Econ Final Notesheet 3.docx

Econ Final Notesheet 3.docx - ln Pmblem 343 suppose Wilfred...

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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 “—= ulna-war —2, m =0 Z'ilfllo : m”; ILI -: 4' 69 D. -SandD;=3. citizen‘ they will all drive D. hours per day, oi Wold '= ”-201 :Ep-l :5 “9:24 455' '2. 1 , ., 4' Modal Ind-nib, [7le .c 1 A “12:”: (h) D. =m-5. Ll -.- W ‘l ”oi A irfi)’ [Erzém44/thllma ““‘ ‘ (c) D.:7.mp3;¢I z m +7441?- =Z‘i.m4-m.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 long-run axiom. at: iKJKmrflumm th- wart: “warm equilibrium attendance for this club'! cmrimtfi'iuyurgin-Lniqmpnii'mbonxfirmmimunrnbuu X I; A P.9y5flh “fliphla fl) «Hwy 3"“ ‘4? ill in prtmh C-0K}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 std-ataxia. but his 3 Noah oduuibrium in mined .t. 4- An all-puri- :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“! “ll-1111191 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 profit-maximizing 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; has-domlmnt muwgouulllbnuminwhinr nobody oonhlbnoor urythlnghpubllep 7"” - zines u eve per a pm to. 1, '1- _ . enter-tn 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 enter-7 (*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 poi-unis 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. div-8. (”1”!er dummy Full Tim (3' repressutedinmemwsbeluw. Colunmsrepreseuttbectufisasofgmd] andgmndlin sacbtimeperiod. Bundllstonsn x,-1,xz-2 x1-Z,xI,_-1 11-2,]:2-2 Pl-l‘ 191-2 5 4 6 Prices PJ-Z'I P2'1 4 5 6 191‘]! 191-1 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—evl-nm 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 Man-n Pom: Price = Average Variable Cost Key-Steps To Prefix Analysis MorgjmlRevsnue= Marginal Cuslmfinrl Quantity Prafillvlanimizmion FrolemudtygouptotbeAverags Revenue CurvetofindPrice FrolemudtygouptotbeAverags Cost CurvetofimlCost Dt'amefitRecmngleberweutbeAvsrugeCthurvs kAvet-sge 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} onlyiulhelimitusH-ppmnohfiinfiuim. kqnplgi; lug-Hp;— a)“: 'im‘lli let"; if (e) lr15<H<3fl l000< 35”0“5fl H 51er < 1M0 Hum 8%” will-mil, V‘W‘ l.7ui+§.2|ia=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 owl-m 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 awn-is 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. bzi-wuh 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 i-mvna 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‘E-n "“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 uquililn-ium 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) Thai-v 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 chili-n.) 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 sum-ii h; Mung-u 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): Hum-in.) (c) 5550. iuo : 24!” “EKG 3,060 = lawn—ska ggfl: 1K5: lZJfl gfiflzzlm K6 : “'0 Kg“:- Li“ 1. RulilrmwsrdMqlviifiqumNunwfi. Luwhiutflityfiumiaxb+clndfldvini utility[unflimaiaXuG‘ihn-Giaflidrmdihn—mfiinpubfiuguulnfliqahuninlhdr ammuflmeLdeumMmMmmmlmcwdm 11in Wanwunttiiuyhlwtuqmfionpflmmudsmd publiugxidaismflll. Thaw muMhuptinflp-Mndumendihmhwbifithmthflbmmhw‘a private nun-umpfimialflllln meudzduthqapuulmpuhlicm‘? (-2 31mm @ 820.000 (r) 310,050 (4) mm (a) Thmiutmflilnmkmhuawbeabhbddmhxfilm. Fabio Orin-milk 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 MCfl-wa rennin: 57 XM tall LI 7;, 7i} = lbw?“ $5,114 _ = ,1 iii?" KM‘FZXM 3’” 34M _ _.'L XM:MHM ‘51." 2‘ (AL-20,!” QXMZJ-i I. Ianblein 34.2,aimpoaelihattliecuafnmtionofthemmng(°flmilA udlh-udfuudrinuufflsapfl:mthA(H‘A):A2fllnwhmuHludAuufll numbndunllxiihmeymdapplnplflmxirxpmflwly.Thnprhthumyiu§mflthe paineofappiaisiawuuit. mAlhathauutpinufapplni‘l‘thefirmamindqien- daifly,mdhtdzbathamlputdappluifthnfimunnpnhflbylpnfibmuimhiig sinfleownc. IE“ 8A — AW!’ "3.: SA! 6-H “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=4mmdAa-45|1 a; = 6l — '3‘” (a) A.=mnarrrlrl,=m (1310,1200) = “30, W- Ru) udOflMfiWiW-rr . 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 ”6,1419chWill-cl,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 fill-ii," musfhs a 5453‘ ”NW" Err bf‘l‘h 4”,; rat writers, I-F a low T Pl’fdlucilrvfilr, wrrL’er ale-hrs 'l-r lie "I“ flzrlnA 1“)" {hi/willirl’i‘ifl Hr; Wren/e J'll bid“ him if. Mile He micro uni-n. Oil eatuiwllz’hfl‘ my ‘5 ll-st'chmgnam Min-lbw .5 Mdhfflflwf bui‘W-erfmna’m‘ irwl—li it/I'in, am! ”My All WI‘Y'HJ’T in”! diam.” Phi/WVJI'Vng I‘ll, [If 1. Summon thah uni-productivity workers I“ have marginal product! of 10 and hish—urodwtivity wot-lien; 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. High-Mummy when think taking this mum in as bad a way cut of”. and bvamduic‘llvlty «what thinkitisaabudauawagoculufsi (1) Thin h a sap-rating Iqullibrlum in whidl Nah-nudimilvllu ml min Ilia man aid tie paid It: and law-pluducdvlty viral-lien do m: will: them and are paid 810. (b) Then in nu Whig equilibrium and. m pooling equilibrium. (ED Than 'I no sign-rung iqiliiihriiim, all: um i: - pooling equilibrium in which anybody in paid 511. (d) Thus in r sip-ruins .quiiiirriuu ih whldi hlgh-pmdudivlity wwli-ra 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 tail-u 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 mil-bum 0.2a Ind driva- rinighi wlth pmhublliv um ([7) Wm mixed “laugh: in which pilryels Ilwmme helm-i 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 play-r sum-m with Mummy 0 i0 and driven maighi will-h 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 +624XP-F) = “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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