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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 setup 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‘EﬂfSjcg
A‘s» @393 sweat) ct @ Eggcm 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;)
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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.‘£%
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(0) Consider an arbitrary price P> AVCmin. In terms of P. find the amount of output (x) the
firm will supply at price P.
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"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)
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:35.) b tab—,ﬁr‘aﬁvaimx? YJVW 425 W  (b) Suppose S > 0, U > 0.
0 Calculate the marginal product of U. l
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an. 2" o The marginal product of U DEC/1Q Whigs U increases ([email protected] constant).
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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
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S’l .w Efﬁgy, Hf 2§+1¢CV~0 (SW (9) Suppose Karicature is planning longterm and is free to choose to any nonnegative 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? AirW ‘www,
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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.“)
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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 MLaJg 3: t‘ that 9s) M Va. 2 O 1% G: S 6 a
VWMJLZ i [12% Stiff/Cheat: Q) l W
114) :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: Milm?»
r; lllQ : $3va
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WW": txem Q “1?
“= Q’ﬁar x. 1.3") «Q...$)‘“”m (PWT) “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. ‘
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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.
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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.
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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.
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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
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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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