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Solutions to review problems

Solutions to review problems - SOLUTIONS TO REVIEW PROBLEMS...

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Unformatted text preview: SOLUTIONS TO REVIEW PROBLEMS Syllabus: Week 5 - Week 12 Question 1: 10 marks (4, 6} Karicature, a small car company has one plant in Adelaide (A). Let yA denote the number of cars produced in Adelaide. It is deciding whether to open another plant in Brisbane (B). The total costs of production in the two plants are as follows: Adelaide: C(yA) = (3m)2 Brisbane: C(yB) = 2(yia)2 Karicature faces a fixed demand of 30 cars. (a) Suppose there is a set-up cost of \$350 for the additional plant in Brisbane. Karicature assumed that the state govt. will bear all of that as it will generate more employment in that state. If the assumption is true how much would Karicature produce in each plant? Find yA and ya. 27A :2 433 ":9 lﬂwaén‘Eﬂf-Sjcg A‘s» @393 sweat) ct @ Egg-cm 3A :2: My, gm :2. \o (b) Karicature was told that it has to bear its own set up cost of \$350 of opening up the plant in Brisbane. Is it profitable for Karicature to open up the additional plant in Brisbane? Q? wig Bwﬂa’bmea ngmt’ 5;) Mal/Mast a: 2x)?— -+. 2J0?" + an 3.: ﬁgs - i - _ m k Mimi...» my? a: 3. G :2 Q do .1 t Era leasedgg‘ km..£c..wﬁ smug 67+, W, L+ (W G’WL we ’0 Wad Question 2: 10 marks (2, 3, 2, 3) A firm producing x units has the total cost function as follows: Total cost: C(x) = x2+ 16 for x > 0, and O for X: 0 (a) Write down the Average Variable Cost (AVG) function for this firm. Gmﬁ 2:: acacia lé 2 (b) Find the value of x for which AVC reaches a minimum. Find the AVG at this value of x, and call it "AVCmin". w 1'3 AVCWY'z‘l :1: 4+LE.‘£% To wwwa- lit-MET; 'vo ‘FWVQX Ava axe-41,53»!ng Va— W W ,gw—pwgbﬁ , aansfﬂ m :3, g (9mg:me Wm: rusmm.) 3L1? w X 3 I (0) Consider an arbitrary price P> AVCmin. In terms of P. find the amount of output (x) the firm will supply at price P. 91 a MIC, :: :3 27¢ 3W“ sd— 92 17‘. Mi” “Th/Ma le W. .._...,.,.t #3.... Wmum. why, _ :mmt-‘Tm-L—“u‘am- . -- . .i r . ..,. _ ..-‘.:....~.\-l;n_r‘,. "a," M55, “Rpm _,_.,w.q-su ﬂ, Aw «Mm/Wm W. as} no) 2 . ' *Hv... set: Mb»: MC, _'>¢+-;..~ m) :2 “éxl’ﬁméxﬁﬁ' "3t )4 (d) Find the firm's supply function. k9 Question 3: 15 marks (2, 3, 3, 3, 4) Consider Karicature once again. it uses unskilled labour (U) and skilled labour (S) to produce cars (Y). Production function for Karicature is given by the equation below: Y = SHE + ul/Z (a) The production fuw above exhibits b EOIZERS: itiﬁreturns to scale. (constant/1' ncreasing/dECI'easing t i Gram (to? =~ Joaé’slw‘iv) .1 a: ’0 (S 1+ 935-) I Iii/{73 QWwﬁ £3“ 6Q); 0 M“ w!“ duﬁabmae W M m imam “t w {wig :35.) b tab—,ﬁr‘aﬁvaimx? YJVW 425 W - (b) Suppose S > 0, U > 0. 0 Calculate the marginal product of U. l 31 z i up?” an. 2" o The marginal product of U DEC/1Q Whigs U increases ([email protected] constant). 2 “E 3 7 a. .... i U 3* <1" 0 Ev? f 4 (0) Let S = 1. Also let the price of S be \$25 and the price of L be \$5. Find the minimum cost to produce Y = 2. a «salsvzwui Jaw ’V=2 '3’) U "-3) =3 U=l boat :. (IS'EH) +é‘ﬁl) 1.; (d) Regarding hiring skilled workers, Karicature has two choices --- S = 1 or S = 0. Suppose the factor prices are as in part(c). If Karicature's objective is to minimise cost. choosing S = 1 is strictly better than choosing S = 0 only if Y > 2 . .,L_ 2 .S’zo'é 7’30 @037 J \ ,s=i =5 we Hot :32 “\$0” L L S’l .w Efﬁgy, Hf 2§+1¢CV~0 (SW (9) Suppose Karicature is planning long-term and is free to choose to any non-negative value of S and U. The factor prices are same as in part (c). You also know that S = 1 has been chosen as the optimal 8. What is optimal U? Also what is the production target? Air-W ‘www, Wm rt V W; We tag?“ '" Mtg \ > i __ J; 5;: ._ w: ~———-————-— -— W7” ME S" 2;“ s 2 it) 5 “4) ‘ I Tswana ii; +153 Question 4: 15 marks (3, 2, 3, 3, 4) A monopolist has an inverse demand given by: P = 12 — Q where P and Q respectively denote the price and quantity. The cost function is: C(Q) = ()2 (a)Write down the total revenue (TR), marginal revenue (MR), marginal cost (MC) in terms of Q. Fx 8: = (ll—«e363 = Ila-"s1 12Lle =M.:2 MC a Q (b) Find the level of output that maximizes the monopolist's profit. g2} MEtMC l1.»1,@=.1g 2% Lita =12 2-) emlé’ﬁ (c) Find the price elasticity of demand at Q = 8. A t m P ..._ EM.ZCF __ \ZMQ) \$6.“) h 8 —- “.1 H a“ P as). PzawlsQ) Q: a; ’5;me (d) As an outside observer you know that the costs are positive but you do not know the actual cost function C(Q). Without any information on costs can you find the largest number to fill in the following blank. 0 must be less than MLa-Jg 3: t‘ that 9s) M Va. 2 O 1% G: S 6 a VWMJLZ i [12% Stiff/Cheat: Q) l W 11-4) :Wzi (e) Suppose the government decides to put a tax on this monopolist so thatfor each unit it sells it has to pay the government \$2. - Find the monopolist’s output and profit under this form of taxation? MR: Mil-m?» r; ll-lQ :- \$3va i0 :3 @3- "2, WW": txem Q “1-? “=- Q’ﬁar x. 1.3") «Q...\$)‘“”m (PW-T) “3 lit—r o How much government earns in tax revenues? 12. )K g 41x26": 5"” U Question 5: 15 marks (3, 3, 5, 4) Consider the aircraft industry which has two firms — Boeing (an U.S. firm) and Airbus (an European firm). Only one can profitably enter the market. That is, either Airbus (A) or Boeing (B) can make profits but not both. To make this concrete, assume that if A and B both enters each lose \$5 million, however if only of them enters the market the entrant makes \$100 million but the firm that stays out makes 0. If neither of them enters then each earns zero profits. (a) Draw a pay—off matrix for the above game. E:: E NTEK NE}, WHO“? EFF—TEE (b) Find all Nash equilibria in pure strategies. ‘ 7 M as (2.! N6: (:xgwawé’r’e A! 322.1505 M39 to EWTE‘L { iv \ a "a R . .. r ‘ J‘s _ I; .9?“ 4“ h (if ~ (Ne-a. (b ﬁfwéﬁﬁﬁf‘v‘ W ‘ NWL’ W“ “l A -—-7 7 guf’POW @kmcre )3. 335 ‘FWIWI ' x. i, Mi; 'bie BE MW Via. a. Ava/U . (E) G’M’WE: , ‘ ’ "La a, . ., , . . I +3 3 013 I W m E J A 8D ﬁt): Q/Lvmoas‘ 4— 15 a . Q/Ew mum. NE 53‘ a” _ o a I; w) E l B #75 Ni; ace. M (c) Now consider a sequential move game where Boeing chooses whether to enter or not following which Airbus decides whether to enter or not. 0 Draw the game tree. 0 Find the eqUiiibrium applying backward induction argument. ._ _ A . a Exsﬂﬁmﬁ shows; La 6 éf‘LR/efm a; r13“? £1615} . «4‘ . )- “M .ﬁ ME #639 J TE . WW1; sot—Ems. Q) can 5?:st) 093’ a) (a) We) (OJ 9) (d) Suppose European government decides to subsidise Airbus. in particular, suppose it announces the following. If Airbus enters it will pay \$10 million worth of subsidies. - How will it affect the payoff matrix in (a) c Find all Nash equilibria in pure strategies. so set N c... w W Tm @ﬁhm -' @‘tr’iv'vimtaaﬁ— F 5’ \ " I JQ-rv'éa’ ‘93} r G r T1; t1. «erases-7! s; C’ , é on. y» , ‘ . A v.3 B "'73: in mime.» “via, I U - 1 Es}; W; ibybm ‘ Question 6: 15 marks (2, 5, 3, 5) Suppose two firms 1 and 2 are competing in the market. Marginal cost of production of each firm is \$6. Inverse demand curve is given by P = 24 — 2Q where Q = Q1 + (.12. For parts (a) — (0) below assume that the firms are Cournot competitors. (3) Write down the profit maximisation problem of firm 1 and firm 2. TE; (2-11 "' 2031+ {32,3363 i '“ égi """“ m. "- ‘ ‘ ‘ ' f ‘ ' ’ V ’4‘- ‘ . ,«g ﬁdwmtotg, twtwu 2 i312 Til-i3 it“ ‘5’» 61. WW: E : ii; =73 (‘8 " 2%: "" 1‘92) %2.,— (b) Find and draw the reaction functions forfirm 1 and 2. N £ng 3%! w :%r- W o Wavga‘l, (6) Compute the Cournot equilibrium quantities and profits for each firm. 53617 @Emﬁztz 3. 1;: 2J1“ 2C3+3) set?“ _ .... - as} at? fr“ an; _.. ilXB (d) Now consider the Stackelberg game where firm 1 chooses Q1 first and firm 2 chooses 02 next. Find Q1, Q2, P and the profits of the two firms in the Stackelberg equilibrium and compare these with your answers in part (0). 13V ShzoakM, ﬂame.) é’tlrmxﬁ 0 WW an E teem, mum ...
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