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Unformatted text preview: True/False Questions (5 points each) Name Lg ' Questions 1 and 2 are based on the following oneshot 2player payoff matrix: 
'
”m 1. Outcome (—2,2) is the only Nash equilibrium in the game. T 2. Outcome (—3,4) is Pareto efﬁcient and there is at least one other Pareto efficient
outcome in the game. T 3. Assuming (aswe did in class) inelastic supply and perfectly elastic demand, and
given the following valuations of buyers and sellers for peaches and lemons: Car Quality Buyer Seller
Peach $1200 $900 F
Lemon $800 $600 Assume sellers know the quality and buyers don’t, and both buyers and sellers
know that there are equals numbers of lemons as peaches. There will be adverse
selection in this example. €053: {930 > 79:) —% /;o~cL~as
kt, . 4. ' In the textbook, the topic of price dispersion was discussed. The basic concept is
' that prices should be changed over time (e. g., through sales), but in a regular and , , non—random way. ,F (ww ‘_ (“9) 3M) 5. For the airline network and corresponding data given in problem ll, suppose
solution of the dual gives the following: y1=200, y2=800, y3=4OO,y4=600, then
fare class for OD pair AD should be closed. ‘4 ‘ ”—an bro A’stoo vaoa 6. Suppose there are 5 fare classes for a ticket from Atlanta to Mascoutah and the
current protection levels are y1=20, y2=30, y 3:35, y4=50, y5=60. A request for 35
tickets for class 3 would be rejected. T bs—L 99‘30330 7. (20 points) Suppose there are two players in a market with P=1002Q. Player 1
assumes that both players will collude and player 2 “defects” knowing player 1
believes they will collude. If the incremental cost for each ﬁrm is $5, solve for
the equilibrium output for each ﬁrm. ?,=l° 8. (10 points) Consider the “trash collection” problem we discussed in class where
you are the bidder. Your costs are: $5M for the trucks (and they could be
salvaged at $3M) and $100000/year for variable costs (gas, driver, etc.). You are
guaranteed to collect exactly 100,000 tons of trash per year, and your cost to the
landﬁll operator is $5 per ton. The salvage value of the truck (in annual value
discounted In addition, you bid 10% above your annual costs for the job. What is
the maximum “exploitable quasirents” (in units of dollars/year) that the landfill
operator could get form you? Assume that for discounting, A/P (annual given v
present value) = 0.1. Cu. b4; ep/,\,,‘.§.¢J £7 #7:!) (910V\ «Ah ‘\ C SH ’ SM» —‘ $v90004/7/ 9. (10 points) For the following game, ﬁnd the response function for player 1 (the
row player) for a Nash equilibrium in mixed actions: 
“m hos/m Phat/l W5 is KC" 0) Z is >\ 10. (20 points) Suppose two ﬁrms are competing in a market with P=100~2Q. In
addition, the incremental cost for ﬁrm 1 is $20 and for ﬁrm 2 is $0.
a. Find the Cournot equilibrium (don’t worry about computing profit, just
state the values for the decision variable for the firms).
b. Show whether there would be a ﬁrst mover advantage or not for the
Stackelberg equilibrium (assume ﬁrm 1 moves ﬁrst). A m: (\DO" 20m 5,34») 1. I ﬁt ; 80' “{q' 'Z7z :0
)meﬂ'v‘i,’ ZO’.§7L  . ll. (10 points) For the airline networkwshown below and corresponding data,lwrite .
V' i thedual formulation (don’t solve, but please'use the leg labels given to define your:  , "
dual variables) for ﬁnding the bid prices. Assume that the starting capacity of each
 plane is 109 seats. Inaddition, asspme that 10 ticketsfor fare class 1 for OD pair BD
has been sold, and the demand in the table below is demand after those sales. ‘ Origin Destination Class Fare Expected Demand A C ~1 300k 40...
A D 1 700 ~ 30
A E 1 600 25
A E 2 300 50
B C 1 100 50'
B . D ' l 409 _“ 33 it
B D 2. 300 "‘60
B E 1 500 36
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True/False Questions (5 points each) Namew Questions 1 and 2 are based on the following one—shot 2player payoff matrix: 1. Outcome (3,3) is a Nash equilibrium in the game. F
2. There are exactly three Pareto efﬁcient outcomes in the game. T 3. Assuming (as we did in class) inelastic supply and perfectly elastic demand, and
given the following valuations of buyers and sellers for peaches and lemons: Car Quality Buyer Seller
Peach $1200 $1 100
Lemon $800 $600 Assume sellers know the quality and buyers don’t, and both buyers and sellers
know that there are equals numbers of lemons as peaches. There will be adverse
selection in this example. / \ ECg3: \000 4 H90 4. In the textbook, the topic of price dispersion was discussed. The basic concept is
that prices should be changed over time (e.g., through sales), but it is very  s o I —/
important that it be done 1n a seemingly random way. i 5. For the airline network and corresponding data given in problem 11, suppose
solution of the dual gives the following: y1=400, y2=800, y3=400, y4=600, then
fare class for OD pair A—D should be closed. 1" A“ 7.790 4 4397400 6. Suppose there are 5 fare classes for a ticket from Atlanta to Mascoutah and the
current protection levels are y1=20, y2=30, y3=35, y4=50, y5=60. A request for 15
tickets for class 3 would be accepted. / ‘ L3: b0 «29: 2.0 7. (20 points) Suppose there are two players in a market with [email protected] Player 1
assumes that both players will collude and player 2 “defects” knowing player 1
believes they will collude. If the incremental cost for each ﬁrm is $10, solve for
the equilibrium output for each ﬁrm. ’{2’/ \ (AJAQ)>DLL7) TC lﬁo~Q3Q
“I, 5‘0,ng0 ’9 Q74)
i.¢21§ / 7" '
7L6 W24 (\qof2?.§ 'ﬁLl°)77—
r) m r2790 4’ 7z=33‘75  P: gsor (zuS’r 3375) : Ll3'73 'n‘c (a3.75'—i§)(22\5) (fl/r (33,7; ~Ia)(33.’7§) 8. (10 points) Consider the “trash collection” problem we discussed in class where
you are the bidder. Your costs are: $3M for the trucks (and they could be
salvaged at $2M) and $100000/year for variable costs (gas, driver, etc,). You are
guaranteed to collect exactly 100,000 tons of trash per year, and your cost to the
landﬁll operator is $5 per ton. The salvage value of the truck (in annual value
discounted In addition, you bid 10% above your annual costs for the job. What is
the maximum “exploitable quasirents” (in units of dollars/ year) that the landﬁll
operator could get form you? Assume that for discounting, A/P (annual given
present value) = 0.1. 7‘“ (310' 1M37'OD’Ow/7/ 9. (10 points) For the following game, ﬁnd the Nash equilibrium in mixed actions: 
"m 10._(20 points) Suppose two ﬁrms are competing in a market with P=100—2Q. In
. addition, the incremental cost for ﬁrm 1 is $20 and for ﬁrm. 2 is $0. a. Find the Coumot equilibrium (don’t worry about computing proﬁt, just
state the values for the decision variable for the ﬁrms). b.‘ Show whether there would be a ﬁrst mover advantage or not for the
Stackelbergequil—ibrium (assume ﬁrm 1 moves ﬁrst). ?\ " Th: (\Qérzéaglﬁg—b) 1," \\‘. '5 $0 " ”‘1"4272 :0
)L\. (0);): 7 7 w».§7z W, = (.loa"7—L1.17»))ﬁz L's pow7, 47,,
' ‘ \ZLLmﬂha Zé—A'W
“Ml1px u; ‘4’} I 5.130 77'7‘}, “)4 94 c‘ 71,4” 13
' M 49* MNJt/ ‘33waan . , ll. (10 points) For the airline networkvshown below and corresponding data, write ,
' ‘ the dual formulation (don’t solve, but please use the leg labels given to define your‘ > . '
dual variables) for ﬁnding the bid prices. Assume'that'the starting capacity of each
plane 'is 109 seats. Invaddition, assume that 10 tickets for fare class l‘for OD pair BD
has been sold, and the demand in the table below is demand after those sales. ' Origin Destination Class Fare Expected Demand A. c 1 300“ 40
A D 1 700 ' 30 ’
‘A E 1 600 25
A E 2 _ 300 50 .
B c 1 100 50’ ‘f
B . D 1 400 33 .
_B ’ D 2. 300 5”"“60
B E 1 500 36 I
Q '33'03')“ {702) I‘; {tow} £799 *1, '4 «20%;. “130%.; "r'z‘ovﬁh *i'gwﬁs ,4 m ,y.‘ .gxé?
Xgu+ A, i )<1 i >18 "5”
YL’)’ X5 fX‘I 5%
<3 i VagiXQ "D7
A 5%;
£16 ‘0 DJJ\
.mfnWo‘l. +ﬁ07b; +QO)’; +(oa‘i4 «rm 75 \9 )‘L '4’ Z§77 7‘ Coﬂg 4 3'37“: 4’73 )1” True/False Questions (5 points each) Name kg 140/ «KM V‘ L7,» . Questions 1 and 2 are based on the following one—shot 2—player payoff matrix: 1. There are no Nash equilibrium in the game. 1’
. /_
2. Outcome (3,3) is the only Pareto efﬁcient outcome in the game. r. 3. Assuming (as we did in class) inelastic supply and perfectly elastic demand, and
given the following valuations of buyers and sellers for peaches and lemons: Car Quality Buyer Seller
Peach $1400 $1000
Lemon $800 $600 Assume sellers know the quality and buyers don’t, and both buyers and sellers know that there are equals numbers of lemons as peaches. There will be adverse
selection in this example. / 1, E (153?" two 7 ‘°°° 4. In the textbook, the topic of price dispersion was discussed. The basic concept is
that prices should be changed over time (e. g., through sales), but it is very
important that it be done in a seemingly random way. T 5. For the airline network and corresponding data given in problem 11, suppose
solution of the dual gives the following. y1=300, y2= ,800 y3= —,350 y4= —,600 then
fare class for OD pair A— D should be closed. / I ’Q/é‘ 793 > 3991353 6. Suppose there are 5 fare classes for a ticket from Atlanta to Mascoutah and the
Current protection levels are y1=20, y2=30, y3=35, y4=50, y5=60. A request for 15
tickets for class 4 would be rejected. /" r— E11: 60" 35': lb 7. (20 points) Suppose there are two players in a market with P=lOOQ. Player 1
assumes that both players will collude and player 2 “defects” knowing player 1
believes they will collude. If the incremental cost for each ﬁrm is S, solve for
the equilibrium output for each ﬁrm. fat p 3) f), 3“ $60 Wt " (we’kv so)u2
”\Y‘I'f amputee «9 Qeu 8. (10 points) Consider the “trash collection” problem we discussed in class where
you are the bidder. Your costs are: $3M for the trucks (and they could be
salvaged at $2M) and $100000/year for variable costs (gas, driver, etc.). You are
guaranteed to collect exactly 100,000 tons of trash per year, and your cost to the
landﬁll operator is $5 per ton. The salvage value of the truck (in annual value
discounted In addition, you bid 10% above your annual costs for the job. What is
the maximum “exploitable quasirents” (in units of dollars/year) that the landﬁll
operator could get form you? Assume that for discounting, A/P5 (annual given
present value) = 0.2. ' f .ZCSH’Z—M) ’5 133,03”) 9. (10 points) For For the following game, ﬁnd the response function for player 1
(the row player) for a Nash equilibrium in mixed actions: 
IEEE 10.,(20 points) Suppose two ﬁrms are competing in a market with P=1002Q. In
. addition, the incremental cost for ﬁrm 1 is $20 and for ﬁrm 2 is $0. a. Find the Coumot equilibrium (don’t worry about computing proﬁt, just
state the values for the decision variable for the ﬁrms). b. Show whether there would be a ﬁrst mover advantage or not for the
Stackelberg equilibrium (assume ﬁrm 1 moves ﬁrst). ‘W Tl": (too'ZCﬁ'+ﬁL)—b)1" “l s 80’ high "Z7; :0
)z\. (0),): 7,7 ZO’Sjl V), : Lloo ’ LL?« 1735)th “I": ’39, 17' —\,7L
' \22.(9,\.=‘)L=“ 2&4“?
“Mi.“ M 1"} I . a .l 1. (10 points) For the airline networkushown below and corresponding data,_write ‘ " the dual formulation (don’t solve, but please use the leg labels given to define your: ' V
dual variables) for ﬁnding the bid prices. Assume that the starting capacity of each plane is 100 seats. In addition, assume that 10 tickets for fare class 1 ‘for CD pair BD \ has been sold, and the demand in the table below is demand after those sales; Origin Destination Class Fare Expected Demand A, c 1 300“ 40
A D 1 700 30 '
1A E 1 600 25
A E 2 300 50
B c 1 100 50‘
B _ D, 1 400 33 . .
B D 2. 300 ”’60
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 Spring '08
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