = 14000 200P if P 0)

P = 100 (1/100)Q if Q=6000

TC = (1/2200) Q 2 (10/11)QMC = (1/1100)Q (10/11)

MC = P => (1/1100)Q (10/11) = 70 (1/200)Q (When Q>=6000)Q = 6500MC = P = 37.50


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b) We want to find price/quantity combination for each town so that the marginalrevenue from each town is exactly the marginal cost at Q = 6500.

MC = (1/1100)(6500) 10/11 = 5

MR F = 5 => 100 (2/100) Q F =5QF = 4750PF = 52.5

MR W = 5 => 40 (2/100) Q W =5QW = 1750PF = 22.5

In fact we can verify that Q = Q F + Q W = 6500

Profit is just the total revenue from the two towns minus the total cost of producing 6500:

5.275454)6500)(11/10()6500)(2200/1()5.22)(1750()5.52)(4750(2

TC TR

c)QT = 10000 100P if P>=40 (when Ws demand = 0)QT = 14000 200P if P0)

The per-round fee price is the marginal cost of selling Q T . Using Q T when Ws demandis positive:

(1/200)(14000 Q) = (1/1100)Q (10/11)Q = 12000

MC = P (1/1100)12000 (10/11) = 10

The membership fee is the consumer surplus under each demand curve, respectively: ForFor W:

P = 40 ( ! )Q =10 => Q=60Fee = 900

For F:P = 100 Q =10 => Q=90Fee = 4050


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BPUB 250 Spring 2007Managerial Economics Final Exam

Instructions

1. Read over the whole exam, and do the easier questions first.2. Show your work.3. No credit will be given for work shown on even-numbered pages. Use

labeled overflow space for work that does not fit between questions.4. Write legibly!5. Initial the proctors class list when you hand in your exam.6. Write your name on every page of this exam.7. Do not disassemble the exam.

Your Name:_____________________________________________________

Section number:_____________________________________________

Cohort name:_______________________________________________

TA name:__________________________________________________

Professors name:___________________________________________

1. DO NOT START UNTIL 6PM.


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2

(30 points) Elmo and Cookie Monster are the only two consumers of politicalmagazines. Elmos demand for magazines is P=100-q, and Cookie Monsters isP=100-2q. Magazines are competitively produced according to the supplyfunction P=20+2Q.

a. (5 points) What is the aggregate private market demand for magazines?

b. (5 points) What are the price and quantity of magazines consumed?

c. (5 points) Elmo reads magazines in the morning and Monster in theafternoon, so now they decide to purchase the magazines together andshare them. What is the marginal social benefit function of the new publicgood magazines?

d. (5 points) What is the optimal level of provision of the public good?

e. (10 points) Monster moves away, and Elmo is the only remainingconsumer. However, after Elmo reads and discards his magazines, Oscaruses them to play. Oscar places a value of $20 on each magazine he findsin the trash can. What is Elmos consumption of magazines? What is thesocially optimal consumption of magazines? Illustrate graphically,labeling all relevant axes, quantities, and prices.

2. a. (10 points) Firm 1 is the monopolist in the market of chandeliers. Its

production function is L K L K f ),( . The cost of capital and labor arer=4 and w=1. Demand is characterized by P=20-Q. What are firm 1s

profits, based on its long-run total costs?

b. (15 points) Firm 1 faces the potential entry into the market of a newcompetitor, firm 2. If firm 2 enters the market, Cournot competition willensue. Assume that firm 1s cost structure now is:

521 2

11 QTC

If firm 2 enters, its costs will be:

4021 2

22 QTC .

Will firm 2 enter this market, assuming that it has not yet incurred any costs?

c.

(10 points) Assume that firm 2 decides not to enter the market. Instead, anew competitor threatens to enter. Should that firm decide to enter, firm 1can respond in one of two ways: it can engage in a price war or it canchoose not to compete on price, but instead to sue the entrant forinfringement of copyrights. Firm 1 is certain to win the case, but litigatingis costly. Consider the sequential game where the potential entrant movesfirst and the payoff matrix is given by:


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3

POTENTIAL

ENTRANT

ENTER STAY OUTPRICEWAR 40 , 40 100 , 0FIRM 1SUE 60-X , 60-4X 120-X , 0

Provide a range for X for firm 1 to successfully prevent entry.

3. Demand for tickets for a Penn football game are given by

000,420PR

Rq for the general public, and

000,28PS

S q for students.

Penn requires student ID to qualify for a reduced student price. Suppose that bothmarginal and fixed costs are zero.

a. (10 points) If the stadium has an unlimited number of seats, then what prices( RS P P , ) maximize total profit? How many seats are sold to each group? What isthe deadweight loss?

b. (15 points) Suppose that one end of the stadium is closed for repairs so only36,000 seats are available. What are profit-maximizing prices and quantities now?

c. (10 points) Penn faces some uncertainty over the demand for football tickets.

Student demand is very stable and, as above, is

000,28PS

S q .

However, the demand from the general public fluctuates and is given by

000,420PR

Rq with probability 0.5 and

000,412PR

Rq otherwise.

Penn decides to sell tickets to the general public at $10 and tickets to students at $4.For logistical reasons, Penn dislikes fluctuation in attendance: its utility from the

profits of a football game is given by U= .

Compute Penns expected profit from a football game. How much expected profit wouldPenn be willing to forego to remove the uncertainty in the demand for a game?


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Question 1

a) We have to add the two demand curves horizontally (i.e. add the quantities):Elmo: q = 100-P

Monster:1

q = 50- P2

Market:3

Q = 150- P2

2

P= 100-3

Q

b) Market equilibrium D = S: 2100- 20 23

Q Q * 30Q * 80 P

(note that both consumers demand a positive quantity: Elmo 20, Monster 10)

c) To obtain the MSB function, we add the demand functions vertically (i.e. add the prices):Elmo: 100 P MB q

Monster: 100 2 P MB q Sesame Street 200 3SB Q

For Q50 only Elmo derives positive MB from more units and MBS=100-Qd) We want to make MSB = S:200-3 20 2Q Q * 36Q .

e) Now Elmos consumption generates positive externalities for Oscar. The marginal socialvalue of consumption is Elmos valuation of the good, plus Oscars:Elmo: 100 P MB q Oscar: 20 MB Sesame Street: 120SB Q

The market will set Elmos private MB=S: 100- 20 2Q Q * 26.66Q * 73.33 P The social optimum is at: MSB=S: 120- 20 2Q Q * 33.33Q

Positive externality

P

Q

MPB

73.33

26.66

S

Q*=33.33

MPB =marginal private benefit

MSB = marginal social benefit

MSB

DWL


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Question 2

a) First, we need to find the cost function of the monopolist. To do that, remember the solutionto the cost minimization problem of the firm (to obtain demand for inputs):

w MRTS r

or L K

MP w P r

. Recall ( , ) f K L K L , so

1 12 2

1 12 2

1212

K L wr

K L. Thus K w

L r , and

therefore14

K L

Substituting 4 L K into the production function yields Q= 2( , ) 4 2 f K L K K . Thus

2Q

K and 2 L Q .

The cost function is 4TC rK wL K L . Using the input demand functions:1

4 2 42

TC Q Q Q . Marginal cost is therefore MC=4.

Next, using the demand function P=20-Q, we obtain total revenue:2Re (20 ) 20v PQ Q Q Q Q , and thus marginal revenue: 20 2 R Q .

Profit maximization entails MR=MC, or 20 2 4Q , so Q*=8.

At Q=8: 2Re 20 8 8 96v 4 8 32TC

Re 96 32 64v TC

b) If firm 2 enters, Cournot competition ensues with 1 2Q Q Q .For firm 1 21 1 1 1 2 1 1 1 2 1Re (20 ) (20 ) 20v PQ Q Q Q Q Q Q Q Q Q , and

1 1 220 2 R Q Q

From the cost function, we obtain1 1

C Q

For firm 1s reaction function, we set MR=MC: 1 2 120 2Q Q Q , so 1 220 13 3

Q Q

Notice that both MC and MR are symmetric for firm 2 and therefore the reaction function offirm 2 is:


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2 120 13 3

Q Q

The Cournot equilibrium is the intersection of the reaction curves. Solving the system ofreaction functions yields 1 2 5Q Q .

Firm 2 will enter the market if profits are positive upon entry:

22 2 2 1 2 2 2

1Re (20 ) 40

21

(20 10) 5 25 40 2.52

v TC Q Q Q Q

Profits are negative. Firm 2 will not enter!

c) In order to deter entry, firm 1s management has to convince the potential entrant that it will

sue. If it did not sue, the entrant would choose to enter and obtain profit of 40.

For the threat of litigation to be credible, the profits accruing to firm 1 from suing have toexceed the profits from not suing. In terms of the payoff this implies that: 60 40 X , or

20 X .

However, even if firm 1 sues, the potential entrant will enter if the payoff from entry is largerthan the payoff from not entering of 0. In order to deter entry, therefore, the payoff of theentrant needs to be negative whenever firm 1 sues: 60 4 0 X , implying 15 X .

The acceptable range for X is therefore 15 20 X


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Question 3

a) Since seats are unlimited, Penn optimally prices as a monopolist over the two segments ofdemand:

*

*

Re 82,000

28 0

2,000

8,000

8,0008 4

2,000

S S S S

S S

S

S

qv q

q MR MC

q

P

*

*

Re 20 4,0002

20 04,000

40,000

40,00020 10

4,000

R

R R R

R R

R

R

q

v qq

MR MC

q

P

The associated deadweight loss is the deadweight loss due to monopoly pricing. The socialsurplus is maximized under perfectly competitive prices, which in this case are such that P S =

P R = MC = 0. Total surplus equals:

(20)(80,000)0 800,000

2(8)(16,000)

0 64,0002

864,000

R R R

s s s

SURPLUS CS

SURPLUS CS

TOTAL

Under the monopoly prices, surplus equals only:(20 10)(40,000)

(10)(40,000) 600,0002(8 4)(8,000)

(4)(8,000) 48,0002

648,000

R R R

s s s

SURPLUS CS

SURPLUS CS

TOTAL

The deadweight loss is the difference between the two surpluses, or 216,000.


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b) Now Penn chooses quantities to maximize total profit, subject to the constraint that no morethan 36,000 seats are sold, or that * * 36,000S Rq q . The Lagrangian is given by:

8 20 36,0002,000 4,000

S RS R R S

q q L q q q q

The first-order conditions are

2(1) 8 0

2,000

2(2) 20 0

4,000

(3) 36,000 0

S

S

R

S

R S

q Lq

q Lq

Lq q

Equations (1) and (2) imply that MRS = MR R, or that2 2

8 202,000 4,000

S Rq q .

Solving for qS as a function of q R:2 2

8 202,000 4,000

2 ( 12)(2,000)

112,000

2

S R

S R

S R

q q

q q

q q

Substituting this expression for qS into the constraint (equation (3)) yields q R:

*

112,000 36,000

23

48,0002

32,000

R R

R

R

q q

q

q

* *112,000 12,000 16,000 4,0002S Rq q

The associated prices are:

* 32,00020 124,000 R

P


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* 4,0008 62,000S

P

c) Penns expected profit is given by S S R P q E . Given the chosen prices of P S = 4 and P R=10, the number of tickets sold equals:

1 1 1

2 1 1

8 (8 )2,000 (8 4)2,000 8,0002,000

20 (20 )4,000 (20 10)4,000 40,0004,000

12 (12 )4,000 (12 10)4,000 8,0004,000

S S S S

R R R R

R R R R

q P q P

q P q P

q P q P

Expected profit thus equals:

1 20.5( ) 0.5( )

(4)(8,000) (0.5)(10)(40,000) (0.5)(10)(8,000)$272,000

S S R R R R E P q P q P q

Expected utility equals:1 20.5 0.5

0.5 32, 000 400, 000 0.5 32, 000 80, 000

495.97

S S R R S S R R EU P q P q P q P q

The certainty equivalent amount of profit is: 2495.97 $245,981.82cert

Penn would be willing to forego up to ($272,000 $245,981.82), or $26,018.18, to avoid thedemand uncertainty.


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BPub 250. SECOND MID TERM EXAMINATION

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Question 3 [ \#8 #=% & 1*&// 681+%(11 &%' $+)( & *&%&3() 4# )8% +4 #% .#8) 6($&/9, W$+/( you are riskneutral ]4$81 1((0 4# *&V+*+H( (V2(54(' 2)#9+4^7the manager is risk averse &%' $() 84+/+4. 98%54+#% +1[

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O K M _ +9 1$( 2)#>+'(1 $+3$ (99#)4 +% $() =#)0 ]-I; `a@b ?: -I; G?:O-?c?-\Y< ;


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eQP C K @A a @;C

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a. After trading pollution permits between each other, how many permits will firms A andB each end up holding?

b. What will be the price of these permits?c. What will the total abatement costs of each firm be?

-$( *&)3+%&/ 6(%(9+4 4# 9+)* P 9)#* 2)#'85+%3 5$(*+5&/1 +1

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W$()( N P +1 4$( f8&%4+4. #9 QI;e?QPc: 2)#'85(' 6. 9+)* P,

Note Emissions, E, are measured in quite different units to the Qs above so dont get them confused.

P%' 4$( *&)3+%&/ 6(%(9+4 4#


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Question 5 , ?4 +1 8%9#)48%&4( 4$&4 g+#/(%4 g+'(# P)5&'( ]ggP^ &%' -#4&//. h(% ]-h^ &)( /#5&4(' &5)#114$( 14)((4 9)#* (&5$ #4$(), -$( 2)#9+4 9#) ggP +1 BAAA &%' 4$&4 9#) -h =#8/' &/1# 6( BAAA +9 +4 =()( %#49#) 4$( &=98/ %#+1( 9)#* ggP, W+4$ 4$( %#+1(7 4$( 5814#*()1 #9 -h &)( 9)(&0(' #84 &%' 4$+1 )('85(1 -h'(*&%' &%' 4$()(9#)( 2)#9+4 9)#* BAAA 4# @AA,

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P/4()%&4+>(/.7 -h 5#8/' (*2/#. CY:;Y %#+1( 5&%5(//+%3 4(5$%#/#3. +% +41 2)(*+1(1 =$+5$ =#8/' &/*#14)(14#)( 4$( 4)&%f8+/+4. )(f8+)(' 6. -h, 5/+(%41, -$+1 4(5$%#/#3. =#8/' 5#14 DAA &%' =#8/' &/1# +%5)(&1(-h 2)#9+41 9)#* @AA 4# iAA ]/(11 #9 5#8)1( 4$( DAA 2&+' 4# C#1(#^

?9 ggP +%4)#'85(' 4$( 1#8%'2)##9+%3 and -h +%4)#'85(' %#+1( 5&%5(//+%3 4(5$%#/#3.7 4$(% -h 2)#9+41=#8/' 6( )(14#)(' 4# BAAA ]*+%81 &%. (V2(%1( 4$(. +%58))(' 4# )('85( %#+1(^,

-$( 9#//#=+%3 15(%&)+#1 5&% &'')(11 4$( 2)#6/(*1 &%' &)( 18**&)+H(' 6. 4$( 9#//#=+%3 4&6/(=$+5$ .+(/' 4$( 9#//#=+%3 2)#9+41[

!"#$%&'() VVA profit TZ profitC81+%(11 &1 818&/ 10000 200

ggP 5&% 5/#1( '#=% 0 1000

-h 5&% 5/#1( '#=% 1000 0

ggP 5&% 1#8%'2)##9 1000 - 400 900

-h 5&% +%4)#'85( %#+1()('854+#% 4(5$%#/#3.

1000 900 - 500

:#8%'2)##9 j E#+1(5&%5(//+%3

1000 - 400 900 - 500

a. Which is the most efficient solution?b. If VVA is required to compensate TZ for any losses incurred through noise, which

outcome will occur (explain and show how much profit each firm will make)c. If VVA is NOT required to compensate TZ for any losses incurred through noise, which

outcome will occur (explain and show how much profit each firm will make)


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*$)+#& ,-#).'($ /

"( ])-3 .@"71 G/+25$ ])-3 .@"71 8$33+1

]"3$ .@"71 G/+25$ O: J: 9 9 ]"3$ .@"71 8$33+1 OO OO J: O:

4( ])-3 .@"71 4/+25$ "32 ]"3$ .@"71 8$33+1 ,( !"1- 2( OO =3+*1 $",-


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*$)+#& .( 0&(12#3 45 V$?/+*$ *-$ #"/>$* 2$#"32 ,=/E$ "1

A N O^: _ :(ODW ' ` W XF '+E+35 '+561 *)*"@ /$E$3=$ ?+@@ 4$

8V' N AW ' N DO^: _ :(OW ' _ :(OW XFW ' a/ N O^:W ' _ :(OW ' J _ :(OW XW ' (

\V ' N 8V' b W ' N O^: _ :(JW ' _ :(OW X(

\T ' N 28T ' b2W ' N 9 ` W ' ( 8) #"I+#+c$ ./)0+*1K '' ?+@@ 1$* \V ' N \T ' )/

\V ' N O^: _ :(JW ' _ :(OW X N 9 ` W ' N \T 'a/ O(JW ' N OP9 _ :(OW X a/ 6 7 8 //49: ; 6 ? @A') ') 77B) %".'($ C-$".'($9

XC61 *)*"@ /$E$3=$ ?+@@ 4$

8VX N AW X N DO^: _ :(OW ' _ :(OW XFW X a/ N O^:W X _ :(OW ' W X _ :(OW X

J

\V X N 8VXb W X N O^: _ :(OW ' _ :(JW X(

\T X N 28T X b2W X N P9(d

8) #"I+#+c$ ./)0+*1K XC ?+@@ 1$* \V X N \T X )/

\V X N O^: _ :(OW ' _ :(JW X N P9(d N \T 'a/ :(JW X N O:^(^ _ :(OW ' a/ 6 ? 8 :44 ; 6 7 @A') ') ?*B) %".'($ C-$".'($

Z=41*+*=*+35 XC6 /$",*+)3 0=3,*+)3 +3*) ''61 /$",*+)3 0=3,*+)3 5+E$1e

W ' N OOJ(9 _ DObOJFD 9JJ _ DObJFW ' F N OOJ(9 _ ^P(9 ` DObJ^FW '

a/ DJPbJ^FW ' N df a/ W ' N gJ Z=41*+*=*+35 W ' N gJ +3*) XC6 /$",*+)3 0=3,*+)3 5+E$1 W X N 99J _ DObJFDgJF N 99J _ Pd N ^Hd

8-=1K W N W ' ` W X N gJ ` ^Hd N 99H(

Z=41*+*=*+35 W N 99H +3*) *-$ 2$#"32 0=3,*+)3 7+$@21

0 8 O^: _ :(OD99HF N O^: _ 99(H N DE94


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C31?$/ P"( ABC! C :(9DAVah&8F

B) $00)/* UX N :(9D:(9iJK:::jF :(9 ` :(9D:(9i9Kd::jF :(9 N E494FDG

k+ $00)/* UX N :(9D:(9iPKOJ9jF:(9 ` :(9D:(9i9Kd::jF :(9 H N PH(JJOg

8-$/$0)/$K \C!CSUV TkaaZUZ k&Sk UhhaV8 1+3,$ E494FDG l PH(JJOg

AVah&8 !U8 ah Ta\AU!ZC8&a! :(9 DJ::: _ O:::F ` :(9D9Kd::_ JKH::F N Of::

mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm ABC! G :(HDAVah&8 &! UnTUZZ ah OK:::F

B) $00)/* UX N :(9D:F:(9 ` :(9D:(Hi9Kd::_ JK:::jF :(9 N Jd(HPP

k+ $00)/* UX N :(9D:(HiPKOJ9JK:::jF :(9 ` :(9D:(Hi9Kd::_ JK:::jF :(9 H N HH9DH4D

8-=1K *-$ \C!CSUV TkaaZUZ k& UhhaV8 4$,"=1$ HH9DH4D l Jd(HPP

AVah&8 !U8 ah Ta\AU!ZC8&a! &Z N :(9DPKOJ9 _ :(HDOKOJ9FF ` :(9D9Kd::_ :(HDPKd::FF N N :(9DJKJJ9F ` :(9DJKgJ:F N JK^gJ(9

@A# (+$#& ') 1#..#& (CC +'.A 0I*J K 1#"%-)# .A#'& #LM#".#N M&(C'. ') 4OEP49: '$).#%N (C .A#'& #LM#".#N M&(C'. (C /GQQ +'.A 0I*J *9

C31?$/ 4( Q+*- ABC! G *-$ $I.$,*$2 =*+@+*7 +1 PP(HPJH "32 *-$ #"3"5$/ ?)/>1 -"/2( 8-=1 ?$ ,"3 $1*+#"*$ *-$ TU "1 0)@@)?1

PP(HPJH N H

8-$/$0)/$ TU N Og^f(fHP 8-$ $I.$,*$2 ,)#.$31"*+)3 +1 :(9D:(HiOOJ9jF ` :(9D:(HiPKd::jF N OHf: 8-$ /+1> ./$#+=# +1 *-$ 2+00$/$3,$ 4$*?$$3 *-$ TU "32 *-$ $I.$,*$2 ,)#.$31"*+)3 VA N OHf:_ Og^f(fHPN O^:(:Og


41/189

6-#).'($ E9

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!)*$ $",- =3+* )0 U /$o=+/$1 O .$/#+*( 8-$ 0+/#1 ?+@@ */"2$ .$/#+*1 =3*+@ *-$+/ #"/5+3"@ ,)1*1 )0 "4"*$#$3* "/$ $o="@

\TC C N J: OUC N J: JUG N \TC G

k)?$E$/ UC ` UG N J:

Z)@E+35 *-$ 1+#=@*"3$)=1 $o="*+)31

J: OUC N J: JDJ: UCF

UC N ^:bPM UG N J:bPM

!)*$ \TC C N J: _ OD^:bPFN J:bPM !)*$ \TC G N J: _ JDJ:bPF N J:bPM

C31?$/ 4(

8-$ ./+,$ )0 .$/#+*1 ?+@@ $o="@ \TC N J:bP(

C31?$/ ,( 8)*"@ "4"*$#$3* ,)1*1 0)/ C "/$ *-$ "/$" =32$/3$"*- *-$ ,=/E$ 0/)# ^:bP *) J: ?-+,- +1 "

*/+"35@$ )0 -$+5-* DJ:bPF "32 @$35*- DJ:bPF ?-+,- -"1 "3 "/$" )0 DJ::bfF( 8)*"@ "4"*$#$3* ,)1*1 0)/ G "/$ *-$ "/$" =32$/3$"*- *-$ ,=/E$ 0/)# J:bP *) O:K ?-+,- +1 " */+"35@$ )0 -$+5-* DJ:bPF "32 @$35*- DO:bPFK "32 *-$/$0)/$ -"1 "3 "/$" )0 DO::bfF( 8)*"@ "4"*$#$3* ,)1*1 "/$ DP::bfFNPP(PPPP(

C31?$/ 2(

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W C N 9: _ :(9 \G

W G N J9 _ :(J9 \G

!)? "22 *) 5$* *-$ 8a8CB ./+E"*$ \G

W C N 9: _ :(9 \G

W G N J9 _ :(J9 \G

W N g9 _ :(g9 \G a/ \G N O:: _ ^bP W

!)? 1),+"@ ).*+#=# ?-$/$ \G N \T

O:: _ ^bP W N O: `OObP W ! " #$


42/189

6-#).'($ : *$)+#&

VVA profit TZ profit TotalC81+%(11 &1 818&/ 10000 200 1200

ggP 5&% 5/#1( '#=% 0 1000 1000

-h 5&% 5/#1( '#=% 1000 0 1000

ggP 5&% 1#8%'2)##9 1000 - 400 900 1500

-h 5&% +%4)#'85( %#+1()('854+#% 4(5$%#/#3.

1000 900 - 500 1400

:#8%'2)##9 j E#+1(5&%5(//+%3

1000 - 400 900 - 500 1000

%9 RR* )(-$NM&((C

19 ST RR* ') 2'%12# .( "(3M#$)%.# @UO .A#$ RR* "%$ #'.A#&

M%V DQQ '$ "(3M#$)%.'($ (& '. "%$ )M#$N EQQ '$ )(-$NM&((C'$W %$N M%V /QQ '$ "(3M#$)%.'($ '. +'22 MC#& .A# 2%..#&

VVA profit TZ profit TotalC81+%(11 &1 818&/ 10000 - 800 200 + 800 1200

ggP 5&% 5/#1( '#=% 0 1000 1000

-h 5&% 5/#1( '#=% 1000 0 1000

ggP 5&% 1#8%'2)##9 1000 400 - 100 900 + 100 1500

-h 5&% +%4)#'85( %#+1()('854+#% 4(5$%#/#3.

1000 900 - 500 1400

:#8%'2)##9 j E#+1(5&%5(//+%3

1000 - 400 900 - 500 1000

,( N9 RR* J(. 2'%12#9 @U M%V) %$ %3(-$. X0Y )(3#+A# 1#.+##$ EQQ %$N :QQ .( RR* .( M#&)-N#

.A# 2%..#& .( )(-$NM&((C VVA profit TZ profit Total

C81+%(11 &1 818&/ 10000 200 1200

ggP 5&% 5/#1( '#=% 0 1000 1000

-h 5&% 5/#1( '#=% 1000 0 1000

ggP 5&% 1#8%'2)##9 1000 400+ P 900 - P 1500

-h 5&% +%4)#'85( %#+1()('854+#% 4(5$%#/#3.

1000 900 - 500 1400

:#8%'2)##9 j E#+1(5&%5(//+%3

1000 - 400 900 - 500 1000


43/189


44/189

!"#! %&'( )*+,- ./0*+1 %''234567*8+ 9 ! #$%&'()*&+ ,)(-%, .$* -/* 0*-1)2 3)04))% 506 #2$', -%, 7'2'08 /& 9$1)*%),

3: 08) .$22$4/%9 .'%;0/$%! < = >??@A6 B4$ ;-**/)*&C D$*08 #)%0*-2 -%, E)F'32/;C &)*1)08) *$'0)6 B8): )-;8 8-1) 08) .$22$4/%9 0$0-2 ;$&0 .'%;0/$%! B# = G?? H >?IJC 48)*) J*)F*)&)%0& )-;8 ./*(+& $'0F'0 K08) %'(3)* $. F-&&)%9)*& .2$4%L6

",07 , :& /8*+76; ! B8) F*$,';0/$% .'%;0/$% .$* -/* &)*1/;)& /& A = MINC 48)*) A /& '%/0&$. $'0F'0C M /& '%/0& $. ;-F/0-2C -%, N /& '%/0& $. .')26 B8/& F*$,';0/$% .'%;0/$% 8$2,& .$*

3$08 D$*08 #)%0*-2 -%, E)F'32/;6 B8): 3$08 8-1) >? '%/0& $. ;-F/0-2 -%, 08) F*/;) $. -'%/0 $. ;-F/0-2 /& G?6 B8) F*/;) $. - '%/0 $. .')2 /& >??6 .,00*50?6 787,->867 @4+>7*8+ *6 AB C 2'' D 9'EFG

",07 H :9' /8*+76; 6)*+I 75L ,+I 5,>< @*0K?6/08@*7 64//86*+1 7


45/189

W+6=50 9,( D$0) 08-0 J = MINU* N = JVM

B8) 0$0-2 ;$&0 $. - ;-**/)* /&

B# = < M IM H ?

B# = G?I>? H >??IKJV>?L = G?? H >?J

W+6=50 9HG O*/0) 08) ,)(-%, -& < = >?? R J D R J E 6

D$*08 #)%0*-2+& 0$0-2 *)1)%') /&

BE D = ?? R J D R JE LJ D = >??J D R J DP

R JE J D D$*08 #)%0*-2+& (-*9/%-2 *)1)%') /&

TE D = BE DVJ D = >?? R PJ D R JE

D$*08 #)%0*-2+& (-*9/%-2 ;$&0 /&

T# D = ,B# DV,J D = >?

B$ (-W/(/X) F*$./0C D$*08 #)%0*-2 4/22 &)0 TE D = T# D $*

TE D = >?? R PJ D R JE = >? = T# D U* PJ D = Y? R JE U* J D = Z[ R ?6[J E

B8/& /& D$*08 #)%0*-2+& *)-;0/$% .'%;0/$%6

E)F'32/;+& 0$0-2 *)1)%') /&

BE E = ?? R J D R JE LJE = >??J E R J DJ E @ JE P

E)F'32/;+& (-*9/%-2 *)1)%') /&

TE E = BE E VJ E = >?? R J D R PJE

E)F'32/;+& (-*9/%-2 ;$&0 /&

T# E = ,B# E V,J E = >?


46/189

B$ (-W/(/X) F*$./0C E)F'32/; 4/22 &)0 TE E = T# E $*

TE E = >?? R J D R PJE = >? = T# E U* PJE = Y? R J D U* J E = Z[ R ?6JA D

B8/& /& E)F'32/;+& *)-;0/$% .'%;0/$%6

5'3&0/0'0/%9 E)F'32/;+& *)-;0/$% .'%;0/$% /%0$ D$*08 #)%0*-2+& *)-;0/$% .'%;0/$% 9/1)&

J D = Z[ R ?6[KZ[ R ?6[J DL = Z[ R PP6[ H ?6P[J D = PP6[ H ?6P[J D U* ?6\[J D = PP6[U* J D = ]?

5'3&0/0'0/%9 J D = ]? /%0$ E)F'32/;+& *)-;0/$% .'%;0/$% 9/1)&

J E = Z[ R ?6[I]? = Z[ R >[ = ]?B8'&C3 C F Q D FQ = ]? H ]? C X'

5'3&0/0'0/%9 A = ^? /%0$ 08) ,)(-%, ;'*1) 9/1)&

" = >?? R ^? C Y'

D$*08 #)%0*-2+& 0$0-2 *)1)%') = BE D = CP?? D$*08 #)%0*-2+& 0$0-2 ;$&0 = B# D = G?? H >?J D = G?? H >?I]? = G?? H ]?? = >C>?? D$*08 #)%0*-2+& F*$./0 /& = BE D R B# D = Q = >CP?? R >C???C 9''

E)F'32/;+& 0$0-2 *)1)%') = BE E = CP??E)F'32/;+& 0$0-2 ;$&0 = B#E = G?? H >?J E = G?? H >?I]? = G?? H ]?? = >C>??E)F'32/;+& F*$./0 /& = BE E R B# E = S = >CP?? R >C???C 9''

J D Y?

E)F'32/;+& *)-;0/$% .'%;0/$%

Z[

]? D$*08 #)%0*-2+& *)-;0/$% .'%;0/$%

]? Z[ Y? J E


47/189

W+6=50 9>6 O/08 08) 8/98)* .')2 ;$&0C D$*08 #)%0*-2+& (-*9/%-2 ;$&0 /&

,B# DV,J D = P? = T# D

B$ (-W/(/X) F*$./0C D$*08 #)%0*-2 4/22 &)0 TE D = T# D $*

TE D = >?? R PJ D R JE = P? = T# D U* PJ D = G? R JE U* J D = Z? R ?6[J E

B8/& /& D$*08 #)%0*-2+& *)-;0/$% .'%;0/$%6

5'3&0/0'0/%9 E)F'32/;+& *)-;0/$% .'%;0/$% /%0$ D$*08 #)%0*-2+& *)-;0/$% .'%;0/$% 9/1)&

J D = Z? R ?6[KZ[ R ?6[J DL = Z? R PP6[ H ?6P[J D = >\6[ H ?6P[J D

U* ?6\[J D = >\6[U* J D = P]6]]

5'3&0/0'0/%9 J D = P]6]] /%0$ E)F'32/;+& *)-;0/$% .'%;0/$% 9/1)&

J E = Z[ R ?6[IP]6]] = Z[ R >>6^\ = ]]6]]

B8'&C3 C F Q D FQ = P]6]] H ]]6]] C &XGXZ

5'3&0/0'0/%9 A = [^6^\ /%0$ 08) ,)(-%, ;'*1) 9/1)&

" = >?? R [^6^\ C Y[G[[

D$*08 #)%0*-2+& 0$0-2 *)1)%') = BE D = C?^^6^\ D$*08 #)%0*-2+& 0$0-2 ;$&0 = B# D = G?? H >?J D = G?? H P?IP]6]]

= G?? H Z^^6^\ = >CP^^6^\ D$*08 #)%0*-2+& F*$./0 /& = BE D R B# D = Q = >C?^^6^\ R >CP^^6^\C \%&&G&X

E)F'32/;+& 0$0-2 *)1)%') = BE E = CZZZ6ZZE)F'32/;+& 0$0-2 ;$&0 = B#E = G?? H >?J E = G?? H >?I]]6]] = G?? H ]]]6]] = >C>]]6]]E)F'32/;+& F*$./0 /& = BE E R B# E = S = >CZZZ6ZZ R >C>]]6]]C [99G99

W+6=50 IG E)F'32/; 4$'2, -;0 -& - ($%$F$2/&06 B8)/* 0$0-2 *)1)%') 4$'2, 3)

BE = ?? R ALA = >??A R A P

B8)/* (-*9/%-2 *)1)%') 4$'2, 3)

TE = ,BEV,A = >?? R PA


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B$ (-W/(/X) F*$./0C 08): 4$'2, &)0 TE = T# $*

TE = >?? R PA = >? = T#U* PA = Y?U* A = Z[

5'3&0/0'0/%9 A = Z[ /%0$ 08) ,)(-%, ;'*1) 9/1)&

< = >?? R Z[ = [[

E)F'32/;+& 0$0-2 *)1)%') = CP[?C 9L%%&

5'FF$&) - %)4 )%0*-%0 ,);/,), 0$ ;$() /%0$ 08) (-*S)06 5/%;) 08)/* (-*9/%-2 ;$&0 $.$F)*-0/%9 /& P?C /0 4$'2, -FF)-* 08-0 08): 4$'2, ,$ 4)22 4/08 08) ($%$F$2: F*/;) $. [[6

_'0 08)/* *)-;0/$% .'%;0/$% 4$'2, 3)J D` = Z? R ?6[J E

5'3&0/0'0/%9 JE = Z[ /%0$ 08) )%0*-%0+& *)-;0/$% .'%;0/$% 9/1)&

J D` = Z? R ?6[IZ[ = Z? R PP6[ = >\6[

B8)% A = J E H J D` = Z[ H >\6[ = ^P6[

5'3&0/0'0/%9 A = ^P6[ /%0$ 08) (-*S)0 ,)(-%, .'%;0/$% 9/1)&

< = >?? R ^P6[ = ]\6[

B8) F$0)%0/-2 )%0*-%0+& 0$0-2 *)1)%') = BE D` = \6[ = ^[^6P[B8) F$0)%0/-2 )%0*-%0+& 0$0-2 ;$&0 = B# D` = G?? H P?J D` = G?? H P?I>\6[

= G?? H ][? = >C>[?B8) F$0)%0/-2 )%0*-%0+& F*$./0 /& = BE D` R B# D` = Q] = ^[^6P[ R >C>[? C \Y^[GZ&

B8'&C 08) F$0)%0/-2 %)4 )%0*-%0 &0-:& $'0C -%, E)F'32/; 8-& < = [[C A = Z[C -%, =>CP[[6.8 /0*>5 *+>05,656L F4,+7*7J I5>05,656L ,+I /08@*7 *+>05,656 6

W+6=50 95 ! D$*08 #)%0*-2 4$'2, &'3&0/0'0) E)F'32/;+& *)-;0/$% .'%;0/$% /%0$ 08) (-*S)0,)(-%, ;'*1)C /6)6C

< = >?? R J D R JE = >?? R J D R KZ[ R ?6[J DL = [[ R ?6[J D

D$*08 #)%0*-2+& 0$0-2 *)1)%') /&

BE D =


49/189

D$*08 #)%0*-2+& (-*9/%-2 *)1)%') /&

,BE DV,J D = TE D = [[ R J D

B$ (-W/(/X) F*$./0C D$*08 #)%0*-2 4/22 &)0 TE D = T# D $*

TE D = [[ R J D = >? = T# D U* J Q C Y&

5'3&0/0'0/%9 J D = Z[ /% E)F'32/;+& *)-;0/$% .'%;0/$% 9/1)&

J S = Z[ R ?6[IZ[ = Z[ R PP6[ C %%G&

B8)% A = J D H J E = Z[ H PP6[ = ^\6[

5'3&0/0'0/%9 A = ^\6[ /%0$ 08) (-*S)0 ,)(-%, ;'*1) 9/1)&" = >?? R ^\6[ C [%G&

D$*08 #)%0*-2+& 0$0-2 *)1)%') = BE D = CZ^P6[ D$*08 #)%0*-2+& 0$0-2 ;$&0 = B# D = G?? H >?J D = G?? H >?IZ[

= G?? H Z[? = >CP[? D$*08 #)%0*-2+& F*$./0 /& = BE D R B# D = Q = >CZ^P6[ R >CP[?C %9%G&

E)F'32/;+& 0$0-2 *)1)%') = BE E = 6P[E)F'32/;+& 0$0-2 ;$&0 = B#E = G?? H >?J E = G?? H >?IPP6[ = G?? H PP[ = >C?P[E)F'32/;+& F*$./0 /& = BE

E R B#

E =

S = \]>6P[ R >C?P[ C \%^[GZ&

A


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3. Answer ALL questions

4. We will only grade answers on the fronts of the sheets (not the backs). Do not unstaple the two pages.

5 Show your work and write legibly. You have a maximum of 15 minutes for this quiz.


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BPUB 250 Spring 2009 Managerial Economics Final Exam

Instructions1 Read over the whole exam, and do the easier questions first.2 Show your work. No credit will be given if work is not shown.3 No credit will be given for work shown on even-numbered pages. Use page

labeled as overflow space for work pertaining to that question only thatdoes not fit between questions.

4 Write legibly!5 Initial the proctors class list when you hand in your exam.6 Write your name and student I.D. number on every page of this exam in the

space provided.7 Do not disassemble the exam.

Your Name:_____________________________________________________

YourI.D. # _______________________________________________________________

Section number:_____________________________________________

Cohort name:_______________________________________________

Professors name:___________________________________________

DO NOT START UNTIL 6:00 PM.


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Question 1 (ANSWERS).

(a) Find the cost-minimizing total cost:

minsubject to

TC r K w LQ K L

At the optimal K and L levels, the MRTS = w/r :

0.5 0.5

0.5 0.5

0.50.5

K L w K L r

K w L r

w K L

r

Substitute the expression back into the constraint:

*

*

wQ L

r

Q r L Q

wwr

w K Qr

Compute the associated total cost:

2

w r TC r Q w Qr w

w r Q

Here, w=$10 and r =$22.5, so 30TC Q and 30dTC MC dQ

.

(b) ADM as a monopolist sets MR equal to MC :


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2100 30

1003,500

$65

M

M

R Q

Q

P

MC

(65 30) 3, 500 $122, 500 M

(c) Call ADM firm 1 and the foreign manufacturer firm 2. Demand in the market nowequals:

1 2100100

Q Q P

ADM solves:2 1

1 1

2 1

2100 30100 100

70100 50

Q Q R M

Q Q

C

ADM's reaction function equals:

21 3,500 2

QQ

The foreign manufacturer solves:1 2 2

2 2

1 2

2100 37

100 100 50

63100 25

Q Q Q R M

Q Q

C

Substitute in ADM's reaction function:

2 2

2

2

63 35200 25

1 128 25 200

800

Q Q

QQ

ADMs quantity choice:

1800

3,500 3,1002

Q

2


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Market price from the demand function:1

100 (3,500 800) $61100

P

ADMs new profit:

(61 30) 3,100$96,100

D

ADM would at most be willing to pay $122.500 $96,100 or $26,400 for its monopolyrights.

3


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Question 2 (ANSWERS)

a) EV= 0.6* 40,000 + 0.4 *0 = 24,000 b) ( ) 0.6 40,000 0.4 0 0.6 200 120 EU loan c) ( ) 120U CE CE , and so 2120 14,400CE d) Since CE>10,000 (the money she obtains for sure) she actually prefers to make the loan!

Another way to see this is to realize that (10,000) 10,000 100 120U e) Note that the best alternative to Lemons CDS is lending the money without protection.

The relevant decisions are thus:

Andy repays (p = 0.6) Andy defaults (1-p = 0.4)Lend Money (no insurance) $40,000 $0Lend Money and buy CDS $10,000+$30,000*(1-X) $10,000

The expected utility of the CDS is:

( ) 0.6 40,000 30,000 0.4 10,000 0.6 40,000 30,000 40 EU CDS X X The maximum X is such that the expected utilities of buying the CDS and goinguninsured are equal:

( ) 0.6 40,000 30,000 40 ( ) 120 EU CDS X EU loan , and therefore:0.6 40,000 30,000 80 X ;

20.36 40,000 30,000 80 X 6,400

40,000 30,000 17,777.770.36

X

40,000 17,7780.74

30,000 X

Kara is willing to share up to 74% of net profits in order to eliminate the risk of default.

4


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Question 3 (ANSWERS)

a) Graph of the Problem:

Since the companies do not incur private costs, they generate emissions at the pointwhere MBE =0.

The socially optimal level is at the point where MBE=MSC. Since C and O imposedamage on the residents of their local communities only, this entails:

5


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The deadweight-loss to emissions os the excess social marginal cost not offset by amarginal benefit from emissions (shaded in gray in the figure above)

b) The total cost of the standard equals the area underneath the MBE curve from E =20 to E max .

A standard of 20 coincides with the optimal emissions level for C . As a result, DWLC =0.

For O, the standard is too stringent, reducing E below its socially optimal level. Thus theDWL is the MBE that exceeds the MSC for emissions from 20 to 40 (see graph below).

6


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c) ote that

BE C (E=19) = 5.25

BE O(E=21) = 13.8

price range that would make at leastne firm better off is a price between $5 and $13.8

neath the MBE

urves, between 19 and 20 for C and 20 and 21 for O (see graph below)For C,

MBE C (E=20 -> E=19) = 5+0.25/2 = 5 1/8

For O, MBE O(E=20 -> E=21) = 13.8+0.2/2 = 13.9

N

MBE C (E=20) = 5

M MBE O(E=20) = 14 M

Thus if C were to sell its 20 th permit to O, it would forego a marginal benefit of $5. O would realize benefits of $13.8 from that permit. Ao Alternatively, we could compute the benefits foregone as the areas under

c the area is given by

the area is given by

7


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d) The firms trade number of permits, x, until

O thus buys all of the permits originally issued to C . The market clearing price is

=10

(A similar solution results from using the area-based approach from part c)

8


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8/10/2019 BEPP250 Fin

bepp250 final testbank

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