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**Unformatted text preview: **1. This problem will be easier If you hove done Problem 18.1. A ﬁrm has the production lunch 8. A ﬁrm has a production function 11.1.11) II 0.410(55” +1.’E""'°)I whenever :1: > 0 and y > El. When.
tion mama) = ﬂweg'”. ﬁitmqumt on whjiuipnt is 40”” line the equation the amounts of both inputs are positive, this ﬁrm has
'2 0 .
@dm[10'~%: rme53;
(1;) n = 40:15. re urns .
(B) 21/1: =i Llo .1 477-” 51:11 l3 bfﬂ‘ (c) constant returns to scale.
(:1) :1:z=40:1:f”"u ‘ 2 “1 risk MP (d) hie-easing returns to male if z + I: > 1 and demeaning returns to sale otherwise. (a) axiom“? liq, , 471 ”94 l; I)“ ll ﬁclﬂ' -& (e) innmasingretums tosoale ifmrtput is In than 1 and decreasing return: to scale il'outpnt is
Bead“ (.pr greatnehnnl. $1
' m ,1 P 4,, Hm" I, 017 3 7 ‘J 0.7 0.7 017 3
2. Aﬁrm line the production function f(e,y)=z“°y""". This ﬁrm has fl? L“ 5" 313125. 0! liai-Ab) + (t b) a”): 014 (.2, (”+6 ))3‘: IOJLI (all 3‘31 )
(n decreasingreturnntounlearuldlmlulnlehlngmnrglml 11111111111512:thng —015' [.7 51H“ 'l'llc Sail») ”1”,le bag 4-,». .eifmpﬂJ-ﬁ 9 Vad- 9,. “Hi-Ml] =3 IRS
4: _ . . .. %
mm“! mum "3 ”'39 “d dimmhh'g mnwl Wm 5“” fut“ x- — 0' f I 7 0 4. In Problem 18 3, if the production function were ﬁsh-1:2): :‘l’me" '“ ,this production function (a) drawing return: townie and imaging marginal 1:211:11an for factor x. _ ’5 would exhibit (mnstnnl, increasing, decreasing) returns to scale and (mid, would not) have
(d) constant returns 11: scale. ‘- diminishing technical rate of substitution.
{9) increasing returns to mlennd demeaning marginalploduct in: fmmrx. 2 6Z0, (A) constant, would 5 [Jun 5 it €¥PIH§Vd5i 016+ﬂl l = 0' 7 < l A)”; r154, H1.- ;
fit/Ll ")1 ﬁtting Sim/I141 (b) eonstant. would not :DDRJ' (a) decreasing, would not
2. In Problem 211.2, suppose 11111: I new alloy in invented which uses copper and zinc in ﬁxed (d) immuing would All Cll’h— pfk5)£15 pwoiuceimn ft: VIC/7L my apportion: 11111.21: 1 unit of output requires 2 units of copper and 4 units gt“ zinc for mid: unit
0111 du Il'noother' isnreneeded,the ioeafc Eris 2,andthe 'ceof deg ' 1 Id - '
zincli‘iysmhm is the engage my): unit when 5, Oogxunits ofnlt’ilie alloy are producgrdl'! reaslng wml ll“ l/(t'. 5‘ 6i! “MI 11 1,5}! I H 9 T5
TC _. Wc -(_ + win 2' 6. Two ﬁrms, Wickedly Efﬁcient Widgets (WEW), and Wildly l'epotisliic Widgets (WNW),
(11) 3333 both pmdnoe widgets with the some production function y = K ”2111/“, whale K is the input
t 8150 - :(2) ((21571!) +(3)(Lf1E-M9) of capital and L is the input of labor. Each company can hire Labor iii $1 per unit and capital
() at $1 per unit. WEW produces 10 widgets per week, choosing its input combination so as to
(a) $0.75 __ g" I ”J to produce these 10 widgets in the cheapest way possible. WNW also produces 10 widgets
$18 3? I,” per week but its dotty CEO requires it to use twioe as much labor as WEW undo. Given
T L _ I = I 6 that it must use twice as many laborers as WEW does and must produce the same output,
(9) 531375 AC = .75 ’- 5-,”! how much larger one WNW' 5 total costs than WEW ’5? N fl +15 4“ < F| rm ”54$
‘ l
5' 3011:1213?iiiglfalll‘:glidiilliinolrlhzillzawew “11,112,13): Ami-‘an*”w3‘m. the Mn“ {3) $10 per week E41108" I Fl rm ‘20 U h I45 V‘c [‘11 $4. P
(1:) increasing, dlnlinishing,nnd constant. (1:) $20 Per “8k J1 Cd rl< ‘— H [5,12 09!:
b dimin 111 .111 'n , nd diminis in . ..
é ”limlje:ngcmse III! (e) Sniper-week if: [ML—L (‘3:
(d) nlldimiuishing. @ 35 1’" weak if "'L '-
(c) all increasing 1m > 1. ) $2 per week _ll_ {L [0 ‘ K1“ 20'”-
614 : L' U“ “’0 : K 7—0
0.4
— I15 , .- “‘
Wt ‘MA Aﬁzﬁjlz ,ncmsmg 1» @, l0 : L; M-K 17- Kl L
C2Pl<+w _ - C=r<+w
(3% L‘- l'M‘)‘l'M12[7 : |I5+ “21)
I
d/lr/ L314» 'q ‘75 [.2 :1?A 7
12W} 1 n6 “”5 ”47 m $2 5. 11: Emblem 29.11:;A1’s production function ior deer il](a:11,zz) = (211=+'52)”‘.‘\§rhere x1 is
z 12 = 11 2 ii 6 u u is ,i *- -= amount 0 p tic and m: is the amount 0 wood used. I the cost of plastic is 8 per unit
5' ii milimndlinlfiifiée'ai i), is‘ii. .7131. {hgﬁdﬂﬁlhgiliihliziilgllinioﬁh‘itf 3‘ the I” “ °f he cost of wood is $5 per unit. then the cost of producing 6 deer is (
a IbItIVWlﬂ/z (an fer-[ed- joins-JJJnDIﬁ. I-IL I5
(1’) 2 51‘“ Cl #1 Use? w
(c) , $126 C‘MPW ' ([[6 J “ 3484- 5 19
J ,— F
(d) ° $180. (5% +17)U > L4
(e) There is not enough information totall. $24 : l 4
‘ ‘ 3‘; : 2147'
471 “Ml A71 ﬁll“? Pfr-[Iec7l 5“}5711‘11471451 A’ 330‘ it’d?
1 r J
W’fl‘zL le‘xltmfl In? firm W-U “R H4 CAM/4;— ,
P 111 Problem 20.3, the production function is HAM) =4LV'M1/2. where L is the number of
one, 2 «“15 MC NL/‘Pvnl Can 1% pHI/ucn/ mumoflahmandMlstheimmherofmsdllnesmed. Ifiheoostoflnborisﬂﬁperunitsnd
J. 1,: ilie cost of mines 13 $36 per unit,tl1en the total cost oiproduclng 10 units of output will be A
l : ' d 3‘ _ _
M Z M 1’ W1 2 32“M 9 By Hm airmen rule, zC‘ wL ml iC— Win/l
a. $150.
wli'lx ll/hn‘l- [/1 4’ _V“_’_— ' 6
a 2— 2’07‘4/ '11) 5305. 9% 36M 0' L: 3’ S'M
2.11.45 we 4.) mi ”2 ilk/1 Inuit; J /p 05% 50,11 1111. (“~12 '11 35' 25.140
1 (2 ‘ i L". M
:D Fulﬁll/l: ill" 4‘""CJ;(:]: 9‘ my I La" 47, 5) $30“- Q0): L M M lé‘ 3L
None of the above.
tr: _ 01124» @410 ‘9’ -532.
W) W». ’ > ”it" Ill - IGL M All 1 ﬂ 61W 1.11 MM bid ' mill—4191'”: $93 .1
C‘
11
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9&2
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2. In Problem 21.3, Rex Corr disposes ours, and has three methods to choose from. First, he .2; g}, a could pay $10 for a. shovel that lasts oueyenr and pay $5 a our to his brother Scoop to bury gig: 5 the cars. Second, he could buy 11. low-qualit car masher that costs $200 a ymr to own g; g 5 and that smashes can at a. marginnl mat of 1 per our. Third, he could buy a high—quality .3‘ 6"." §
hydrouliccersnmsherthntcostﬂﬁﬂperyesrtoownandcoulddispooeofcsrsotnoostof H ll :1 Egg; $0.50 per car. It would be worthwhile im- him ho buy this high-quality slumber if he planned 2. In Problem 219' suppose that [mar production Emotion is 11.21.22)—(min{m1,2mz})‘" 1f
“dial’m'” 3mm level ,4: “ﬂan-f M unmimdfmlnw,=§rsomduupnoeornmziauu= $B,thenhersupplyfunction J isgiventwtheequation lit 4,- 91¢ 0 #1.}!!! »?b‘ '2
attmtmmwm 44‘ LL! 5531 doc pied-{uni} 2mm sown/13151,,“ e {‘3 :1” M. u n c ,-- ’3
(b) nomomtimnlwcarsperyenr. “V4 6%“, I {b =1}! C(19): Wan/Wu.
' (b) 5(9) =lexlwliﬂwallﬂ- z (1:) utlemtS-lﬂcmpuryear. ”0+6: 357+. 5—3 S _ min a 2. t 5’ + $11 (d) no more than 300 cars per year. 0 (c) (p) -—p{ [w1.2tna}) ' 2W (9) at least 150 cars per year. 6-0 :. I 5— (d) 5‘9) m 91" ,5 .—. 3M (9) Sipi=min{5p.lﬁp}- WC)
3. Mary Magnolia in Problem 21.4 has variable nosesequn to 1.2/1». wherey 1'11 the number of Sc‘l P534 C “7 P" ”'36 :3 0:19/[5' bouquets she sells pa month and where F is the number of square feet of space in her shop. If Mary has signed a lease for a shop with 1,400 square feet, if she in not able to 3d. out (i 2. If in Problem 27.4, the inverse demand far bean sprouts were given by Pm = TED — 41/
maimecrtoexpandhm‘stm‘e in theshort run, and iftheprloeofebouquet is 8pm unit, and the total cost ofpmdudng Y units for any ﬁrm were ICU) = 401’ and if the industry hm" “W ““4“" 1"” “mm" “mum “be Ed] in ”'9 “'0” "1"? consisted of two Cournot duopolists, than in equilibrium each ﬁlm's production would be ‘M l’ a 4m5¢+ P; M: P1760 ‘IYI ~‘le Yt‘lO“ W'Lé:
U :2le ( ): 2(5 2/15 ,3 (a) 91111111111 I 2.
g 7110 MC; 40 : HM __,__ (b) 45min! 11?,2 F‘i’l- THYI ‘l‘l’ —-‘l. Y1 Y1 :‘M-‘lf'ﬁli 2.100 d 6
(d) 3.150 [322 F W 3011111111. MKF $59 750* 3“ ‘l Y1" ”"49 A“ ll’ *4? q
_ ﬂ —— so nits. ‘3 _ ”l 1' _ '
(a) 2,310 55+ :9 3: 700 e.) {3 , 2 MW @ " i”, 72" 1W1 6Y ”Md" Y1 2 £0 (e) 47.50 units. _
Yr- 70 % Y, 411- 121 7. The city of Ham Harbor has a perfectly competitive market in taxi cab services. The marginal The demand for Professor Bonsmme’s new book is given by the function Q = 7.000 - 100:2-
cost of a cab ride is $5, and the daily capacity of a cab is 20 rides. The daily demand for If the cost of having the hook edited and typeset. is $9,000, if the marginal cost of printing
31d ridezgisdDm 11,500 — 100p. The city council issues licenses for ear-h existing cab. Soon an extra copy is 4. and if he has no other costs, than he would maximize his proﬁts by terwor , emim increases to D(p)=1,700—100p but the number of cabs remains restricted , , . . .
to its original number. As a result of this, the equilibrium price of a cab ride rises by . haw“ 1" “mad and typeset and ”smug 3‘3”“ ”pm” P: 70 "‘ g (A) $1 5 5+ P: 5" ”‘00 .. NWT): who My]?! (b) havingit edited and typeset and Belling 3,500 copier. ME ‘_ 7" l i? ‘f _ 41
$2 61‘” Aemed, (it‘l‘y ”fl/“95 1'0”" 9"" (c) not having it edited and typeset and not selling any copies. 6 — '5? ‘— 1 C
(c) $3 I"la/22‘ : Y0 lax I r. , (0‘) having it edited and typeset and selling 6,600 copies. 6 3 62/57 :> Q: 33 M (‘9 *4 0 I000 f 1700 2 M0 P f (3) having it typeset and selling 1,650 copies. P :3 7
(9) $5 100?: 79ﬂ FY r-é rls‘ll‘ W
PF - . P z 7 5 h '7 “(37) (3300) {4){33/2) — WM 3. Problem 23.4 descl'lbes a perfectly competitive iildllstry. Suppose that cooh ﬁrm has thc cost I
function c(y) = pa + 36 for y > O and (2(0) = 0. With industry demand given by 19(32): 60 — p, I: q 4' q [a
the equilibrium price and equilibriuﬂ number of ﬁrms in the industry (in that order) will be 36 I F A], C : 2 ’3 AC: ’5 + ‘73 Rae-ll that Touchie Mcﬁelie’s pmductian luuction tor comic books is lJ‘I’L‘I‘ Suppose
(a; $3 and 10. Zﬁ um 'Dmchie can my both join. and cuwonixts’ labor, [fold jokes .2... :2 mil nnd cur-
|2, - ______ 2 = ‘I‘ worms no.» cost: on par hour, on m cheapest way to produce comics books requilcl
01) $6 and 9. , - A35 3 usingjokes Ind labor in the min |
_. L 4 ya e':
(c) 55 and 54. 6 _ ,5 ’D — ,5 (t) J/L=o. Efﬂmn ’- -
@l) $12 and n. rm“ ‘ll 3 -3g 0,, ”,5, z 1 3pc : .2ng — 23’
Ind-red.) _ (c) JIL= 2. 1-3 C
(9} $12 and 48. — r ’3 — é (d) J/L=2/3. 2 "l
lincl) lr-x plrdblfp 6 _ .l/L=4.
‘ 5 mm 1 3 m. 12L
Indus 4:7 0“ m4} Ll 5 2 ‘l L .5 “g ﬂ : L ‘1. In Problem 24.6, if demand is described by pm) = 200—1], there are no ﬁxod costs and marginal
. z 0— I2 ,1 3 cost is constant at $20, the price elasticity of demmd at the proﬁt-maximizing level of output
ﬂ 2 3’ {r rmr - q 5 1+ ‘l is
6 r 3 g _ H” r w “12:21qu :20=MC
Smugglrr 3945 pawl .‘I bird lulu and is unlttdfdJ-U’l‘ r “50: ?C ‘ I, (3 :2“: “012,5
Palm dr mold-add): FUN“ Palm/HIM“) ""' MEMO' 0-4 3 6 244 @ 4.22. w
1. Suppose that the cost of cumming a on too and tl'umportlng him to the US is about 840 (‘§ C) = ?— C = A? ' q a
per bird. Codmtooo m drugged and smuggled in suitcases to the us. Hui of and smuggled (‘9 439-
cocllutooo die ln transit. Each smuggled cochotoo has n 10% probability of being discovered, (e) 4141. V: ”(5
inwhlchcaaetheomugglerlsﬁncd.Ifthoﬂnolmpoocdforeudimugglodooclmtooialnv (,3:qu
creased to $1,400, than the equilibrium price of oodutool in the US will be
@ . :2 .. mm“ on. o. 2, 9mm)” exports 3 g: M 2 L10 _ _} 22
400- 7“: “":"6M’ .
(b; 8180. 4' "‘8'" 0'45? MC= 40+(0'l)(lqm) : [35' 8F 3
(c) 3110. ,_ [$0 2. Suppose there is a constant marginal cost of 85 per ounce for growing marijuana and deliv-
d) m 0 I45 P ' using it to buyers. But if caughtl all marijuana in that shipment in siened and the supplier is
;) 33 ‘ P __ 4 a; ﬁlled $50 per ounce. The probability that any shipment of marijuana in seiner! in 0.10. The
9 1111- ' illbrlum rice a! marijuana ounce in
9111-1 p pet a. A proﬁt-minding monopoly faces an inverse demand function described by the equation SC ”if {Ypéc'}: l1 We, 4." 0.4 P My) = 30— y and its total costs are 11"”) = 5y, where prices and mats are mounted in dollars. 811.11. Intheputltwasnottaxed,but nowitmustpmvatuxol'ﬁdollarsperuuit ofoutput. After M C t 5‘ + 0" {51) . the tax. the monopoly will + + ‘ (b) 510- In 41hr; e n billfl Var M n (c) 955' ': [0
£
(a) imeitspricehyﬁdollazs. WWS -Hn5_ sl’il ("wimp/l). To (d) 3450. 0'0] {9:110
g: mrupmelryndplun. (”We {mrrrlfd/I‘I } 5.3+ MﬁuML (e) $5.50. _ H H
inc-me its prloe by 3 dollars. P — l d m.“ . m t and Sllln For PH”. Thfh 5182'}. Apﬁee-diacriminuﬁngmonopollataellsintwonepuutemuloetssuchthutgoodssoldinane H 1 PW” 3'" market uremwer resold in the other. It chargestdirrone market and $12 lnflleohllef mur- re) N... .......... M K = MC + 2‘2 W .. M 2‘» 2n .2 .2 2 22 222 222.222.22.22 22222.22 2.222: 2222.2 sewn Ill!!! l3 — . . 0 l 1' In 11
1. In Problem 24.], if the demand schedule for Bong'a book is Q = 2,000 — 100p, tho cost of proﬁts? 113 p0 honing tho book typeset in 885”), and tho marglunl oust of printing In mm book is 34, than 2 H MR: [if] + _L
he would mlxlmlne his proﬁt! by P _ 20 _ 9/”! (a) [m M {£4 E
(a) musllupuomdmlunnsmmpnd TR:P-9= zlﬂ‘ @7/14 @ M”: I; S; -0qu H,“ MR2<0
(b) havllls it Wet and Idling 1.000 copier. MR = 47K : 20 - (9/5! (c) Rnisep. and law “I l \ . a ll
G9) m“"mm'm’mmmmmmwwmmgw a) u — Ill/177:4 (d) Ralnebothmundpx. Flv‘m cln rune P2 A52 w.” I
(d) huvluglt mantandsdling 1,600 oopiu. 4 _ 340 - 20‘ 1d: l2 {2) “Whammﬂ” ‘ i
(a) hminglrcypmlandnllirruoodopm 4/77””: =7 (- ’ ‘ ill and TKZ W|ll increas4 IF=02VW)~ («)(rwl— 8m . - W lProblcm 24.2, if the demand for pigeon plea is given by p(y) = 70 -v/4 and mo(y) = 0, then
the level of output that will maxirulue Peter’s profits is = 13-1, TK=H < 6‘7 a (TM! ml; . 2
MR: [6-21. Sarah frlre m/mrrllhl Fwdvlwr ﬂan/7.47 @ 140_ TR;- Prl’: 70Y _‘ Y/‘f
: b . =
M C 0 a P: g You must work HARDER! 2 ( J 38 M R %TJ§ _: 7’ - Y2...
MCT-MKQ [(773) (c) 280. Y
(d) 420. M R-tMC => 7
4. A ﬁrm has invented a new beverage called Slaps, It doesn’t taste very good, but it gives a : p—
peopls a craving for anreuce Welk’s music and Professor Johnson’s jokes. Some people are (9) No.3: 0! ﬂu glam; 'L
willing to pay money for this effect, so the demand for Slaps is given by the equation :1 = 167?. Y;- J (’0
Slaps can be made at zero marginal cost from old-fashioned macroeconomics books dissolved “
in bathwoter. But before. any Slaps can be produced, the ﬁrm must undertake in ﬁxed cost of
369. Since tho inventor has a patent on Slaps, it can he a monopolist in this new industry.
5. In Problem 233, market demand is equal to D(p) = 20 — 31a and individual ﬁrm supply is
(s) Th: ﬁrm will produces units or Stops. Sﬂp) = 11/2. The ﬁrm cost structure is such that if P < 3, all ﬁrms in the industry would lose
@ A palm immmmem mum be achieved by having the gamma” pay the an“ a subsidy of money. The equilibrium price and numger ofﬁrms operating in the market are (in that order)
$74 and insisting that the ﬁrm oﬂar Slaps at zero price. ? y 5 If P: 3 D [3) 3 267 HTP : I l
(a) non the point ol’view of social eiﬁciency, it is has! that no Slaps he produrcd. $333 and 7 b’ A 1 -
- - + ghj’ «h lndlwdh/ {mm
(d) The ﬁrm wrll produce 16 unlts oi Slaps. I . (é) 05%5 [7.8 (b) 3330 and 6 P3 . I f
“7 (e) Noneoftheabove. rm“, (“NW”), 51”,; u; :5? .1, I ’ (c) 33mm” /' gnaw“ % “nil; ’4’. you/1m
C5 > DH (15+ 1? SIMS If A”; jib/Vina. (d) $3.14and3 D H p, M} prey. {7 ”(wail/4’ by
ll ﬁlm/7 we ”34 '5 will, C m m (e) $3.33and5 P ”3 3/2” “/1 : 7.3}
an 5 g 7 2 J
ymlm-lwnl tr+ ; .l/ R55 : ( ) .._ : :3 N - .. :3.— H
[g 57 7 2 2 20 F “D 20 1' [13 F a.) F: 56" Ed? The city of Ham Harbor has a, perfectly compétitive market in taxi cab services. The marginal
cost ol‘a cab ride is $5, and each cab has a daily capacity of 20 rides. The daily demand for
taxi lidas is D(p) = 1. 500 — 100p. The city council issues licensu; for each existing cab. Soon
afterwards, demand increases to Duo) = 1,9uu — 100p. If the city council wants to maintain
the original price of a cab ride, how many additional licenses would need to be issued? 5[£l=‘lf’ diam“? 2:) 21:. 7? =2 3’: g = 2.86 4. In Problem 23.9. there is free entry and exit in a perfectly competitive industry and the demand curve for pollicles is negatively sloped. If the government imposes a tax t on every :3 :0 0'} Vein Inf’ UV UL? "1 4 Ad 'FM halal“) [ 11M - M067) : ’qﬂﬂ unit of output sold by the industry, in the long run P
- I
(c) 15 ‘r hold w I l l l72 d9 ,1 1.. ,g C l l (a pm a . f fewer polliclw will be sold. k 5
or J ”1 ‘ . S
20 (h) more pollicles will be sold. -a
.2? (e) 25 n q 5 Purl/L) ll He 5" 4")“ f 311 3 f I"? It!” —/ﬂ/ﬂ 3W0 (c) each firm in the industry producing more polliolos. r‘l A? 5 ‘ I 4‘ (11‘) each ﬁrm in the industry produces tewer polllclg. D ’5 P‘lﬁ/l (e) the same number of pollioles will be sold. Cal? Mn 3M 20 his?
- / 00
“('94 %;:20 more lull:- I‘Crt’ﬂf-PS in ‘l'lla LK‘ Firmi exr‘l l'hé’ [ho/W571“, timid}
rgmnlnlm‘ 4‘,er earn 24*! Flu/n} “jﬂ‘rh ...

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- Fall '12
- North
- Supply And Demand, WEW, Slaps