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Unformatted text preview: ln Pmblem 343. suppose Wilfred. a typical citilen. he: the utility function Utm.d.h) 2
m +114! — ti“  animal). where d it the number at hour: per day that he Ipﬂndl driving 16 000$  IMO/5‘ I
‘———— nrottnd. h lo the total number of how: not thy spent driving amuwd by the other man Til Fer b..4 u 4’ people in his homo town. and m is the mount of money he has ten to spend on other atuﬁ
‘H‘ i” = 2m»  [pug M n... 5&2 besides gasoline and auto repairs. GI: and auto repairs cost $1 per houroi‘ driving. [teach
l“ "'4 him, I ”:0 —‘m citinen believes that their own driving will not affect the amount of driving done by others. they will all drive Dr hour: pm day. If all citizens drive to maximize the utility oi a typical “—= ulnawar —2, m =0
Z'ilﬂlo : m”;
ILI : 4' 69 D. SandD;=3. citizen‘ they will all drive D. hours per day, oi Wold '= ”201 :Epl :5 “9:24 455' '2. 1 , ., 4' Modal
Indnib, [7le .c 1 A “12:”: (h) D. =m5. Ll . W ‘l ”oi A irﬁ)’
[Erzém44/thllma ““‘ ‘ (c) D.:7.mp3;¢I z m +7441?
=Z‘i.m4m.t1 (d) Dr=snmlno=o Jul/0H 7 24 l __7 0! _, '5
a5: 2mm ~2.”I¢=l rel nr=bonno, =1. ‘ ' ' z
a. _
”k;— l1 5. (See Problem 23.1.) n the number of persons who attend the club meeting this week is x,
/\ 1. 5m... Mn. N, W “warm“. H... t... r. "M P. then the number of people who will attend next week is 12 + o.1ox. What is u longrun
axiom. at: iKJKmrﬂumm th wart: “warm equilibrium attendance for this club'!
cmrimtﬁ'iuyurginLniqmpnii'mbonxﬁrmmimunrnbuu X I; A P.9y5ﬂh “ﬂiphla fl) «Hwy 3"“ ‘4? ill in prtmh C0K}L(I(/)‘Iln but
mmﬂiﬂﬁgtﬁ'nﬁﬁmﬁtﬂwﬁfﬁiﬁwuwb (a) 12 x: I’ll“ (7‘7 2. (SeeProblemﬂjJAmullomnmunlwhas10wple.eadlofwh0mhmawenlthofslﬁ,000 "an;
(b) 11.14 ._ 7 5C Each individual must dinoee whether to contribute $200 or $0 to the support of public enta )
w xmmx“ ~00)! 0‘ tliumentfortbeirwmmunity. Themmwyvalueoftbebmeﬁttlmtoponwnmﬁunthia 9" 7
(a) X: "mm Xz'm i” 24 0 3X ’  ,2 public uttertninmsnt u 0.55 turns the total mount of money oontributrd by individunn in “ct I
= = @ 40 . — the community M?
(ED x.u..dx,—u __,\, —, h:
(d) X. ”and Xx=m (a) 23 0 ‘7 503 (u) 1:: gaunt bu nNuhequilihg'umin whinh5pevple ourtributeMuud lot public atth Iran», W;
X : u soeoplruontnbutouothlug, W‘ “9 .
I I . " ' ' ' ' " ' (b) This game he: no Natl: equilibrium in pure stdataxia. but his 3 Noah oduuibrium in mined .t.
4 An allpuri :8 located next to a housing developmnt. Where X is the number olplanen that Imagine. “"5 ‘5 4 ‘
land PET dW “'1 Y is 1‘3“! “ll1111191 01' Mum in all housing WWW. Pmﬁlx 0‘ the li'PDl" (c) This wine has two Nunb equillhrh, due in whim everybody mtributur run undone in which re 4’0”“5
are taxi)!“ audproﬁts a! the developersromY—Y’—XY. Let 3', bethenumbernl'hnm nobody muibutruaoo. i will’
built it a single proﬁtmaximizing Pompom lawns the airport and the housing development. (d) This gum hue dmuillantmategy equilibrium in within all 10 alum contribute mo tompport «H. o , M9,.
Let H; be the number of houses built tf the airport and the homing development, “a operated public entertainment. M ”I”
$199???de IElie alil'pul'é has to pay the developer the total “damages" XY done by the L mount; hasdomlmnt muwgouulllbnuminwhinr nobody oonhlbnoor urythlnghpubllep 7"” 
zines u eve per a pm to. 1, '1 _ . entertn mneut.
 wk 29'  a» n' = 1 _ 1 .
[fl _, 33m '1 f) ’5 ’1) 0 5/3 13 (”pm
(a) H: a H: = 6. A “I d A "D J 3. (See Problem 28.2.) A smnll community has 20 1350312, each of whom has a wealth of $5,000,
_ , _ ... —; _ ., ..e Each individual must choose whether to contribute 100 or $0 to the support of public enter7
(*3 ”l "' E “d H? " M m ’ 3 g 7‘ a" ’5 a 4:) ' 2X 2 '3 tninment for their community. The money value of the beneﬁt that a person gets from this
(c) H: = 14 and H: = a A n l L‘ 1‘3 public entertainment is 5 times the total amount of money contributed by individuals in the
' I. ‘29 _Z/ID _. I» 40‘ 3 community.
(or) Hl=Bnnd 32:13. T ““ _
H] = 13 and H; = 17 '3 2'5"? ’5 L as If 20b > 1, everybody in better all if ull contribute to the public entertainment fund than if (a) 334.2
. Fiﬁ—[33:0 H_ =6 1. (See Problem 28.1.) Alice and Betsy are playing exams in Wills]: each can play either of two
strategies. “leave“ or “ntw'. [23—143) ~45 :2! B
leave leave stay at If? C < 3J0)
—IL_
”“9 my mom Him "Slay" rs When is the outcome where both play “luvs" a Nash equilibrium a 63 ,L V?! P0“ 5"? 5’1 (5) Never. since l900 > 300. (b) unmnmu>cuudn>900butnotwhenooo>n 1”” we”, Plﬁfﬂ‘
(c) erono>candc> 300. C—llMSth is)“ i:
(d) Whenever D < 900 4. (See Problem 23.4, the Stag Hunt) Two partners start at business. Each has two possible
strategies, spend full time or secretly take a. second job and spend only putt time on the
business. Any proﬁts that the business makes will be split equally between the two partners,
regardless of whether they work full time or part time for the business. If a partner takes I)
second job, he will earn $20. 000 from this job plus his share of profits from the business. The
folluwing table shows the total income of each partner in thousands of dollaln. Partner 2
Full Time Part Time
—‘m R111 Time Partner 1 Part Time This game has two Nash equillbxlu, one in which each partner has an income of $100,000 and
one in which each partner has an income at $30, ODD. (I)
(b) In the only Nash equilibrium for this game, one partner earns 860,000 and the other earns
$40,000. @ In the only Nash equilibrium tor this game, both prrtners sum $100,000.
(.1) In the only Nash equilibrium for this game, both poiunis earn $30,000. {3)
845+ ref/PWUI» 7L0
Ht: mill/er Plﬂyer ell/ﬂak? FM” This game but: no pure strategy Nash equilibriu. but has a mixed strategy equilibrium. div8. (”1”!er dummy Full Tim (3' repressutedinmemwsbeluw. Colunmsrepreseuttbectuﬁsasofgmd] andgmndlin
sacbtimeperiod. Bundllstonsn
x,1,xz2 x1Z,xI,_1 112,]:22
Pll‘ 1912 5 4 6
Prices PJZ'I P2'1 4 5 6
191‘]! 1911 3 4 Recall that ifbuudls {xl ,xz) was chosen at prism @1,p1)h031,y1) was also uﬁiJrﬂable
if and nut).' if p11] +3321; 2 pm + ply}. If ﬂux!) was chosen when (y1,y1)was affordable, than (lulu) is Revsntedl’refsrreu
to Ul’ylj' nobody contributes. but ll 20!; < 1, everybody is hotter elf if nobody contributes thou it all
contribute. (b) Everybody is worrr 011' it all oounlbute than it nobody contributes it b > 1, but if b < 1,
everybody is better oil it nobody contributes
(a) If 20!: > 1, there is a dominant strutey equilibrium in whim everybody contributes.
(d) This game has a dominant strategy equilibrium in which nobody contributes anything for public
entertainment.
(e) In order [or there to be a dominant strategy equilibrium in which all contribute, it must be
that b > 20. I {J1 3/ )£
:4 2th». lb Sam M w w w e w m r
' l— e L e ”/5 H 2
Plﬂfﬁ ”h .1.“ Pwl’llc enJ—evlnm when X Pareald I‘M/nunme I"; Inf/+4” min 4.2)
04+ MC Wm» lji Mare Hi4 Cambium/x, ‘ZﬂbLII ‘Hen CM}; exam ”3"
Pvt/tin {malpqumlnr/nmf Pill («=9 0h Important Microeconnmll: Formulas Total Product = Quantity (Q) Average Pmdllcl[AP)=To‘tsJ Product[Q)II_abour(L) Marginal Product (MP) = Change in Total Premier .’ Change in Labour
Proﬁt = Total Revenue (IR}— Total Costs (TC) Proﬁt = (Average Revenue — Average Cost} :1: Quantity Total Revenue ('TR}= Price (P}thuuutily[Q} Total Costs (TC) = Total Fixed Costs (I'FC) + Total Variable Costs (I'VE)
Total Cost (TC) = Average Cost (AC) ll. Quantity (Q) Average Cost (AC) = Total Costs (TC) I Quantity (Q) Average Fixed Costs (AFC) = Total Fixed Costs (TFC) .n’ Quantity (Q)
Average Variable Costs (AVC) = Total Variable Costs WC) .n’ Quantity (Q)
Average. Revenue (AR) = Total Revenue (TR) .r Quantity (Q) AR = P = Delmntl (Dd) Marginal Revenue {MR} = Change in Total Revenue .i Change in Quantity
MarginalCustﬂvlCi= Chaugein TotalCuslfcmangemQuunﬁIy LILIUULILILILILILIUUUULI Hoﬁ: Maximisaﬁon Qttanﬂhiimi: Marginal Revenue = Marginal Cost
Wit Point: Prior. = Average Cost Mann Pom: Price = Average Variable Cost KeySteps To Preﬁx Analysis MorgjmlRevsnue= Marginal Cuslmﬁnrl Quantity Praﬁllvlanimizmion
FrolemudtygouptotbeAverags Revenue CurvetoﬁndPrice
FrolemudtygouptotbeAverags Cost CurvetoﬁmlCost
Dt'ameﬁtRecmngleberweutbeAvsrugeCthurvs kAvetsge Revenue
Curve9AR>AC=PrDﬁtIAC>rAR=LDESIAR=AE=BWII :hlﬂl‘i'.‘ :l. Suppose that in Enigma, Ohio. Klutm have a produutivity nil' SLIIZO and Kandos have a
pmduchivity of 93,000 per month. You can't sell Klutneii from Kandoe by looking at then
or asking them. and it is too expensive In monitor individual productivity. Rwall 2,!3 of the
labor fame in Eila‘igmum Klutws and #3 are Kandos. Knndois, however. have more Mam
than Klulrm. [rimming in an hour uf dull luittuns iii as bad Inning 31M {or a Klulz and 350
for a. Knuth). There will be a separating equilibrium in which mlmdy who attends a mum
of H limits of lectures is paid $3.000 per mint]: and anybody who dos not is paid $1,903 per ....... Kiri» all» off in“. nu... .r
@ If20<H<ru 3M0 —IMH< folio
(DJ lrzo<H<su 22‘"; :AMH {c} for all positive values of H. {d} onlyiulhelimitusHppmnohﬁinﬁuim. kqnplgi; lugHp;— a)“: 'im‘lli let"; if (e) lr15<H<3ﬂ l000< 35”0“5ﬂ H
51er < 1M0 Hum 8%” willmil, V‘W‘ l.7ui+§.2ia=l400 ﬁr. usd Mr:
Bwlr rl His phi—e, M 3!”! Mrs W'” l" ’9’ 9“!" All cars on H: l’MIrlQJ“ J""'"”""°'*"'"”3ff"ii M £3 JW 2 1 ' lust slippase aim in New crunhrrhrrih PA ill: quiliiy dlltrlbutinu of tile 1,000 ml at: an the
mum is eunh lhhl ihr number oi Med cm of will: has ihrur v is viz. Driginal when
man all their hurl Lara. Original owlm know whlt theix an no mih, hill buyen can't
detaining a (21's valu: until thny Ipptliiii: it. An owner rm either tall: his car lo In Ip
nraisar and w the upprailer mu ho appraise um ur (lacunllely Ind credlhly) or null ll.
car unappmlaed In equilibrium, car awnis will has ihur can appniled if and only iftluiir viriurirsniimh
A’i’ Sa‘wu Value V S‘:ller [y lnlﬂ‘fw (r) we. J (b) ism. bziwuh AMI") l+ “from""J ”’11
& slim. dump” ”L an “Hf minke} hug—4 (a) ma.
0 V 2] m Avj mi.“ w!» a 84V Lulu/am 0 ”V is 5%. I'p 0L Cay will Vi:
“PIM‘W', Sell” Wall/(5 U~2M “4313,. “\l’PWl ﬁr V
a {5 ‘2’: V~2M =3 V: 4W nurth of the tawn of Muskrat Onﬁxio in Pmblcm 37.1, in the tuwg 0.5.5!“ Monkey,
i a. In Runtbucloet, Ml. that: nu ma lulled can for all. hull'ol'thcni are good and. hunt them population 11 200. Bram Monllzy like unique has a single publlc gm town alum
m hm 0mm of imvna are MIND: w u" Wm fur 34W Giuliani of 970d M m rink andasing’laprivate cl leiittaale Evelyn, ne'l uniii. function‘s up: y) — x —iil/y
am willing moan them in prim lime 51,500 hill wlll imp them if the price i. lrmr than _ 3°° ’ ' y . . ‘ " _ .‘ . ‘
51.500 Tlmm in a large number of putoiitial buyers who Ire wllliug in pay STD) ﬂow a lemon rm" ’51 '3 “‘9 3%;th ﬂ‘j’iﬂﬁ 9‘ 19 oonggfd a: and‘ Yf aha? “ﬁeﬁﬂ‘En
"“1 52.160 for a pond w‘ am“ my” ”'1' N "m m" bad. b” original owners km‘ Srisiﬁisgum méier Estuyunellmamun inﬁrm of; mag; Gill) What E1511; Putzto 211;:an
(a) Tim will i... an uquililnium h. whlch ul uud cm lell ix slim ﬁge for the town 31:1;ng rlnkﬁ m I i 4 r
@ Tliaonly rquilibiihmumir. willulilllulldculnntha mrrhmrrrirmrrmllhry :llh " aué‘f _ [I 100 I L : 7 : ML
"'1“ 320 aquaie maten. a a“ /d ‘ F Y2 (c) Tim will be an cqullilzilum h. which him. all irrr ma mi ml ulad (inn rril ior aim (b) 440 I mm mm L=l Xi; rd) Thaiv will ha an equilibrium In whlch all med cau so]! iw susa. q ' '1 n 290 (6 I!) (a) Time will be In oqullllu'lum in which lemma ml her 8700 mi mod and can all [or ﬁJﬂl. (a) 220 ”um mm' Y _— I _ 3 2 0 (d) 645 Iqume mabora. 7 
' .J "'v III ‘9: (a) Nomafﬂieahcws. A clothing store and ajeweler an: located aide by aids in a shopping mail. If the clothing shun: spends C dallars on udvextising and the jeweler spends J dullius on advertising. than the pruﬁm oi the clothing store will he [all + J](,'— 6‘ and the proﬁts of the jeweler will be (43+ 0).? — 2}“. The clothlug sum 9m to choose in: amount of advertising um, knowing 3
that. the jeweler will ﬁnd out how much the clothing store advertised belorie deciding how much to spurid. The amount. spent by the clothing state will he Q _ Arr . llZlL‘lj =6 TE=(2‘l+(IvJ*%))c~<z
j; 331 {bl 3: lame} = 34.x l (”3.5
M 69 This is H. Icinler'; =3“.5c “Emil
(d) ”50' “464“” "(Mac J‘lﬂ‘h '1" AFC (a) 34.50. “It chilin.) 541MB dim; 3:: 335" 311:6
C: Lagr—a—x'gg‘) : 23 3 Recall Bob and Ray in Pmlalau 37.4. They are thinking of lawn); u sofa. Bob's utility
function is 03(5, M5) = (1+S)M3 and Ray’s utility function h Hamlin) 2 (4+ S)MR. when
§l=m“m“e§"ﬁl.y i sumii h; Mungu indium. than."
81.200 to spend on the sofa and other stiiﬁ‘. Ray has a total of 3 2,000 to spend on the sofa and other atulf. The maximum amount that they could pay for the sofa md stlll arrange to
bath be. better oﬂ than without It is (r) 31,5011
(ll) 35m i200 = 2(l200_r<,3) Mum): Humin.)
(c) 5550. iuo : 24!” “EKG 3,060 = lawn—ska
ggﬂ: 1K5: lZJﬂ gﬁﬂzzlm K6 : “'0 Kg“: Li“ 1. RulilrmwsrdMqlviiﬁqumNunwﬁ. Luwhiutﬂityﬁumiaxb+clndﬂdvini
utility[unﬂimaiaXuG‘ihnGiaﬂidrmdihn—mﬁinpubﬁuguulnﬂiqahuninlhdr
ammuﬂmeLdeumMmMmmmlmcwdm 11in
Wanwunttiiuyhlwtuqmﬁonpﬂmmudsmd publiugxidaismﬂll. Thaw
muMhuptinﬂpMndumendihmhwbiﬁthmthﬂbmmhw‘a
private nunumpﬁmialﬂllln meudzduthqapuulmpuhlicm‘? (2 31mm @ 820.000 (r) 310,050
(4) mm
(a) Thmiutmﬂilnmkmhuawbeabhbddmhxﬁlm. Fabio Orinmilk mP’l'x'i “'4' If ”M“ '5 ”ﬂi’“ Lac iii .. ”MW’1! was?"
23 5 = I} a I
i M Luv! :l le Alleluia l MCﬂwa rennin: 57 XM tall LI 7;, 7i} = lbw?“ $5,114
_ = ,1
iii?" KM‘FZXM 3’”
34M _ _.'L XM:MHM
‘51." 2‘ (AL20,!”
QXMZJi I. Ianblein 34.2,aimpoaelihattliecuafnmtionofthemmng(H.tl)=H°flmilA
udlhudfuudrinuufﬂsapﬂ:mthA(H‘A):A2ﬂlnwhmuHludAuuﬂl
numbndunllxiihmeymdapplnplﬂmxirxpmﬂwly.Thnprhthumyiu§mﬂthe
paineofappiaisiawuuit. mAlhathauutpinufapplni‘l‘theﬁrmamindqien
daiﬂy,mdhtdzbathamlputdappluifthnﬁmunnpnhﬂbylpnﬁbmuimhiig sinﬂeownc. IE“ 8A — AW!’ "3.: SA! 6H “A‘k'HiA'PA
:3 :1:f:::3=m $3 3  Ill/fa ta = TA +‘H_% _i,:;
(a) Ar =225mim=4m 1*. = ‘100 All; @ Ai=4mmdAa451 a; = 6l — '3‘” (a) A.=mnarrrlrl,=m (1310,1200) = “30, W Ru) udOﬂMﬁWiWrr . Recall Bonnie and Clyde from Problem 36.5. Suppose that their total proﬁts are 1443',
where H is the mambo: of hours they work per year. Their utility functions are, respectively.
05(OB.H) = as —0.04.H" and Uc(Gc.H) = on — 0.023“. where 03 and ca are their privaté
goods consumption and H is the mlmbci' of hours they work per year. Iftliey ﬁnd a Pareto
optimal choice of hours of work and income distribution, the numbm' of hours they work per ““53 CB+CH= [44H =0 Q= it—HH *Co
(a) 1,300. an“: uﬁluc: C13 ”6,1419chWillcl,J horn Hz (b) 1,500. _ 1
@3 . Will .%H 1,200. :3 3:31 539;: : H4 —.le=0
H: lug—’0 For 4 Serial“) ,9 m'lglmllm in elus‘i',
"+er ﬁllii," musfhs a 5453‘ ”NW" Err bf‘l‘h 4”,; rat writers, IF a low T
Pl’fdlucilrvﬁlr, wrrL’er alehrs 'lr lie "I“ ﬂzrlnA
1“)" {hi/willirl’i‘ifl Hr; Wren/e J'll bid“ him if. Mile He micro unin. Oil eatuiwllz’hﬂ‘ my ‘5 llst'chmgnam Minlbw .5 Mdhfﬂﬂwf bui‘Werfmna’m‘
irwl—li it/I'in, am! ”My
All WI‘Y'HJ’T in”! diam.” Phi/WVJI'Vng I‘ll, [If 1. Summon thah uniproductivity workers I“ have marginal product! of 10 and hish—urodwtivity
wotlien; all hand marginal product: bf 12. The community lian aqunl numbers ol'udl type of
worlmr. The local community collage oﬁan 1 mm in nicroocmmlu. HighMummy
when think taking this mum in as bad a way cut of”. and bvamduic‘llvlty «what
thinkitisaabudauawagoculufsi (1) Thin h a saprating Iqullibrlum in whidl Nahnudimilvllu ml min Ilia man aid tie
paid It: and lawpluducdvlty virallien do m: will: them and are paid 810. (b) Then in nu Whig equilibrium and. m pooling equilibrium.
(ED Than 'I no signrung iqiliiihriiim, all: um i:  pooling equilibrium in which anybody in
paid 511.
(d) Thus in r sipruins .quiiiirriuu ih whldi hlghpmdudivlity wwlira iii. our «in. .rri m
poid :1: and low mummy worms dri nol ulna Ibo mm Ind m paid no.
(9) There is a awarding equilihriiiiu in Which high—Mummy m tailu the mun mil in
plid 512 Ind low mummy woﬂurslaspakl‘ll. u. (Sm Problem nu.) ma player! in rhghgrd in B girlie of "chicken". Thur: In two pmible
atrnwgiua. swim Ind Drive rlrriyrl. Flu/er 2
Swerve Drive
Swerve o.n ms
“W1 Drive mu 724.724 This gum. hrr two in"! slutty equilibiia. ml {5) a mind alum nuilibuilim in which each prayer mm iiiih milbum 0.2a Ind driva
rinighi wlth pmhublliv um ([7) Wm mixed “laugh: in which pilryels Ilwmme helmi waiving and driving ﬁnishi (D) A mixed draw equilllxiuin ill which one plum lumen will: mummy uni mi LII: Mliu
Miles with mummy mi. (d) I mixed um in which gum playr summ with Mummy 0 i0 and driven maighi willh
immunity 0 vi). (a) m mixed llﬂ‘ngiu Le‘l' FMY’V Z SWerirL W"H‘ PHALA/iiiy P EI(§i//eru¢): OrP + ﬂ[I‘f) :0 Glynn): TM +624XPF)
= “W —2<i +ZLtP ﬂ 3 r2“; —2‘i CWPCJWI P471136 mm} [)4 efm/ +1 MAX/nice aver 5M},
0 : \20 ‘24 — 29 q 2415129,: P‘E'Q‘Z ...
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 Fall '12
 North
 Utility

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