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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/(WWiﬁi Awe Jifftiip’”; dwm‘“ 4 (21¢ /
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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
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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 ,
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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
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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
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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
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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. WlﬁFis the beneﬁt of pure bundling for the ﬁrm?
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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
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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 damm7 emf??? "I”? 175” 10m” r r , ‘ ﬂ/aﬂw Our/.691”?
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yﬂ/e) Jaw/i my“ 7“” Player B
Low High Low I25,25 50,0
High L0,50 110X,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.) ZQW” if)?!“ I) (iiiH 5&3”? flirt! r1 €211le :: . “ism. as» (3) We gW'aﬂx <2.» a a m "f” r. ," ("r , .  "fur, '\ "J
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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
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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
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