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Econ 106 Managerial Economics '1‘
Homework TH" P..Q\‘ ‘ 1* WWW” ﬂu)
Spring 2011 1 171,17!”  (to \
; 1725.71. 7,261. 7
Due date: Wed June lst at the beginning of class. TC. 7 43 L. '3 . . . N — r\ (Tot
Homework guidelines can be found at http.//econ.ucsb.edu/ b 71,; , 4%:qu  (w + ”a. 14 * 77$“, 6)
1. Read the following case studies 4219,2212 . “I 7‘”
Deutsch Telecom. Last names AL. ‘  1 lg ,\ \ao
Heinz. Last names MZ. TiaL , ’5 0 . 1v 7 {9 7 (VP "D\&" You are responsible for both articles but only asked to provide answersifor one article. Answers for question 1 (including all subparts) should not exceed 4 pages. Please use Times New
Roman size 12 font. Also, line spacing should be 1.5 or 2. (not single spacing).
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2. The 1nverse market demand 15 P=200— 8Q. The ﬁrms have cost functions
TC1=10+22C11+C112 ill" " 721*14" I“? '1‘" 70a” 21, TC2=10+22q2+q22ML1 ’L’L ‘* 24x1, K F Q 6; Pg
{Ti”#7 4b?" 100 ‘L$\\‘—?—'q‘l 4'21’211) 7’00 8%1’llaii (77. +212)
(”77 524‘1 '— % l 10f”?&_— 1.2 \ ( Assume the ﬁrms act simultaneously
a. Find the proﬁt maximizing quanti/y for ﬁrm 1 and 2. % 9M004~ 618’? lit/<12. 1 ”1211‘ ‘18‘1— 02.4%
, 1
b. Findthemarke ce. * ”5" ““7 0‘1”" c2 .. q gq, ,, 441.22.
11,._?.Q..r Tbzo‘ 45,: nL(Li’1’\o§rl"/ 5L3“ . _,../'”" j  ‘ ‘
‘E1: v.0— (c ; ,, LL": WK 41,. 2 9:4 1.4 2: 1131.5! 9. Q0511 \ Assume ﬁrm 1, has market power arid ﬁrm 2 is the follower.
c. Find the proﬁt maximizing quantity for ﬁrm 1 and 2. d. Find the market price. 545““ :;' L44 '.' ‘1!—
Mng 'K. :. <1. « “M.
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3. The 1nverse marke}der£1;1néi 18 P: 75 2Q. The ﬁrms have cost functions
0 2 ‘7
ML' 4' TCIZ 3‘11“] 12 “C  ' EC 25 vi
. 4.11,, ML 1 ’ 2 1
mu. m 1: 1.1 TC2=18q2+q22 ‘11 < , 2‘
.; 4;» 3; 2.1 (La—.12 : 1. Q33 ' 1C.
1 ' it ix ’1 Assume the ﬁrms act simultaneously 0" 3 ( “Z .22 a Find the proﬁt maximizing quantity for ﬁrm 1 and 2. _ i ( ~ "‘x ,
Q‘ViIZ {far 2".li.‘ .3”? iii, Sitzi‘ i‘ :QZL '3‘ 17.799 62;: 73722. ‘3! b Findthe marketprice 414 W .. 2.95312" ‘22. 4,27 l/x, . 7;, ‘7: .4 ,3“ f» ,_r_.<_ _Vg / u a.» .. . , 2:; a.» 1:152) Assume ﬁrm 1 has market power and ﬁrm 2 IS the follower.
c. Find the proﬁt maximizing quantity for ﬁrm 1 and 2 (GS 22 2711.1. ~31 4‘, . ; 3,, 111.22 +:2:.l
: ’24; 22. 2 22; i 5 ..
d. Findthe marketprice. “1:531..— 31.} HQ
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4 The 1nverse market demand 1s P: 200— 8Q. The ﬁrms have cost functions mg “a 1' , Z 2 /
5,? ’
TC1=10+22q1+ql2 (j ’ 17., £77391???) ,
TC2=10+22q2+q22 W " 77‘ ‘ ’ ”7 " ' 8;, 2,,”41
n 2 \V/ :9 , ,L/  v i '7'; ’I
a. Determine the indu y p19ﬁgrrlax1miz1ng output unde1 colTr M a; q z
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b Calculate the éeqiuilwibriuﬁi/pﬁce under collusion. :4 17 2 37
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c. Determine if the ﬁrinrs shouldc foTluciie (compare against your answer found 111 2a b)
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5 The 1nverse market demand 18 P=75 2Q. The ﬁrms have cost functions f z 2 A
TC1=3C11+C112 T > 3”; z ""9" it“ ’i’ ' [f‘  {fair}; : H? JUL—Lani 7 Z, 21
TC2=18C12+C122 ”’4 , ”K 21  2212/ “ti ~ ’92»: ’ it 714:”? 4/
9 . w
a. Determine the industry proﬁtmaximizing output under collusion. :2“ a, ,7 z, 1 ,r  2 z e . 3 , . i
(p.  \2 a ‘ 51111.
X Calculate the equilibrium price under collusion. g1”— 7}
F7 41511 Z rightg?)
0. Determine if the ﬁrms should cpl] de (compare against your answeLfgund in 3a ,.b) q 4
ﬂ ' r l 3’4 ’ (?°\' (94014 L 4‘; (D‘Wk \l M Z. 3:L ing ":z
1:0“7ﬂ7)1~u(, 7C“ 7 i 2 5H! —(‘1Fb'i 01") ‘— (H7 (ls ”FL :4” 09‘ Lﬂié—‘(U “ 6 J 9 m
1 6. A monopoly ﬁrm has the following 1nverse demand and cost functions _z, _ m
. V {ML [(,(.("_1_‘ 3‘11" 1
X P=75 2Q a. , s;
\\_./ Vane TC]: 3q1+q12 N. (.1 _' P f__.—$/'—1_]
3+ 1%. ' "‘9 ~ ’1 <1 4a : ‘72 (11 g L_7_.\_1_"_.i:1
a. Find the (perfect) ﬁrst degree price discriminating quantity and proﬁt. a ,3 a 3;). 1,7»
b. Find the block price and quantity. i 1‘ 2:3  37"“
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m f4». C ‘0‘!”qu tits, {[email protected] Q25“? q”. “.90 cfﬁim 1: 1m  M? .jcon 106 practice test ch 17 key . http://econ.ucsb.edu/~benelli/tests/practice tests/106_testl_key.htm 1 0f6 Econ106 (We 5’13? ““97 Practice test suggested answers
Ch 17 Chapters are not separately identiﬁed. Questions 110 are from ch 13 and the remaining questions are from ch 57. Note if you see do not see A (you should see a triangle representing change) and instead see a D or possibly something else, then
please be aware of this when looking at the key. Different computers will covert the change symbol to different notation. 1. Good Sleep anticipates the following earnings for the next 5 years. Years 1n the Future Anticipated Proﬁt
__ If the discount rate is 10% and the machine costs” $90';"is it a good purchase? PV= 22/(1. 1) +24/(1. 112 +26/(I. 113 +28/(I. 114 +30/(1. 115: $97.12
NPV = $97.12 9000
= $7.12 ' " Good purchase? YES 2. Do elasticity and s'iéﬁé mean the same thing? Explain. 3. The demand for sodgis given by
Qsoda — 10— 2Psoda — 4P crackers + 21 Soda sells for $1, crackers sell for $2, and consumer income (I) is $10 a. d No. Elasticity measures the impact of a percent change in one variable on the percent change in another. Slope
measures the impact of a change in one variable on the value of the other. Since elasticity compares percent
changes, it is not sensitive to the units in which the variables are measured This is not the case for the slope
which is dependent on the units of measure. 13..,..111,w>+1<91 ass2.9 , . eni'l'
. f o. t 1‘» 'l ”‘6 "A "
3a; ‘1: . 41  1’0 2 — ‘
Calculate the own price elasticity of demand. (1’5 Q; 1 'I
Own price elasticity is 2(I) / 20 : —0. I Qd=20
In words a I %change in soda price changes quantity demand by 0.1% (You should be able to reinterpret this in
words with the negative sign.) Calculate the cross price elasticity of demand between soda and crackers and state whether they are substitutes or complements g Gs 52¢ “r . 4 J L, .,,1
Cross price elasticity is —4(2) / 20 2 ~04 ‘:‘;Z’ ‘ 7;: ». " "7‘3 7'“ ’1'?”
Since elasticity is negative, the goods are complements. . ‘ ,1 ( ,. .
You should be able to interpret this in words. _ ( 3 101“ 1,1313 M?“ 1,4. 1:14 ; 3; V; . A n , '1‘ , it“ ,1 / Calculate the Income elasticity of demand and state whether the soda IS a normal or inferior good. Income elasticity lS 2(10) /20 :1 \ 2H ‘ 4 10  .j t) in" ,;,( , Nag”.
.. a a 5 . 1 .. 1 7‘  ' 1
Since elasticity [3 positive, soda is a normal good 4),. ‘ ,W . f 1 ‘1  w ., we ;
You should be able to interpret this in words. "3 E {95 "to g ‘ r1 may 1 . . ,1." »
, . 1 The company is considering dropping the price of soda by 1%. What IS the expected change in revenue? Assume . ‘5 .111... ,. ~13 4AV
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l x)“ Econ 106 practice test ch 17 key http://econ.ucsb.edu/~bene1li/tests/practice tests/106_test1_key.l.a.1 AQ U W 1 soda revenue is $2000 and cracker revenue is $3500. Assume the cross price elasticity for crackers is —0.3
x L i‘h "
11 / ’ . ,
1 ”‘ 1 . a Usmg DR=[RX(1+prqx) + Ry(qup§)](%DPx)
c i >11 ‘“ DR=[2000(1— 0.1) + 3500(4). 3)](— —1% — —7.50 e. Based upon your answer in part d, could you tell if the revenue would increase or decrease before you used your
formula? Explain (simply basing your answer on the revenue you calculated is not sufﬁcient).
Can’t tell in advance. Since price elasticity of soda is <1, prices should not be decreased since TR of soda will
fall. But this does not consider other goods. The 2 goods are complements so when the price of soda decreases
the quantity demand of soda will increase, this causes the demand of crackers to increase. This means the
revenue of crackers will increase. The formula in part d tells us the drop in revenue of soda is not offset by the
increase in revenue from crackers. 4. “The winds of the recent hurricanes in Florida are bringing soothing ﬁnancial gain to California citrus growers. Due to the extensive damage to the Florida citrus corp, California citrus products are commanding their highest prices ever.” ~
Graphically explain what’s happens to the price/quantity of Florida’s oranges and the price/quantity of Cali oranges. mV\°' , at My“
Graph should show the supply of Florida oranges has decreased. lhis causes the price to increase and quantity 
‘ ,; l demand falls Since Florida oranges are likely .%b’stz—tutes for California oranges, people will switch to
, ,1. ‘ , California oranges which causes the demand for alifornia oranges to increase. This results in an increase in
1;" ' r1 ’ przce for Cali oranges and potentially increase in quantity (depending how you drew supply curve ﬁxed or
with some slope). 5. Suppose the chairman and chief executive ofﬁcer of General Motors has decided to a) Raise the company' 5 auto prices by 5%. In addition, suppose that the following events have been forecast for the next
year: b) the price of competitors cars are due to rise by 8%; c) consumers' incomes will rise by 2%; and _  d) the price of gasoline is due to fall by 20%. You, as head of production, must decide what all of these events mean for GM's car sales so that you can plan production accordingly. You hire an economics consulting ﬁrm that provides you with these estimates based on econometric studies: Q5115 elasttclty of demand for GM cars is —2. 0 ___ 1.... @ismee Elasticity between GM cars and those of 1ts competitors is +0. 5 Cross price elasticity between GM cars and gasoline 1S —O. 3
Income elasticity of demand for GM cars is +1.6 Calculate the effect of each of these four changes on demand based on the estimates provided. a. Increase the company's auto prices by 5%.
Increase the company ’s auto prices by 5% then price elasticity of demand for GM cars is —2. 0 so —2(5%l= qD/k'il‘u ‘, 1 _
., n b. the price of competitors cars are due to rise by 8%;
1,1, t ‘ V. .. the price of competitors cars are due to rise by 8% and cross price elasticity between GM cars and . 
7 ’1 those ofits competitors is +0 5, so 0. 5(8%l= —4% ,7 ,7 «a 1 74 , “. 11 ‘7 ’ 1’ 9 "1f? :QJJ.‘;/.ll 5.“
"f”? ,. g 'f f? .. 1'}. 917w ‘in/ ’1' i . ‘ d 1“": c consumers' incomes will rise by 2%; and 9‘
consumers’ incomes will rise by 2% and income elasticity of demand for GM cars is +1.6 so 1. 60%) 3. 2%
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d. the price of gasoline lS due to fall by 20%. '
the price of gasoline is due to fall by 20% and cross price elasticity between GM cars and gasoline is —0. 3,
SO 0.3(~20(%}) =6% __ 0‘ 1'7 ‘c 7 10 '2’. “F a. 73;” 7 \it .
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6. Joe has the opportunity to operate a business renting beach umbrellas next summer. He will operate the concession for 3
months. Looking at weather patterns, Joe observes that rain is frequent along this stretch of beach, and on average, there
are only 60’rwentable days in a summer In each of these days, Joe believes he can rent 40 umbrellas per day at $7 per rental. Joe will run the concession by himself day, and must pay Beachcomber Enterprises $9, 000 for the concession (the
use of the umbrellas and for the beachfront rental location). Suppose Joe could earn ”$45.00 working construction. _ . F . . (:2 1"x, 1‘ .2.
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2 of6 3/28/2011 9:19 Pm .scon 106 practice test ch 1—7 key Jof6 ﬁle“
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V , a. What are Joe’s Accounting Proﬁts for undertaking the business? pA : TR ~ TCEX
= 60(40'$7) — $9,000
: $16,800 ~ $9,000
: $7,800 b. What are his Economic Proﬁts? pE : TR — TCEX — TCIM
: $16,800 v $9,000 — $4,500
: $3,300 c. What would you advise him to do?
Economic proﬁts are positive so open the business. 7. Suppose the market demand and supply curves are given by Qd= 20 » 3P and Qs=P.
a. determine the equilibrium price.
P:5 31.). b. determine equilibrium quantity. Q=5 c. If the government imposes a price ceiling of $2, what is the quantity demanded and quantity supplied?
Qd’=2() — 3*2 =14 '= .. "14. .. (NM,
QS 2 i P: (95 +5 1; >1 . :,\\. _,.._._ 4) I "A. y . J: t‘"
d. Calculate the full economiqprice. i _ _____;,,=_’ 1* ” Ex 1 llcwéj
QS1=Qd  . ‘ _’ _—,_,.... L (>10 :' 1;0_ 9 '_
2:2031? 32,, _ , .7. . _
P=6 Full economic price is $6 with $4 the nonpecuniary priCe. 8. Delta, Inc is expected to grow at an annual rate of 3% for the foreseeable future. The current proﬁts of Delta are $1,000
and have not been paid as dividends. What is the value of the ﬁrm assuming the market interest rate is 6%.
Value = 1,000*(1.06/0.06— 0.03) = 35,333
'. 3 5' 3 3 3 . 9 A ﬁrm produces 2 goods, x and y with the following demand functions
Qx— 98 —10Px + 4Py
Qy= 50—513y + PX Price of good x is $5 and price of good y is $3 The ﬁrm 1S considering Wiwhe price of good x by 2%. Show if it «'1; ._ 1 is agod 1deato drwopwprE; pap? ow‘ VIN/Q El. 1., '11 a 0 $37 /
 3__Q1 1i" .\ \{)~‘,/ : »~W*:>
sz60 EXX T 3?”: ’64 Va . i",
: 40 1 N .[ ..
QJ’ J . Km £51m nGc.ii‘
. we 0" _ a». f P
RevenueX:$300 f 30 x Q ,1 P , G  2'34 9k ’ 1 ,If fog? . SW4" 1 at 4
Revenue Y: $120 “I: if 3 i “0‘39 x  2:; 'J( i at: i i 4'9 I fr," 1 ,1 .1 ”i
EQx,Px : 4.833 x : ‘ ‘3 _
EQy,Px : 0.125 (the goods are substitutes) AX? : 21:20, 7( y ( \ gown}; 15w ’5; l #71 i :3”
Ar:[Rx(l+Eijpx)+Ry(EQy’pj)]%APx v , (1; 0,72 3/28/2011 9:19 PM http://econ.ucsb.edu/~benelli/tests/practice tests/106_test1wkey.htm e um New“ Econ 106 practice test ch 17 key http://econ.ucsb.edu/~benelli/tests/practice tests/106_test1_key.l...n Change of revenue * ,$1 30 don’ t drop prices. In this case, revenue of good x falls since it is an inelastic good.
Goods x and y are substitut§so the drop of prices of good x causes people to demand less goody Therefore, good ” y sees a drop in revenue 0n net, the revenue for x and y jotntly falls causing a negative change in revenue.
Sim, 4311111: 7 ?3, ‘(k \/ {24 712.1 \‘m elm 10. The Burrito Barn is considering a price reduction on the Firegut Burrito, which currently sells for the price of $5.00.
Giuseppe, the proprietor of Burrito Barn, knows thecplrice elasticity for the F iregut is roughly equal to 2.3 over the range
being considered for the price change. The Firegut has been selling at the brisk pace of 500 burritos per week. To
increase market share, Giuseppe would like to increase sales to 750 per week. What price should Giuseppe set? “ A few ways to answer. One way is to use the arc point formula for price elasticity,
9W 1'1 @108 J 2 3 A EQx Px: (Q2 ;Q11L2 + _P1L w .2‘ c g 5 (Q2+Q1)(P2— P1) /2 Q P " ' 1 .. A 9 v.1 (1‘7) y. ’  EQxypx : 2.3,' q1:500; q2:750; p1:5; solvefor p2 7’ 2
2.3 = (500750)/(500+750) /(5—p2)/(5+p2) (97 "0.111;? *91'1/1 , {$113, am: :1131’4’52? A
2. 3 : 250/1250/(5p2) /(5+p2) lj W i .. ’ , F 
—2. 3 — 0.2/(5p2) / (5+p2) {1]— r.) (111 61.“) 1'1 _ 2 “7;... s ,,
23  ~0x2(5+p2)/(5P2) 2 . ““1“ . " 1‘ A
—2.3(5p2) : 0.2(5+p2) ” I < . 71,011194‘93/7.’ 1 , + 71 A
ll.5+2.3p2:l 0.2p2 72771.3( 12?”:‘1/1 14171 ‘ ' i
2.3p2 = 10.5  0.2p2 , ... ‘_ " A
2.5p2 =10.5 1 Lye"413,; __ 61.11,; A
p2=4.20 bif‘P MS —\._‘__ _. ......_.. “Mn—mm A
I 7 ~__ _.... "JanMM ~~~ﬁﬂmuwh W Cl’W (1 L1,] Jake’s Free Runoff'Bottled Water Company Produces with the Long Run Production Function .. '2 
Q = K2/3 L2/3  Currently K: 4 and L= 4. If Jake’s doubles inputs to K=8 and L= .,8 will the ﬁrm realize (hereusing, constant or
decreasing returns to scale? Explain. 1 " “ha". 115l6 ' la 3)) klt.l/’6 (#95) ﬂ 1’0va > ,mfcﬁog A
Q(4,4)=6.35 .. ‘1 . M , are 1W“ VmW :. lt“7\'1".«‘5' .. .
Q(8,8)=16 e“ 11“ re '9"? 93‘ 7" V“ A
(“increasing returns to scale since output more than doubled when the inputs were doubled. To see how this affects profit, calculate profit for each Q and for ease assume p=10 and w=r=$1. You should find that profit
increases as Q increases. (ll/q; ( (g 12. A multiproduct ﬁrm’s cost function is estimated as
’ TC= 75— 0.25Q1Q2 +0.1Q12 , .1 a. Are there1econom1es ofc copejins producing 10 units of product 1 and 10 units of 2? Explain. ,‘i' L1“ 77777
n? «Willi : V'W. a. . According to your Bobk, for a quadratic multiproduct cost functton economies of scope exist 1'ff— 22911;}; > 0. In this case, _ j = 75 and 13 =,_ ~11 25, so economies of scope exist smce f is a fixed cost, which is always
nonnegative. ‘ b. Are there cost complementaries in producing products 1 and 2? Explain.
Cost complementarities exist since a = —0.25 v: 0 .
l '2} AM A» 41 av ,1 c. Suppose the division selling product 2 is ﬂoundering and another company has made an offer to buy the exclusive rights to produce product 2. How would the sale of the rights to produce product 2 change the ﬁrm’s
marginal cost of producing product 1? , Since a—  0 ’5 0, the marginal cost of productng product I will increase if the division that produces 1H 13 "f 6% “ / x' is. ;’ .‘ ~ . .«7 7 .’ r" ' ’ , t. 2 A
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71(1, 18. A local telephone company charges $0.10/min. TC : 0.02 + 0.08Q ($0.08/min. marginal cost). What is the Lerner Index? {11.1% 1 . V'ML '
'1 Y 0.2 Lei/My 5519,11,,“ ’, /‘F'—“‘ 01500! g r; I}, yr, Met" 01: 17.17‘11‘1‘ L?! («15'5” "
19. The chemical industry has a Lerner index of 0.67. L a. Based on this information, a ﬁrm with TC = 25 + 10Q should charge a price of
,1 . 9 ML 1“— 5 .1: 1 L , g I; «a
$30.30 1, £111,121 mar « '5 ”g’ 9.57 v11” ~02 ; '1’ =7 1V ‘7 ‘0 ‘ Z
a r " b. What is the markup factor? 3.03 (interpret this in words) L : 1, 1 a 9121.11 1 ' . K “Y ‘qutv.1 4,4»: Fair , . u . 20 Consider a market characterized by a Herﬁndahl Hirschman index of 5, 000. One of the ﬁrms 1n this market has a Lerner index of 0.89 and IS considering (horizontal merger with a competing ﬁrm Based on this information 1s it likely that the
m 01qu U S. Department of Justice will approve the merger? Explain. ,1“ [AWE 7l1fWL/ " O Q"! ':1/';i"'1,. Reject the merger since the industry is highly poncentrated and the firm proposing the merger has significant market __.. 7 LC—T 71
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ju/ /~
, 7 , (TL) ‘ K I 72 3\ 7
13’. Suppose the cost funct10n 1s C(Q) = 50 +1Q — 10Q + 2Q . a. What are the ﬁxed costs? a ,
$50 A
1 b. What is the total cost of producing 10 units?
1AM: iii/:9 ,1 lob L C 591 19 .: 1006 + 106:.
$1,060 \
T. {010 c. What is the variable cost of producing 10 units? A‘VCZ 9d,”? .501 $1,010 t 1O ’ 1.712s ‘ MM l
. > 11,1;‘; 3 w“ / x 1 7
d. What is the marginal cost of producing 10 units? 1 Mm)?“ HM” ‘
Q Fr: 5, ,, 1  c a 1 4:2 ‘““ “MW.“ 3 10
NW“ $401 1 1 , 236 4 W ..
‘— 4'71 e. At 10 units of output, is the average cost curve increasing, decreasing, or constant? In the increasing stage Om, 1.4 There are over 5, 000 banks 1n the United States which is more than 10 times the number per person than 1n other
“ ' industrialized countries. A recent study suggests that the @ngjrun averagecost curve for an individual bank 15 relatively
131% , fla If Congress took steps tokignsolidaté Banks, thereby reducing the total number to 2, 500, what would you expect to
L.
— appen to costs within the bankipﬁg ih‘dustry? Explain.
m M 76 ,. 111.11 Wm 1., 11m With a ﬂat longrun average cost curve “there are/neither economies nor diseconomies of scale in banking services. Consolidation would mean that 2_, 500 banks would each have to double their outpmn order to service the consumers " initially served by 5 000 banks. But the corresponding average cost per firm as well as total costs for the industry.
wouldbgmw 75"” :71 6111111 1; (11,» 11M. 1 I11, . slim 1“me 151}. gm . 111» 11 ‘
16/. In 1995 the U. S. Justice Department sued to block a merger between Microsoﬁ and Intuit, the producer of the nation‘ 5 n A (,L‘ F 1’1 bestselling business software. The Justice Department argued that the merger would lessdh competition and raise prices of
business software. Is there an economic argument that the merger might actually result in lower prices? Explain.  If there are economies of scope or cost complementarities in producing operating systems like DOS and Windows in
conjunction with business software, then the merger might lower costs and therefore prices to consumers. 16. Suppose there arefive ﬁrms in industry A with sales at $5 million, $2 million, and the remainder at $1 million each. A
’ WW 7 F1 (p1) 1, OAQ q    , ’5. A « = ‘ (a ‘ o A
a. Determme the fourﬁrm concentratlon rat1o. ‘ , ,1 4 1 . l ‘ A ,1. 0.9 (interpret this in words) 0’ T“ o . 01 ~
*3
L L .  f ‘1, g", l» ‘1
\ 5 1"? “ ‘
b. Determine the HHI. 1111.... S M c
3, 200 (interpret this in words) ; 1 .1 .1 . 1 ,1 1 1" f; ‘: a .3 7 : 1,2 9 C
.31 fr ill/H, k; Wt (To? l '1: J '73 .1 E 733‘“ 13 7 ”\(CO‘ ) a
/ 0,13 "" a 3‘ 1 n1 C'
U" 1 17 The industry elasticity of demand for telephone service is ~2 while the elasticity of demand for a speciﬁc phone company
‘ is —5. What IS the Rothchild index? 11 < ' , ’
E: “N 1W“ » ii. (/71 / ~ , 1 «15‘ 1‘ c
0.4 K K; J/wwwrw ~~ , ....... :7 0‘51, ,1 1 ~ . . , 1 w 1 t 
I], g 1 ) g 7 5 of6 3/28/2011 9:20 131:. Econ 106 Practice questions suggested answers
Ch 811 Chapters are not separately identiﬁed. Questions 19 are from ch 89 and the remaining
questions are from ch 11. l. A perfectly competitive industry inverse demand is P: 60— 2Q You are the manager of
a ﬁrm that sells its product in a perfectly competitive market at a price of $40. Your >4 . 1
ﬁrrn' 5 cost function 15 C= 60 + 4q2. / e g, . * . W
" l are Y: “0
a. Determine the proﬁt maximizing short run output ,9“ 7 (a; .,
k,“ 7 . . ’ ,~ 7; “ I
2' \ . J 4, r
. _ In the short run, 1 , M C (A29; \6 1.
zli» Jr, P: —mc 4,); '69 ’ \rnD
(7:; ’ r3" q:5 \(1
. I I]  {O _,
Proﬁt=40 .1 i . . . .m
F'TL' T ' ‘ t ' ,3, «Le—31. 1' (“All. I‘D") ’ “0 _o. "; ‘ —.gxs ; 4’7
2. A perfectly competitive industry inverse demand IS P= 60 2Q. Your ﬁrm' 5 cost
function IS C= 60 + 4q2. a. Determine the longrun proﬁtmaximizing output of a single ﬁrm. f q=3.87 " f i a : — 2. av “Li \s ‘1 ‘; ‘ ﬂ“ "
b. Calculate the marketprice.
7"C 13:30.98 A‘M‘ w. '13'1’. 9.2":"1ENL' 3"
.M " [M 1W = 7 “""“*"~\ ~ ~ a r {2 W
 .. (212'2919 vlv€ﬂ\ 0 , ‘ L ”I. "r' \
din ‘ o 1 \ i v / ‘ M“ ‘”
Y: a t; ”1,1” c. F 1nd how many ﬁrms are in the market.
‘1 MarketQ=14. 5] "Fr .1». _~“, ‘7‘ ‘0 1‘9 3 ’
3_. 75ﬁrr_ns __in the industr ' G
3 A ﬁrm' 5 cost function IS C: 20 + Q2. The industry faces an inverse demand curv
85— Q.
W1 (‘"L
a. Determine the monopoly proﬁt maximizing output.
Q: —.21 25 P P? <31 N
M32 .9 —2£2'« ,2
b. Calculate the market price. ‘3 r
P263. 75
proﬁt=883. I 3
= 2*.» Q
_ {i i “J
a T ( Z 22 ll 3, z
. . (1 b ’ 9 V 4' "
4. Aﬁrm's cost functlon IS TC—10+22Q+Q2. Tl or ‘7 7 2.
= _ . mrz 00' La ‘2.
curveP 2008Q ; 3416*? mo, (,4, 286‘ ; Z4:
. .»? . ‘C \ L
a. Determlne the monopoly proﬁt—maxim r7 K 2
Q=9.89 , i 1;} _,
L 1% ‘ 6‘ 2
b Calculate the market price. m n 51 7'
P—120.89 ’ 9.9.7.;
7 Prof F8701] ,; g. ;
i \ 12° ft)? ~C' 4 k,
/7 5. The Inverse market demand 1n a market wherW
/V\'\$ ”W The ﬁrms have cost functions 3.243;, (a: .; (ommm o : 7: ifam‘lw‘
/v’( r ‘»'11 A; .
rm  ,. .5
m TC1=3q1+q12 Mt; : jun. 3/: ,1 ”Wm
TC2=18q2+q22 W}: 1841?” m9" "33’”a‘wx'1‘1m
‘1‘”!  : f1 a’aL'L
a. Determine each ﬁrm’ 5 reaction function. m... 1 . _ c
w . L .
Cournot. :jmcj‘o ’ 131:14H110 ns—l‘L.—Ml—Ui+2t1\£°
q,=120.33q2 '1 ‘ M ., _ ,
‘ ."y ,_.“._‘ w:~Lqﬂ, Li "9
q2=9.50.33q1 1 “'1 ‘ t “ __ _ . _ . .. _, 1
“L kitty? \1 OTS'thﬁm “‘wl‘;__‘_“* r vi.
b. Determine each ﬁrm’ 5 proﬁtmaximizing Output. , _ 1..
q1=9.94 “U“ 4“” 7' ’
_ _ _ 0.;1'thq'g,c‘a:§‘h\3
q2_6'19 q“ ‘2 a (l _ f‘e_q'139x.(.ﬁ7‘“‘ri
1.21:»: :'+_,~qEM,._. '1”: _,..y
c. Calculate the market price. a w J _ «mg: “L
Q=¢74+914 ~ ‘1 ‘ ,—m.
_ \3 P=42.74 35.,'*N+Y «. .1. 
""1 Proﬁt1=298. 04
“ "W“ Proﬁtz=114. 79 (:1. Suppose the combined cost functions are C(Q1Q2) = 25 + 14Q1Q2 + Q12 + Q22
do cost complementaries exist?
+ 14 >0 so no cost complementaries. 6. The inverse market demand in a market where ﬁrms act‘simultaneously is P=100
2(Q). The ﬁrms have cost functions TC1:12q1 .4 ‘ “L1 — Mfr q
TCZ = 20(12 F2 . :’ ,1; ?\::Z
a. Determine each ﬁrm’s proﬁti'maximizing output. 1 1r)
, 29/2. ~
q1 = I6 ! . / ,, 7
_ Z" 11/:ﬂ{2.0r.ﬁ§, 30'}
q; — 12 ' ‘ ‘ ,,»~
‘5‘ 27.404412 A 7’  “
b. Calculate the equilibrium price. 2‘3 a, «2“ q .. V /
Lit \ P = 100~ 2(28) = $44.
proﬁt] : $512
proﬁtg = $288 Mgzr 17/015363w 9..
ML; game — (0%. 9 7 ”in 7. The inverse demand for a market with a leader and follower is P=20,0005Q. Assume ﬁrm 1 moves ﬁrst. The ﬁrms have cost functions é? 9 5‘ 9 5 79 _ 5;:
TC]: 3,000q1 ff ; 0“? ‘ ‘“' 1, TC; = 4,000q2 M': . “’0" 7"}: 1,690,090 — ‘9 9'9 9 12)“ ”7"“‘9‘ Determine the reaction functlon for ﬁrm 2. : Z. (mm , 5 92., ~ (We ’ 19 92' ) _ 5002 4
Stackelberg: ‘0 7; \ ,7 .
Q2=1600— 0.5Q1 4 < (”9999  79.919. 9999 «1; lowal’g‘ti
b. Determine each ﬁrm’s proﬁtmaximlzing output. M“ , M / 4} a 1 0
Q; = 1800 3’ 9 3"“ 1 WW,
Q2 = 700 ”1?”; . ‘L; ii. '9 WO\
‘ p \ l?r’“"“ __A.
c. Calculate the equilibrium price. 6
P = 20,000 — 5(2500) = $7,500 $1 Hz}; , ‘1
Proﬁt] = $8.] million ' 7 3
Proﬁt; = $2.45 million '31; 9 ‘10.;
~ 7i, #07
. . I  . w 2 ' ’ l
8. The inverse market demand for a market w1th a Wand follower lS P=752Q. .f
Assume ﬁrm 1 moves ﬁrst. The ﬁrms have cost functlons ( .
TC1=11+3q1 FWFCL)“ “Sn ’9 (if;
TC2 =17+18q2 949 05» 293.9%.. 9? max. 7 49' '4' ,‘W
L——‘’"' ' l L ‘ 91:;__,,'_
C1. 1+
a. Determine each ﬁrm’s proﬁtmaximizing output. _ a. 1 j «5 0 €
Stackelberg:3( TM" ”/50“— Z‘A.‘— 11,71; ""WH ’
Q1 =21. 75 E 4 . _
Q2=3.375 9. : a — : z @929.) — t *3 2.
,9»? (1‘ , ‘ T . S: L 4 1 I ' fa ’
b. Calculate the market price. ‘/ ‘ " " i ‘ ll" ‘“ ’ 3 A
l
P=24.75 S”; gr a 1‘ pig; 41%;)
Proﬁt1=46206 i 9
Proﬁt2=5. 78 “37!; , 9, c. Is there an advantage to moving ﬁrst? Brieﬂy explain.
Yes, ﬁrst mover has an advantage. 9. The demand for an oligopoly is P=752Q. The ﬁrms have cost functions /V
[y/ ML : g +77%“ TC] : 3q1+q12 New“: VS — 4' Q — Kiri/1Q
ML; a. :; zzTCz = lgqfr‘lz2 M L / a. Determine the proﬁtmaximizing output under cellusion. JfO/M}\TT\.Y WP} WY) /, 9 in; 9", l
4 x.) ., .
7‘99 «"f 0’ “0. '2 9 ’6 «9
{'11: ‘JA
r: i? [48' l7
/ 3‘3 N e«
14—: (111471? 1 It; 191*" e 'M K '1
Qt. Q2129 0% “v 1’ b. Calculate the equilibrium price under collusion.
P:492 TL, 4 path/(gogtcolkott);
4t... ., UAW/(42y; 7.27:, : '
c. Determine if the ﬁrms should collude (compare against your answer found in
#5) 1,.
(“WW ; Joint proﬁts under #5 are 298.04 + 114. 79 {112.8}
Proﬁts under collusion are $416.02 which can be'shared in any manner. afsigu, £34 L4 ; 10. There are ﬁve horseracing tracks in Kentucky. The Kentucky legislature allows only
one track to be open at a time. How does this restriction affect the price the track can
charge for its product? By making sure that there are no close substitutes for the open track, the
Kentucky legislature lowers the elasticity of demand for the track that is open and
indirectly permits each track to charge higher prices. If the track owners had agreed to
this on their own, without the help of the legislation, they would be violation of the
US. antitrust laws. This would be. a form of collusion to eliminate competition between
them. When they get the Kentucky legislature to do it fOr them, it is OK because everyone
is allowed to petition the government—even colluders. 11. A monopoly producing a chip at a marginal cost of $6 per unit faces a price demand
elasticity of 2.5. Find the price they shoulgharge to optimize proﬁts. HE '
. P //;M£ l \— 0
$10.00 per unit if? . t; D I ,  (7:; .
:73" " "ﬂ 9 = 6 ' 12. During spring break, students ave a price demand elasticity for a trip to Florida of 3. The general public has a priC/jcémand elasticity}; Calculate how much an airline
f/“charges for student tickets if the price it charges "the general public is $360. r/ I+E\7— (”51* .BD,P(E\
$270 Ed 3'; ) ' l’ L 73/3) 3" ‘ " 1
n \ Z 2"!“ : l’ 13. You are the owner of a momandpop store that buys milk from a supplier at a cost of $1 per gallon. You estimate the price demand elasticity for milk sold at your store to be 3.5, determine your proﬁtmaximizing markup and price. ?(%)<M‘ :(‘Siilﬁ ca. L‘ P = [Er/(1 + Ep)]MC = 1.4MC. Thus, y ur price should be 1.4 times marginal cost, or $1.40 per gallon. Mikey ‘< 5‘ t
833,9...
14. A ﬁrm with monopoly power wants to practicWrice discrimination. The
ﬁrm faces an inverse demand curve P=2008Q with TC = 10+22Q+Q2. Mr 1 ) 12+20 a. Calculate the ﬁrms proﬁt maximizing quantity. ,. H. ﬂ Q=I7.8 (ﬁom P=MC) ‘ M ’ 9 a . :1 .4 5} _ ./ if“ . . V , . ,,( 3: ("1
K4 559,! zdl'aet 3f; 21/ ,n ‘ l; .
, 290’ 47“ ” a To @402? 2
9’ “oz—4&2 ’WWQ (my) ( j
7 , gala/r (19" ' \ 0 TL: W444
’ @5520” 26’ "I ’ 4
”'1 2292.b4"7’o‘>.49
M/ w ' TI ” l E 04 Z
b. Should the ﬁrm practice ﬁrst degree price discrimination? Compare your
answer against your answer in #4.
Compare proﬁts under price discrimination vs monopoly proﬁt ($15 74.20 vs
$8 70. 1 I which is ﬂow So yes, they should price discriminate.
0. ‘1 H . m .
15. Suppose a typical consumer's inverse demand function for bottled water at a resort
area where one ﬁrm owns all the rights to a local spring is given by P=153Q. The marginal cost for gathering and bottling the water is $3 per gallon. Calculate the
optimal number of bottles to package together for sale and the proﬁtmaximizing
price to charge for the package Each package should contain four bottles while the price for each package is $36. 16. A monopoly producing a chip at a marginal cost of $6 per unit faces a price demand
elasticity of 2.5. Find the price they should charge to optimize proﬁts. $1 0. 00 per unit 11‘1” {L716 AL; ‘
.1; 'k; . l. (20 points) The demand for good X and good Y has been estimated as Lo
Qx = 300 — 3Px —— Slgy : 300— 30 (z; : 7,4»?
, Qy=325—81:Y— 3133: », 325, +0, '30 :Zﬂ’ Suppose that X sells for $10 per unit and Y sells for $5 per unit. 97c Var
[email protected] the own price elasticity for good X (Eprx). 962% 7
,~/~~P/L: '3‘ [(7 ' ,O‘IZ 24770 (32.70 W; I (3 Interpret the own elasticity (numerical value) as discussed in class. Answers of it's
e tic/inelastic will earn 0 points. W Fv‘ve A” 9003 7C incheNes b7 l'ﬂ, (gummy 40V gooJ 1 (14066565 Wm M
by 0‘ I “L M .
c. t 'lculate therstrice elasticity of good X in regard to a [glee change of good?)
y)~
@x (‘9
2/'~/ 2 .1 . ,(7117
3.? y 62.» Z45 ' '
u hat is the relationship between X and Y? Brieﬂy explain.
a may . I / 0‘10 Wcﬂhs goods/1am) jr GM (th‘tkvénk we“ MRI”. \ ‘ v a“ k V» ‘ v M0545
bemmlft PVH’cp" 3‘ t CV‘MKS k, l / Q 53::sz 1 $66 I an; Qua‘ALBJ) 7C 0‘50 JCCM‘U‘c’S' TA he government want to impose a price ceiling of $25
0 (5) Find the full ecgomic pr’ige.
ll+$p:zoo‘2l° " V1 ‘2’? Opus:
From the prior7 page S v 7t : 73677 62471
QX = 300 — 3l3x — SPY 2 Z4? (:1 l 45 }Q,+ 9x to
=325—8P—3P : v ‘r: ”L /;,3./
Suppose that X sells for $10 per unit and Y sells for $5 per unit. a ’ {7 '1}
V1, 9‘? ‘
e/(»¢1terpret the cross price elasticity (numerical value) as discussed in class. Answers of , complements/substitutes will earn 0 points. is sotlg (M55 [nitL Claﬂi’ci‘j \«F 909190 M regard
/
(r0 yaw 0+ foOé 1 Ur “an; m... :5 Moe W them!“ 5; (‘4, QM? 08le \qujoo.1»3c decreases. 5:344 penis. in“ 7 Emma (0 ””7 0M (ewféhéog‘ 2.9 4 m
f. he firm is considering ' g the price of good @y 2379. Calculate the change in
' = enue and determine if this is a good idea. # 09W ,, (gaming; aw") + (2cm: Q's5619.9»)XAP,‘ l answer (worm rW’CC) (2W0! Of? + [145 x 4M7, )co.oz, ( angle 0.1% )4‘0‘01
2003 (’o‘0 ;) n‘nw 03¢“ ‘5 ”9““ d 9'»er aim:
FQVC " 40 of. [Fauna mu Macaw W W V0? .tux. Tl”; m 9‘” l
2. ( Suppose market demand and supply are given by Qd = 200  2P and Q8 = 11 + 5P.
h 2,”?  2% t Z \
9:? \\ if? = W?— Zl’ 27 Qé’ , . 7_ QP;‘[K “36 I ’6 L7 . r
l) > 191*” raw26‘!
b. (5) End the HW cost. 1%: 0”,?
U,(§(;(9b’?/V
(1911??
Fill.” t0 ‘ ssume the demand for the following goods is elastic
obiles c. 1968 Ford Mustang convertible
Rank these goods in order from most elastic to least elastic. Then brieﬂy explain why your first choice is the most elastic. A
W Van! manna W?” W‘“ “‘7 Mk" 900 ‘ . 5”“ *5 . 0" Q {I 5
most elastic C 777‘: '9 \k View \ I400 FWJ M «Sit—0v“? ' I *kmk FO'A “Ammab e
2M1 mOSI ClaStiC#‘0_{;a;‘6T \ \\\\\ \N\ male {in ML 9 «in! Mqo an “hype ,Ovla’l’y (”A
. . . . ' "50‘". “WNW leokh‘ﬁﬂkﬁhmbﬂﬁhS'ﬂlféjj‘fﬁ
least elastic 2% mos+ 61am . [F Print 0} F°rd (‘95 I,” 0W» am.“ y , Work (as
t a . r
LQCGV‘“ I‘r/J we“, 5(6‘7 ?0°cl5 cur VJ ' Man/M‘ Q g C 6% V)“; WW5 5‘07”“ 0+ four MhSVo/«mh‘m fny'elvv .‘Z‘wwﬁy ﬁtﬂmvﬂobilc is #1. low elfMg CHM—c lv buy \ \
0\.\Q, ()ﬂ 0‘02} 5. (10 points) The demand for good X has been estimated to be Qxd = 25 Px Py'8 M6. a/gCalculate the iszoih/"e elasticity of good X (EQXM). Show all math for full credit. m ﬂ“ W» «.
03 3—73. it " r b. ) Is the good normal/inferior? Brieﬂy explain. / ‘4, m {AMoum’c is Vasih‘uc, 1 ts Nova"! 50.1. \{Qg
l ,,
J . H W AM°“‘“‘* ‘5 WWW“, xi) with“ 7” . c. [Miterpret the income elasticity (numerical value) as discussed in class. Answers of
Z normal/inferior will earn 0 points. FOICXMTK‘I TH vii/MM"? a} in com elﬁSﬁU}? ‘3 2, ll: ﬁlth”, L5 NOIM“‘§°°J~ LC C“‘”’*
)4 COM ice} U? *7 \tl. I M F640“ VI.“ \‘nCVfIK 04%;? 6"” plmﬂﬂé A” (100; 7L V7 17. ‘ THNQVI, ”’3 "Orwd 79"1‘ Circle the one best answer. Some answers are rounded. Round to the 2nd decimal ie 1.23 1. (5 points) Which of the following cost ﬁmctions exhibits cost complementaries?
@100 ' 4Q1Q2 + 8Q1
b. 250 + 8Q1  4Q; 0 125 + 6Q1Q2  Q1
d. 100 + 4Q2Q1+ 8Ql 2. (5 points) Following are the costs to produce Product A, Product B, and Products A and
B together. Which of the following exhibits economies of scope?
Ca) 50, 75, 120
b. 50, 75, 125 c. 50, 75, 130
(1. Not enough information to determine /_ illion, and the remainder at $1 million each. The fourﬁrm concentration ratio is: 3. aims) There are teiiﬁnns in industry with sales a{ $6 million, @lionrg? million, (a
a. 28.91 nee . .0
4972.73 @ V"
c. 52.89
d. 81.25 16
e. other: (ﬁll in value) 7 : 172.7;
2 4. (5 points) There are Q ﬁrms in industrywith sales at $6 million, $5 million, $3 million,
$2 million, and the remainder at $1 million each. The HHI for the industry is: a.2891 , ~ 091139” I 2.? . \
b. 1530 ; 0* 5 7"“ ‘i”
C. 5289 ! b 'V 2 2 Z 3— 1 I ’L (L L
a? MC (if/17,114 (3%) “(a )4LLL24gTZt)+x{1l)
e. 0 er: . . ‘ ‘ (ﬁll in value) WNW/J MHZ M A; 5. (50 points) A ﬁrm is operating in an existing market and unsure what type of market
conditions it faces and wants to use the tools of economics to see if they are proﬁt maximizing. The ﬁrm's owners have requested that you analyze the market based on the
following information: a N" Because of consumer’s easy access to price information on the intemet, the ﬁrrn's owners
" ’ “ want you to analyze the market for product X to determine the outcome if the market is
b perfectly competitive. The ﬁrm's cost function and inverse demand is estimated as a TC = 400 + 4q2
P=225  8Q
a. ssume the market price is $88. Determine the shortrun single ﬁrm proﬁt
‘mizing quantity.
@ '3‘:
&_ ('MK r:/V‘L TU; (1’,r(/,
' 8"". 3'4 1994" (“90+quﬁ)
' 2 it?  r W
@
: 27$;
4 , _
nu '— M‘ b. ﬁNow predict the longrun the longrun market price. £9
‘ 1 ; r \ q 0
01“" Mo: Mb ‘ 1t 400 f“ F 91“”
Se+ MP— ' I a" ’ ﬂ
fb @591 ‘ quéllﬁz
Pin 2 q‘ 1 CW"
we: are ———————~—/ ﬂ .2", O M
a.  f
490 Heath8'61 400‘ 44‘7“: 8’93 gmk‘ ,, 0
l 400‘ ‘E‘U $1 {‘7’735—0 '{f ($1 (/8
\\ {gowa/ Ix/Jﬂ‘fu (+90: [111 at _ g 004
F 0. Determine how many ﬁrms will exist in th  arket. (round to 3 decimals , e 0.123)
@ 4151841 Q P // \) I
&; M8"; 2 44%, q? : Liv/Kg",
pm Iqamg 2'23:le some: 3‘8707 Vi: zztsrll 7L ._ inﬁgj C‘M' Finn; d. /5{ Find the equation for the longrun market supply curve.
l7 : M 9 Mﬂz/‘M W 1 (M Z ?Ls\~n\;) ; 8 q‘ I 0
i ~— (Mo l . Ococw—FH , 2 Now the ﬁrm's owners want you to predict the outcome if the market is @stically
[email protected] The cost function and inverse demand is estimated as
' TC = 400 + 4g2 96 Nylptcmo‘. =225  8Q ”Wmm ‘ __
{U m. e. Determine the siﬁgﬁrm shortmm proﬁtmaximizing quantity. (Do not assume
m P=$88, you may need to ﬁnd the market price. Round answer to 3 decimals ie Qi‘hg’“ ’ 0.123) MM PH“: F: 99‘ : [~1qu 1/1"?"{ngiﬁ'fﬁ
F” [5’0 Z (”0" F L——.‘“. ._...W~/ z
7 (799m 119m 17% 52;. ‘1! 1504;) M043 — (uao+#(w.oes))
[2" ‘ I“ 8% t« 
IMO/“NZ (“was _ : 1531.03!“ HWY”
[of/TUNE :7 ; 307 9517
, , f. Wetermine the longrunproﬁﬁﬁaximizing quantity. For ease assume, P=$116.
f‘707r n‘ Tb'o r,
‘ ,; A1L( F 4&1 'ULQ «PW: 0 14
’ —,  #00 1‘ 4 l + 4 l:
(b ”sz in t 9. 3:2 4/032} We “WEE—4am»)
 4+1 CH
.  a + ,, L
9x£_7,1.¢0 ' W 44‘? U ‘2‘ ”Li” pg,” “5"” ~
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g. Find the equation for the longrun market supply curve.
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inverse demand is estimated as TC = 400 + 4Q2 P=225  8Q '
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 Spring '08
 Sengupta,J

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