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LA prac soln - Long Answer Questions for COMM/FRE 295(104...

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Unformatted text preview: Long Answer Questions for COMM/FRE 295 (104) Final Exam (2008) Review Session +w0 1. Consider a monOpolil'st selling to two groups of consumers. (a) Provide conditions that are necessary for the monopolist to engage in price discrimination. (b) When all consumers are identical, which yields higher profit: perfect price discrimination or two—part pricing? Explain. 6i) (i) CuY/(WWi-fii Awe Jifftiip’”; dwm‘“ 4 (21¢ / .. I n r ! ‘.' . .1: ! a 1‘31: eflc 1 (2/; iii) We easier-3w? (fa-swim”: :2 x fat-r4 5’? J" W l 'J: \ I , 'i ii’?€; b) 8&64 964414763 )(t'fC/A ‘flfie 35“”C {5/63}?! "Jr Aeamle “4 éd‘fq‘ (“NC 0 a m film/wow raj am] am (Mww rum/«r? 0/ 2. A monopolist faces demand from two groups and can price discriminate. The total _ . demand from the first group is QA= 10— P and the total demand from the second 9?: group is QB— " 12 2P. The monopolist 5 total cost is C(Q)= 5 fiQ’ Provide the optimal prices that the monopolist will charge and the quantities that the monopolist will sell. _ , _ ./ ‘1' an :3) Waffa (59:7; ,1: (2W5 ‘7’”; 9”” Pffit’r (J of _ . . . .r- "' “~- I, ‘3'} -‘ . : art‘s-.4 5‘ '1 ~79) Mam-m fitb-ei'wr? H 6"?qu “.59 A190?“ tJ‘i’r" f f‘ KM)“ WA“ a _ g 5 f1]! f1? ": é __ 5:7}? ff fix jag: 5,! xix 1/? ..i :3 MszC :9 [(242ch 3) (if-:3 m yaw-p ft 6-&:Q fl Cfirét Far? fl/fdufag V"/c1‘g‘3§ Far y/W/fi r}: “3109 _— Lr e»- MW I9 3. Suppose that a monopolist wants to sell to two groups of consumers. All 10 individuals in group A are identical, and the total demand fianction for this group is QA = 100 — 20F. All 10 individuals in group B are identical and the total demand function for this group is QB = 150 ~ 20P. Suppose that the monopolist implements a two— part pricing system, selling to all consumers, with a price per unit equal to 2 dollars and a common fixed fee Calculate the total revenue of the monopolist. with F“? E”; .3 1t , A? (a. ( 59141116 3'fl2fl?13’m-{ {Pa-~512W F” 1’ -1 .4 Lg) (W49 Mafia (“Sal‘- I?’?.yL/fi{ffi g whe’hf’l (,1 , r 1' “.11;- J',‘ is”? {ill 3636,6112? {ff @i51“1[?54’flg 11" F“ I K eu—f P1016 __ QM»? ’9 , (0971900): (:0 Q85 1 W—Qgi—QJ-l 7 fig f, .4’ w . 41- -7{( g Pf") M g 91:9 - / Jr: A I“ s L PF 1': 5’. u, gig} Q E Qa+ 69(9) “i“ gt) "t H0 (3)“ 920 Cfldqfi KJ 4. Consider a monopolist producer of flowers, facing demand QD = 20 — 2P, and constant marginal cost equal to 2 dollars per unit. The purchase of flowers yields a positive benefit to neighbours of the purchaser in the amount of 1 dollar for each unit purchased. (a) How many flowers does the monopolist produce and at what price? (b) What is the socially optimal quantity of flowers that should be sold? (0W? ymm mo poly et’gieomem‘ompared’lotr" 411))“; opt1 outco 1n thism”Imlw/WMk 1:»; arm =1 141/1 tr 42 faflrfitC “:21 M’Q: Q. arr/f We”? 41“ 114111310 6 3—“) Cky?’ 87 $1 F: [Oi/1&1: G: "rear” ffif ~ @141 Wflr’wwflli’f err g guy/£51111 ale/1? Qtfg 5. Firm A is an incumbent monopolist in a market with total demand given by QB: 20 — 2p. Firm A has zero costs. Firm B is considering entering the markethntzm w W = “/4" ' ' _' ' . Firm B would $0 incur a one—time 4””; " entry fee 0 5'10 ollars if it were to enter the industry. The goods produced by the two firms a 'dentical. (a) Suppose that if firm B does enter the industry; the two firms will compete in quantities. Will firm B choose to enter? (b) Suppose that the incumbent Firm A can choose to spend SY to engage in an advertising campaign in an attempt to secure its position. If this campaign is undertaken, the only way that Firm B could enter is by first matching the advertising expenditure of $Y. Will firm A choose to engage in an advertising campaign? If so what is the correct choice of advertising expenditure $Y? Provide a clear diagram of the relevant game tree, including the payoffs derived from producing in the industry. . (“I u" ~ {07) (“Amt 5mg W P: [grates-£53m} [v ‘ r f .\ 7 £307? Qflj/Qwfi (10“; 054/ ’ r - as- :20 Firm 8 WW/ “M yaw?“ S 7} 6g” Q‘ ’3’ i a rift-,1 ewm/ t r a: :13 WW" "’ f“ s, [’3 kit’s: if } "i “re I 20.“; ‘Ja/w " Trfiififi_ _;,(_;/_ f”, A CKRS Q) ti gassr/ emf a 1%? 9732913 aw. 7%: Mia-saw”? {gm/415W” eflligfi 6:2,: . x; Q 99‘ QU”X Fling-ii) Fair FL) 5"; A .x- E/ I £95,5-; mama‘ffly 6. Consider the following market for inventions. There are lOtlQn’ventors, each of which owns the rights to one invention. The value of the inventions, if develOped by the inventors, is uniformly distributed between 100 and 1000. There is an unlimited number of firms that are willing to purchase the invention. Firms attach a value to any invention of 150 dollars more than the inventor’s value. a. If firms can identify the value of each invention, what will be the total quantity of inventions sold? ' b. If firms cannot identify the quality of the inventions before buying then: i. What price are firms willing to pay for inventions? ii. Which inventions will be sold and developed by fimis? iii. Which inventions will be developed by the inventors themselves? C. What is the cost, in terms of lost profits, attributable to the asymmetric information in this market? , A r a ‘.,.r~,.!.;£§ WW Wl‘tlt Ffrfgc‘t‘ [flit/"0772947134; ear? fl 7‘ '9 [J09 m“ J {l} ’C 9‘? [If {lime-’2’]; l'flfit-Pétx‘itflhé 6€Cflwif quél S‘kflfrr’.}7 rfl/t: if? [S (.3; «a; r) , _.r . .Hx' {9'13 7‘3" t‘ Va 113(- 4 Q "fhfg t” 5‘ {2mg 3’“ JZ- ‘ I ‘ _ t , . I) A r / b) Warsaw ELM r‘wft’flt’m‘w’r 9M5 Katha? nan“ at” Frame #9 - t I 7 _ I”? ’ ”+45. em 'Jrzj Waxy“; [95} 7‘46”» P w mm warm w w w (MIC-V , ., . Value af‘flI-VJE’ MaS?// (f % _ Efw'b/me SM, W Mme Keywflifl lo +190: P 3:) f): 3&0 \Awpfl'aw WVflZ/Jr/Méi ? . , 1 in") J l9? x.’ 71570 '+5 W zfo'fwf 0" and PM - [50 m pm , Sc? 4 " mg} m) . 7r" if / _,_ 4 -. we)”; dt'V/ tiff 7-67 MU. Dr: Cl 7&0 m” 7. Market demand for a homogeneous product is PW = 38 - Qw for women and PM = 14 7 0.25QM for men. The marginal cost of producing the product is constant at 10. a. If price discrimination was possible, what pair of prices would a monopolist set? b. If price discrimination was not possible, What single price would a monopolist set? c. Use a diagram to explain Why in this situation a two—part tariff raises less profits than first degree price discrimination by a monopolist. C ,9; f .; sari if aslerimfl A :f . safes}; t” War? a? java} 10"!” ”a“ ‘ fl ’ _ _ ~ Q {$2 apt-"1"” ‘ ‘ r 7 a a»; 2-”; «flat? far . Mfih’ gig)” ‘ ’ Q —— 3?”?i $472 if 9’“ “3”" ; J MM . W I ~ “ .. » 45:15»? fr Oat v s? P" ‘ " .x' ’ ‘ A )3 FL; , . ..‘ i g‘i‘ : pic i a. fur ,: {Se - .g if» my: gym i. r- ma?" . ‘ Er, ,p- JG ' / ’ v ‘1', “/{H /) iii-iii? 9;: C r Qi- !; .3} :1- {if _, j‘ 5 . . u ‘ C R 4_ gm; f3“; Hire . -1 ”3‘1th ”£2 4w??? ' t Ame/f Fdl‘r’i'fi'f M I} 1 . I 1) i if“ ‘4‘ g I L i —7' 4%? xi" 66‘} . , 4 ‘Y 3 .‘r 35f :"12rfiwff‘? 5054'; 2' r— '1’?" _‘ , __ i ‘ ’E; 5 {f .33 : f3 " r' ‘~ ‘I/ ,;,1pf?i;.'.W‘- “,l C [a fi QM“, W 17/ KL,” M} §’f‘ki7lfywflf fig—3 if. [Jr-{Cf b"? ' ‘ , _ 7_‘ 59’" ’1’” j: W y- i F "I JU’ , h éfr‘smff ”a 1 . w. u’ PM]: 5%?” [if ‘I 2' if?“ fig-£5 22') $0,”..E'IEKE 14%;; (dfitgu'll’flrf: Si;".:";:;=.nl ‘ 5” H" {I Wag): if? if. I. V 3* it t/ ' d} [aMVfw‘i'b/l‘ ew ~— fif’?’ -'( 175g:;22 :9/1_ 5—?” S 8. Customer A and Customer B will each purchase a maximum of one item of products X and Y. Their reserve prices and the firm’s marginal cost is given by: Person Product X Product Y A . 1200 600 B 7 l 500 400 MC 1000 3 00 a. What set of individual prices maximizes profits for the firm. b. What bundle price maximizes profits for the firm c. W-lfiFis the benefit of pure bundling for the firm? flay-[.6404 . ) PK ’3’, /QWU aid/ix P/ 7 #90 (My? MaXrl’rer}c flflajtif} a l 6) F5 we; [(3—ng wtf/ ’YlflaXri/Lvnifl fife???” 1 / a C) W '2. 31(l7001l009figdc9) v .590 ' Bumm Wraith-M : $402001 {5M0} r 13(an — 3W) '5 éfla 1;) g2 Wis-7’ : {éflfl 5 9. Two oligopolists (A and B) produce a homogeneous good and face market demand P = 100 — Q1 7 Q2. Marginal cost for each firm is constant at 10. a. Calculate the equilibrium quantities and prices when the two firms engage in Cournot— Nash competition. b. What is the maximum amount that A would be willing to pay B for the right to be a Stackleberg Leader instead of playing the Coumot—Nash game? What is the minimum payment that B must be paid to agree to‘be a Stackelberg Follower? Is it possible for a deal to be struck between A and B? c. If the two firms competed by simultaneously choosing prices instead of quantities (market is shared equally if two prices are the same), how surplus will consumers earn in this Betrand equilibrium? ml; i (j (59:1 ram?" [Van/1 Ml r ill—1: Np; £104" Qfi— WELL [0 will Pr r, , v” c r‘ ., r 0 (Elli , I a" 0591: W)? [(9 data m ‘ 5'. r, .«i l\, fEbff WK} (aif’€ * Xe"? ifiwtixfi {‘ f H" i y; f} feta-"v ) l r a a H 37:51 .3. 0-: fl ,, 02%: M '2 a" ' a; air“! "’ .,_ {VA " 6/fi ’59.? t f ‘ ~ '" .2; ' a‘“‘“ , , x . ,m "" i {sf-«12s; 5 L? [2,1 "WE-r. flgflqc) C ' 6" {53a J 5 “f I) 3‘7 my a; 2 ”W - $9 ' 6’s ”[0 : O :2) a: [£30th9"““} * dG’Efi (F, I f’ a —:_ 00 a" "T .« ll r‘fJJ'grfafl)! I (le \ C “firm“! : it uh) ' / 12’ SO a (r .11 J A t - {“11"} I :.-,r . if}, i _ Q i F \Td {aflflf V: fegdajklw ~€s529 H99 PMFH J V M, _ (r Qgfi/Q} (325) p L @293 , 5700: }_h full f§{[§ fl Tit-'— ‘Z” [Mam/1T FM 8 M curefl 7w 55"” 7'5”” 6700 77 2/2") #65?! 1: Km We / ., ‘ M 6?“ 5.1m“ 6 a]; J x 519”“: r (w’ page re " - , (1,: " f 9 Cl&fi%m:m mwmarQJwfi ' :aUW’” 10. Consider the following game Player B Low Player A - , Low [.15 w 15 High 11% 18, 18 a. Identify which players (if any) have a dominant strategy. 11 Is this game a prisoners” dilemma? Why or why not? c. Without doing any further calculations, is it possible for one firm to enjoy a first—mover advantage if this game was sequential? :) Bails [we a dam-m7 emf??? "I”? 1-75” 10m” r r , ‘ fl/aflw Our/.691”? -r \ (CWW’W' éfCfiQM'C /6.’ /0 .f-t-r-y "MP/ES. if A §Irflhfl 1:52”... gI/Ig/ (H4192: 1955551} CU? '9 - P a: ' {:g'pgfl’ moat-4f High game I.) it Vfl yfl/e) Jaw/i my“ 7“” Player B Low High Low I25,25 50,0 High L0,50 110-X,110—X a. Identify the range of values for X which ensure that neither player has a dominant strategy. I b. Ide t' y the range of values of I _~ I 'ch ensure that the Nash equilibrium occurs: $) in the left corner; (ii) ulnar c. Are there any values for X which ensure a first—mover advantage for Player A? Ci) X5 60 :3) HIB Agvf Pia fl/fltnfhawf rit’fi’gfil/ b) X “p 69 :3.) Z-QW” if)?!“ I) (iii-H- 5&3”? flirt! r1 €211le- :: . “ism. as» (3) We gW'aflx <2.» a a m "f” r. ," ("r , . - "fur, '\ "J Sam 2. amour?“ )0 73:) f???“ MJWP‘ 9‘7--/"W‘Uflf 9i i; 12. Consider the following game Player B Low High Player A Low [Q10 g ngh 20, 5 1, 2 3. Identify the Nash equilibrium if this game is played simultaneously. b. Identify the sequential Nash equilibrium if Player A is allowed to move first. c. If Player A moves first, What non—credible threat will B announce in order to try scare A into choosing a different strategy? d. Suppose B can sabotage itself so that is payoff from playing Low is reduced by an amount X regardless of What A does. What value of X will Low choose, and why Will she 46 choose to purposely destroy some of her payoffs? . x Mimi‘s? [7/511 5) wagsfivwflew: M? Q A a , ~ _, Ar? 9 [3 w“ Pfjffiil'i‘ g) 8: WW 6 fl 6“” alt/f 514% flame 51???) WW ELL-Mdi " u . 7W4, "5) 5W“ We“? vie-«t z+ mu came Ham gf H CAM V: {shire/f} y} Mad ngk wa é 8 MM. , {1+— Wfl} . If fihA€_ {’ £3 {17:24:93};me Q +0 /9 , KEV- ! "1% {23;} Cot-ddlé? [10?4, [Z15 Way «s, 7-; I" r {Track a) 77;) name ”fife ragga? (/6924!th 5 mm}, (“war X73 woe . ;’ F'u 5 _ _ ".2 :r’ _ 1 ‘ .f‘; r" 5 a . _ -1i 595,53 ’12", .A: “5—“ ‘étvjl 0V?) fiefiqgkf fflf?€mf {a} [1.1 M31: iLf :52}; xA/A 8r If: pr ‘ E r we,» miss 9km. i? w MM}: Wow 9 to /9 r " "i .f '. ‘N ‘ . is m w a 13. Assume a firm hires a risk-neutral worker who has a cost of effort C = $20,000e where e is effort and is'either 0 or 1. The worker is risk neutral and monitoring the worker is impossible. The firm can have either good luck or bad luck (probability Bad luck = .50 Good luck : .50). The following is a payoff matrix showing revenue based on effort and luck of the firm. Revenue Good luck Bad luck Maximum Effort e=1 400,000 200,000 Minimum Effort e=0 300,000 100,000 a. Suppose the firm wants the worker to choose maximum effort, and will achieve this by giving the worker a fraction of the revenues What is the minimum fraction which must be given to ensure that maximum effort is chosen? b. Suppose instead the firm pays the worker a fixed salary plus a bonus if revenue is equal to $400,000. What is the minimum bonus that the firm should offer the worker to ensure that high effort is chosen? With this minimum bonus, what fixed salary should be offered to ensure the worker has the same expected level of compensation as in part (a) 0. Which scheme generates the highest expected profits for the firm? Sufism WM ei fiemefiesign ' Wet” schem uld the er prefe ' s e wa ' yrisk—aVerse? "fl“ I. , a “ * Jr» allow) 7‘"!— (‘QWV’WOfl * 2099,50 " ] wwwwfiww W“ 6 1/ WM 74 B’ffwsr’WWaflflé‘w) _ . K “My .f jiffy" ‘ gfldjpdwy “,5ny fjfl , 7720K” 0/50 C? a» h I ,. Qéfifiéfi z 0.9 M...“- 30Q0m/y— Qgflw "3. 2555””? 35' a?” (k " ”(qud’ 'L-f wart/(Pf? gadgfi fire-Mr? 50 EMS”? €:{ ’5‘ 6405”“ Wig flaw/re, gr 5': _. I F} my? \ ‘ 9.!) {£36.33 54“" W“ C W ‘ f we kcfl €r’f-‘Wi ! +’_ k "2“ i) x g ’3’) fl ”1%,“: (a :r' (J in" f" SQUWQ W kg WW gé/wlf‘ 63/ {f BW’WJ Z (far/”690 A 7 (in A 1' g i . “L. If 0‘iwa} a )5 F5 4 11W" Wigwam = U:2[§(W.letg‘ " C 1}!) LU. " t 5% .. , r ’ a; z: 40W“ are(awdrwwlkMW K ) {’flm“) expects/M flflafi‘fl We?“ Pita/79+ Wig/rm}; C ---I _ 9 . ,A .. 9;?ka Emmi/i —~ [mafia ‘ , is: .r-:-’»-- __ 1 7 (away; :3 W Same ...
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