Exam 2 Solution - Widgets are produced both inside and...

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Unformatted text preview: Widgets are produced both inside and outside Freedonia but consumed only in Freedonia. The market is competitive, with demand D(p) = 43 — 6p for p 5 8, where p is the price per unit. The supply from producers in Freedonia is SFQD) = 2p and the supply from producers outside Freedonia is So(p) 2 4p. For simplicity, ignore transportation costs between Freedonia and other countries. a. Freedonia has imposed a tariff of $3 per unit on imports. What are the equilibrium price for widgets and the resulting consumers’ surplus and aggregate producers’ surplus? Answer: p* = ‘5 consumers’ surplus = a 7' aggregate producers’ surplus = g 4. 8 ‘2 3 3 Show your work/eXplain: F‘V'ms eu‘l‘grele Fr'e—Coiflnta‘ #ce' Prune P_3 HC‘l' ca {- ‘Hte “Fax—9C4: ,f-lmus ff; 5 «rd-{S (1‘85 t 4, t ' WP) - SFCP“) + 50(6) 3), 1"; 3 5 Pt; 5 8 4443 Correc‘l" 4obM$LQ§ CH4; ) W8~GP4¢ 5’: affiri Lin't'fi) m- Go = .194: We enemies. 34§4 8) Se. 1W5 afiovmwkqg insect ave Carver}. b. What are the sources of deadWeight loss at the equilibrium and what is the size of the deadweight loss due to each source? Answer: (list each source and the size of the deadweight loss due to that souree) gcuvce, §feze Q “+60 “SMOLH (o Ine‘xfl—Cmfenf prochchon (0 Show your work/explain: i. 'wijrkod- Mme fivrvfllli aggreguhe Sawfly weekch be YEP): 63,) erh DCp) = Sf?) ed“ P214 CLon Qovrespoucrug Q = 3%” “Hue wtqufi-F’ Q: 1'8s ‘ ‘ Q. There is no rfli$€LHGCCL+iem 0-? 44M: 18 unH-g among Cowgumevs’loegmmge Q” wkn Weak 3' f3 Lucr‘HA 5' 0‘1" more gef f1") O‘errs &0 WA“ 3. Procfluffom Os MVP o‘oue. C13 Q‘P‘Ct‘ciehJ-ty as posgfialel Co$+ 0.; prchwcecli @Cé‘Xm + (have) = 33 ng+ Lui‘Hx 6¥Cfciew+ C’ Proolu+€ab1 o‘C QZIB ” cm: 12-) we) + an men an) (o [635 ‘H’wm 33 Consider a market with aggregate demand D(p) = 350 — 0.5;) for p s 700, where p is the per unit price, and a single firm with cost function C(Q) = lOOQ + 2Q2 where Q is the firm’s output. a. Suppose the firm is a monopolist who is able to firstwdegree price discriminate. What quantity does the firm sell, what is its profit, and what is the deadweight 1055? Answer: Q* = I O O profit n '30 000 deadweight loss 2 O Show your work/explain: Inuevi‘ C92 3 3S0“ 0‘5? "0 Obi‘cfih IHVCYSQ (lemme—l) PM) 2" “Morgen 3'1} Q .4. 33—0 pfivg+~ caegvee, (JVELC AISCrtwtimi-t‘on 1"ng monopo i {9+ '39.“; eack “(Anni t. ae‘i‘ a CQi‘cwceveut‘h {fierce our»ch marginal revenue ‘Ig MKCQ)= FCAQ). mRCQ) 1"— ole‘ie'rmt‘weg "HLQ OP‘i’l Wti Q; "TOO~QJQ "2 [0044a 90 Q*= (’00 The Momo'fmiig‘i' Cufl‘i‘uveg flu SKYPiLLS Owed “Pnere Is no bwL. Betas/L96. ’HLE— garb/wit margiuad Benefit-{‘3 (Luci Cari-S are Flu: Ell-m?— ‘13 44x9. roth mwgmfl bench?“ acw'l CGSi‘i, MC ( c2) meaJr = @Xhomtaoxloo) : 30000 Pfatmfiav (Have are. no .. ‘5th 0*" (00 & QVol‘Aab la £1“: ace GOSH) b. Suppose the firm is a “regular” monopolist. What quantity does the firm sell, what is its profit, and what is the deadweight loss? Answer: Q* = 7 f; profit: 2 :2 3—0 0 deadweightloss= I 8 7 g Show your work/explain: For 0» \\\l‘€—&u\ak*" maixofeii‘gi‘ ‘CIMCMJ Tnvcrgt“, anmqnoQ HQ): 700*510) MQrarmi revewwei‘s Waco): 700~ m if” Q < 3270. (“Mm =V‘4CCa) aie‘iermrwe: 44w. ogii‘meri Cl: “Toouticqz'foow-IQ 3o Q*=7§ pra—ge‘i‘ 2‘ (5:1)(700 40690 g) .7: Q1500 C-qure cue. V10 5"“"k I“) a“ oiue‘i‘o Eating/“'7 berm; 400 “DwL: (990* ciao) (loo—7s) : L875” Consider a market with two firms and aggregate demand D00) = 400 —— 0.5p for p g 800, where p is the per unit price. Each of the firms, 1' = I, 2, has cost function (3,.(QE) = 240Q + Q2 where Q. is the output of firm i. a. Suppose the firms act as Coumot duopolists, simultaneously and independently choosing quantities. Find equilibrium strategies for the firms. Answer: strategy for firm 1 0 ( Qt» strategy for firm 2 7 O C 69;) Show your work/explain: Envev+ [7500“0‘5-(3 1‘0 Chain invavge otter/113mg mm : 800~ our :43 <32 “00 IQ- :t'flm I Pkcckuia eg at chk ‘Cu'rmz (VOCLRLES Q1) 'Hvte {Jaye—f4 in ‘CCV‘M 0‘1 would‘ be 7. 3 67; (item lot-262;) .— Z‘fO @1— Q; 3 Q; (590 “EKQpBGD ("F (:91 +6723 bloc) Wyimtttuf Tl";L wad-k respite-fir 4:: Q1: 3%; :. S—EOF-ZCQ‘“GQ7_=—O Goa) 3-2;— : “G4 0 "ms #12 said-Hm +0 too is ofjnmal Celt: Gandhi/e) ELSO‘FQI n ( @703: 3 'J; 62""180 0 541629180 Qfij {8 CW egtxtllbh‘um {‘0 k. “L Q4“: Qfiaf‘? OLWCX afzcaxa.) j flat-+116?“ fiwuu‘I‘lJ-Y Comm (018 71—wech (9.3.). (v? Q‘EZO) Hem c , 80 '- ' 627,“: (2:10): 2;“) her c2.*(?‘-g~)~—oj,_ .3 ‘ -— f rt, 2330-432 TLULS ngk : gig-QM?— Qhrx Q. i I“ 63 mcl}‘nr;‘uw 3 3 ‘45 . \ Ce Q '9: __ .5 Sci Vtwj :32) I 3 _ 3 ,— 6. ‘6‘- 01' Qfg': + 76124” wi‘H'x Sétufifiom Q» “ 70‘ "*Hbem Q;: @3170) :70] at each cal =?o For Parts (b) and (c): Suppose the firms choose quantities sequentially: firm 1 chooses Qi; firm 2 7 sees Q1 and then chooses Q2. {Recall D(p) = 400 — 0.5;? and Cj(Q,-) : 240Q + Q} b. Find equilibrium strategies for the two firms that satisfy backward induction. Answer: strategy for firm 1 8 O ( Cal} strategyforfirmZ CQZK(QJ :_ (“l2 Q\ E 280 Show your work/explain: C) r Q\ 5 5.18 0 “(Re alvq‘i—ggy 4;? jfirm 2 rs {AEVLJN‘CCLI Hate beS‘l’ haSFoaSe ‘Funclw‘o “Ft” “Chm 2 £6““& rm 'me‘l‘él’), An'l‘ictpctl’lvy Q-fCQI)J El: ‘Ctrmi almooteg Qt (n+3 (M11045 w?“ '06 mum: QKP(©1+Qf(QJ) - Cam.) 2 Q (800 amt—2 aim) — Her Q? 2 Qt " BQ‘ 'RQ2¢(QJ) : mam- 3w new) . = 62. use .— 1Q, at c9. < woo Clinic #340 3 $6 ‘H‘Le Sclw‘l‘mn +0 FOC c. What is the deadweight loss at the equilibrium in Part (b)? Answer: _ . w __ a? l [/00 deadweight loss = ‘1 qoo + q * Ci Show your work/explain: DWL 1‘3 01kg ‘F0 02 SOMVQEQ “ guamliLt {S 1%“: gmqu MA graham“ Rag mt been aUc-caflecfl m +ke momL emu-94+ my bdww m films? Those §Gburce§ o—F “DwL comLA (as. commhd’ $¢pawe+ely av tired Surptus (Quick (43 “WWW £0? Paw+ Qa\ cum} {Eomyaretfl +0 TS FF J;ng ¢L¢+€Cl M. frict +qlKe‘rS', 1-?- £Irmg «QM as; GDP‘I‘CQ RREV‘BJ emu/[x would Raulfi $9»?le S (P) CD.§P- 120 {For P; .1310! DC?) 2 ELEC‘M q+ PC: [2-8—0 cud QC: ) WH'M Eack ‘Erm Precinct“; 5 . z 3400 due '90 Emn‘H-Y 1‘00 Ema“ k -_ 80+ Q7(80)— 5 EVA-a (09+ ‘Qw leao) Q1; 2.3.0 :‘MS‘LQMX ofi Ql2QL-z: 12C) ‘ A firm with production function f(K , L) = KO'2L0'4, where K and L are its inputs of capital and labor respectively, is a monopsortist in the market for labor. It faces price 9 per unit for capital and the supply of labor function S*(w) = E , where w is the wage the firm offers for labor. a. What input levels should the monopsonist use to produce output Q? Answer: L*(Q) = Q K*(Q) = C2 3 Show your work/ekplain: L Inve-l- L: {13; 49 olo‘irain mad 2 CL, r s 3 The expenoli'l‘ure HQECXEIJ‘L» kiwi is wadL: Chuck 'H‘le matrétuql expcnattLut—e on labor- 1‘3 0! (GL3) :: .. L1 mgL T , re . o.?. “0'6 m? 0.4 K L K S : _____‘: :2 i 2 __ MRT MPK 0.1 K‘°‘3L°“ ‘2 L For (ll/t ltd-Lariat»- Qdiufl‘fihw ., me :81." MR” 2 X ‘9" 51%;: T 0) (9‘2 -é-‘-l (Luci K L :Q (2) [Or uSe 'H’Le. LQ?bctI/Lgi&v‘ afifhaack] Fro-m K 2 L3 9 “Sins, in Q)/ LEVY“ —.-— a Uta) 3 TLWLS Kat-(Q) 7’ Q b. What is the firm’s cost function, C(Q)? Answer: 1 3 0(9): 16639 Show your workfexplain: can: mica) + M6022)? Em.) = Ci 623 + CCL‘YGDZLHCQ) 1‘1623 4— 6&3 2 [SFQB o. Is C(Q) from Part (b) the same as, or larger than, or smaller than the “social cost” of producing Q? Answer: Choose one of “same” “larger than ” r 7 “smaller than” Explain: 7- . l. The Mantoifl$oni9+ uses MEL: {8'— ncL‘Htev Ham. :1 _, G 4'1“ “He “marginal Social 603+ a": labor} w 3 in» [3" K4:- (1 [Anne ‘ flu; does “SQ Hie rLthd' mix WILLIA ‘er [owes‘l’ “Sacral (0371 , g 3 1- "Ike monopsemgl- useg w(L‘*7L&= 6%) 49‘ch (108+ a‘p 44m labor 1+ ages {3 Mikey- ‘Hattk Wm H Li. L __ __ if “Sam-J 005+ I WU.qu : L QLZJL - 4L3}- 033‘ Va: 0 \ I I ‘_ I ‘ '7'}; Ppka 444e, tSoci‘cL\ as ; (LlrwoSe {-JK ‘fn (Wmlmvfie qK + gu‘djed‘ 46 Km?“ La“! 2 62, T21 “Sccfal 3 . amt” is 30%) : {Mafia 2 3176?, ...
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This note was uploaded on 04/02/2012 for the course ECON 340 taught by Professor Mostafabeshkar during the Spring '08 term at Purdue University-West Lafayette.

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Exam 2 Solution - Widgets are produced both inside and...

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