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Unformatted text preview: ECONOh/ﬂCS 20]
SPRING 2008 EXAM 3 Instructions; Please mark your answars clearly. No class notes or other materials are allowed. 100 points total. Each question is worth
6 points with the exception of Questions 4, 6, 10, and 14, which are each worth 10 points. 1. Roberto Goizueta likes to watch loud foreign ﬁlms in White Hall. Robert Woodruff is taking a test in
White Hall and dislikes noise. Goizueta can either watch loud foreign ﬁlms, which he values at $15, or
take a nap, which he values at $8. Woodruﬁ“ values taking the test in silence at $20 and values taking the
test with noise at $10. a. Without communication or bargaining, what do Goizueta and Woodruff decide to do? What is
the combined value of these activities? Gotzue’m mums loud §onefan films, and Woodrué‘é ﬂ“; ﬁg
{(254, Win. noise. CambSnCd value: l5 + to : 35.
b. Assume that Goizueta has the right to watch loud foreign ﬁlms, and there is now bargaining. What do Goizueta and Woodmﬁ' do? Is there a transfer? If so, how much? What is the combined
value? GoilUCi'Ct hues A nap, and wandwﬂ takes the test in Si'ifnlf‘
mnsar r“... wardruH +0 swam. 7 5+: 10 “$736”: Wham+43 c. Assume that Woodruff has the right to take the test in silence, and there is bargaining. What do
Goizueta and Woodruff do? Is there a transfer? Ifso, how much? What is the combined value? Gai‘zugra *«kes 4 mp, Clad Wanda/H rakes +1.0 +as+ In 5.16M?
No +p4n$+ep. (Pmloi'nt’r, Wilde: 8+3\0:13. 2. As a byproduct of the production of “y”, a competitive ﬁrm produces ﬂuoride and dumps it into a river.
It turns out that the town depending on the river for drinking water is better off, since ﬂuoride helps to maintain healthy teeth. The price of “y” is P, and the firm’s cost function is C ( y) = ay2 . The town’s
beneﬁt of ﬂuoride, in dollar terms, as a function of “y” is 901) = by2 , where a > b . a. What is the ﬁrm’s choice of “y” as a function of P (assuming it ignores the externality)?
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b. What is the socially optimal “y” as a function of P?
Mom P1‘471‘+bja‘
[3] P2qj+353:0 =9" Pzaiaebw '79 ll "am—g) c. What perunit subsidy would induce the ﬁrm to produce the socially optimal level of “y”? mu pj « «31+ 53 To make “H55 M likg P: M0635
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911a!” S. 1 Ab 214—) ’9 aw 3. In the following ﬁgure, the marginal social cost (MSC) and marginal private cost (MPC) curves are
labeled. The market price P is also labeled. What are the privately and socially optimal levels of output,
y? and y5 , respectively? Please label the ﬁgure clearly.
trite. 4. Suppose that a monopolist faces an inverse demand function of the form P( y) = a  by . The
monopolist’s cost function is C( y) = ky. There is a negative extemality associated with the production
of the good. Assume that the external cost per unit produced is 1.. t 10 points) a. What is the social marginal cost of production (including both private and external marginal costs)?
K + l b. What is the socially efficient price PS and quantity yS ? (Hint: Social efﬁciency requires that P5
equal the social marginal cost. Then, use the deﬁnition of inverse demand to ﬁnd yS .) F51K+A s_ qv —
mazebf T? 535: “VAT? 3 ' t c. What is the price PM and quantity y” if the monopolist does not take the extemality into consideration? M .— q K :3
M¢X P ’ q—L(ab)
#OA "‘6 LE. :7Cl—*Dl+l<.: q+k
Di a“bj'K“ 93" at ' 9x a d. For what value of 2. is the monopoly price PM and quantity y“ socially efficient?
M ..
P‘: K+X:‘WK:? ﬁhiqilil<=i_l<_
1 9x
, s n sd A
when A:%/ P:P inl ,va 5. We can rewrite a monopolist’s proﬁt as a function of price rather than a function of output:
P * y(P) — C(y(P)) , where y(P) is the demand function and C( y) is the monopolist’s cost function. What is the ﬁrst order condition when the monopolist chooses price to maximize proﬁts? Max Pjff) CHM)
f of 4:4
( :O
[P] 30+ PAP dj “3 1 l
6. Previously, we found that for a competitive ﬁrm, % = EX—z or equivalently % 2 MP2
WI “’2 W1 W2
f (X ],X 2) is the production function, X1 and X 2 are inputs, and w] and w2 are input prices. Does this
also hold for a monopolist @es 0r no)? Use the monopoly ﬁrst order conditions to justify your answer.
(Hint: Using this notation, proﬁt for the monopolist is P(f(X1,X, )) * f(X1,X2)— w1 * Xl — w2 * X2 .) , where (lOpoian) M N F P P JL
v ‘~ ’ W 1: 
FOC‘: ﬂ 9% A3 1— i j 5:. : _
iﬂndﬂﬁ~w¢ymﬂg£IW50 77 §J+q
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11 M an ex» A I J“: ) 3L r 872 Yes /
, w‘ "" ———* 7. True or false. Unlike the competitive ﬁrm, the monopolist produces such that marginal revenue (MR)
equals marginal cost (MC). Explain FAKE. BOHn ‘HaE CObei’H’iVe 65ml Monofdiw‘S’h'l ‘6‘“‘75 froiVLE
Wu“ 'Ht’t‘i’ MK: m<' ‘FOI‘ “PM. Lamﬁ’e‘ﬁi’ioe «ﬁriva MR:.P ‘ 8. There are two ﬁrms in a market, Firm 1 and Firm 2. The inverse demand function is
P(y1 +y2)=10— 0.5(yl +y2). Firm 1’s cost function is C(yl) = 2y,2 +3. a. WhatisFirml’sPMP? e 3..
Man Do—0.5(31+51)],‘jl“ 313) — 3
l b. What is Firm 1’s reaction function? In other words, what is the optimal yl as a function of 32;,
the expected output of Firm 2? v __. C
[3.] 10—3,«o.53f—45];o 2*; 53“ to 0.5111  2 art a
if I: 12.353} or 3] Z a “ ya
5 IO 9. Find all pure strategy Nash Equilibria. ﬂower B 10. Find all Nash Equilibria (pure and mixed suate . (10 points) rUl bide FUJ‘E ﬁnicky] NE 5
(LlJﬁlpeil) (we
red (red) Blue)
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blue 1 i V
l 5 J 7’ S l 1. Let’s consider the following game. n0+ SW41 5+4“! 9...], I'Aflai 0'15 a. What is the NE ofthe game? (Sway, sully) b. Supposc Player B agrees to reward Player A if Player A does not study. For what values of R (the transfer ﬁ'om B to A) will the outcome (not study, study) become a pure strategy Nash
a h” Sk’Av Z S £r R "Pa LLHSe m It? "0* 5M: W» 5 will“ R25 wi'l/ induce
A [Séﬂ 3 lA‘R «cow 5 9’9 ('1‘? Shut, 541/137) 43 5m, 15,0 (A0456 $1“de klan ’0‘ 0 NE J doeanﬁﬁ—n 7. g v _
c. Suppose now that the players agree to purus eac other If one studles wh11e the other doesn’t. That is, a player who studies while the other doesn’t study loses K. For what values of K will the
outcome (not study, not study) become a pure strategy Nash Equilibrium? TM US i1; lSk a, a «r. muse K33 wi'l/
w smj “hfn 5 Jam‘s} gar/17, ,‘Mﬂe
i
lat Z ’5*K W 3 ‘YO airbase (mmr 515d} I My $4527)
nor 54ml? whenll Man? ml], 45 a N6 4 12. A bear and wolf ﬁnd food in the woods. Each animal can either ﬁght or share. The corresponding
simultaneousmove game is the following. . w our well __—J_.._.
Wu g nilEL
Sc 5 “I; 0
NM 5 < OH
will
s 1. 1, a. In the sequential version of this game where the bear moves ﬁrst and the wolf moves second,
what is the pure strategy NE? («($313) Slang) 535 Seqvewl’i‘al Jame 4120x15 b. In the sequential version of this game where the wolf mot/es ﬁrst and the bear moves second,
what is the pure strategy NE? (Show, gi'jm’) c. 15 being the ﬁrstmover good or bad? 600A. 13. True or false. Multiplying all payoffs by 2 does not change the pure or mixed strategy NE of a game.
Explain. l— R l'
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:31 P11: + 901): 40' P)q,€b£}PJ0»7U\3I Devils/v5 045W; mlvelj Waller 416 fxrf’ﬁ‘lbﬁl 14. Let’s consider the modiﬁed Prisoners’ Dilemma game in which k is the cost of confessing when the do {’5 ﬁll"
other player denies (same as problem set). What is the mixed strategy NE of this game? (Hint: Since the £114 ll game is symmetric, you only need to solve for p or q.) (10 points) a,” my
l “D 01) E J Sym’xl‘f
(«Mus d «'1 “Yam Wall. ‘ z “#77 4/5! 99,03) + P(l«1)(—l<)+
((9); (9) +(lPJU'1)(”)
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462 + (of) : O
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 Fall '08
 NINKOVIC
 Microeconomics

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