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**Unformatted text preview: **Touchle MacFeelle publishes comic books. The only inputs he needs are old jokes and cartoonists. His production function is where J is the number of old jokes used, ii. Is the number ol hours of cartoonists labor used as Inputs, and 0 Is the o = n.1, i.) = 0.1..rlf2L3f4, number of comic books produced. a. Does this production pro-ass exhlblt Increasing, decreasln , or constant returns to scale? Increasing, since rpm) = imam.) > mu). 1 v Consider a perfectly competitive industry with a large number afﬁrms, all of which have identical cost functions 00’] = Y2 +1 for y > O and (2(0) 2 0. Suppose that initially the demand curve for this industry is given by
Dip] : 52 v p. (The output of a ﬁrm does not have to be an Integer number, but the number afﬁrms does have to be a it Integer.) ' a. What is the supply curve of an Individual ﬁrm? Sip] = 9/2 t/ V if there are n ﬁrms In the industry'
what will be the industry supply curve? Y = rip/2 J v
' b. What is the smallest price at which the product can be sold? ,0 = 2 J v o. If the number of old joka used is 100, select an expression for the marginal product of cartoonists’ labor as a function of L. of labor increases? Colonel Tbm Barker ls about to open his newest amusement park, Elvis World. Elvis World features a number of MPerLam JV Decreasing J V Is the marginal product of labor decreasing or increasing as the amount n=5o J v be and see if it WOI'lG.) l c. What will be the equilibrium number of ﬁrms In the Industry? (Hlnt: Take a guess at what the Industry price will ' d. What will be the equilibrium price? p=2 ~/ v What will be the equilibrium output of each ﬁrm? y=1 JV exciting attmctions. You can ride the rapids In the Blue Suede Chutes, climb the Jailhouse Rock, and eat dinner In the Heartburn Hotel. Colonel Tom ﬁgures that Elvis World will attract 1,000 people per day, and each person will take Np) = 50 — 50p rides, where p is the price of a ride measured in dollars. Everyone who visits Elvis World is pretty much the same, and negative rides are not allowed. The marginal cost of a ride is essentially zero. ' Er What '5 each person's inverse demand function for rides? l b. If Colonel Tom sets the price to maximize proﬁt, how many rides will be taken per day by a typical visitor? FU)=1-Yf50 «v 25 J v
I c. What will the price of a ride be? $0.50 J V
l d. What will Colonel Tom's proﬁts be per person? $12.50 J V
' e. What Is the Pareto eiﬁclent price of a ride? so J V l I'. If Colonel Torn charged the Pareto efﬁcient price For a ride, how many rides would be purchased? 5t) JV ' 9. How much consumer surplus would be generated at this price and quantity? $25 i/ l I'. Now suppose that the demand curve shlﬁs to Dip)
(Hint: Can a new ﬁrm enter the market and make no I e. What will be the equilibrium output of the Industry? Y 50 JV = 52.5— p. What will be the equilibrium number of ﬁrms?
nnegative proﬁts?) 50 J v I 9. What will be the equilibrium price? p=2.02 J V What will be the equilibrium output of each ﬁrm? y=1,01 J V What will be the equilibrium prioe 51 JV What will be the equilibrium proﬁts of each ﬁrm? Amuhn n.n2 J v l h. Now suppose that the demand curve shifts to Dip) = 53 e p. What will be the equilibrium number of ﬁrms? ?2 JV ' i. What will be the equilibrium output preach ﬁrm? y=1 JV What Will be the equilibrium proﬁts of each ﬁrm? 30 J V Toucnle MacFeelle publishes comic books. The only inputs he needs are old jokes and cartoonists. His production function is
0 = f(J. i.) = o. 1J1 121.3“. where J' is the number of old jokes usedl i'. is the number of hours of cartoonists labor used as inputs, and Q Is the l h. If Colonel Tom decided to use a two-part tariff, he would set an admission Fee of $25 price per ride of 30. J v
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.. msmnmmnmimimmmmuzmm And by outﬁitukicm. Touchie has an irascible business manager, Gander MacGrope, who announces that old jokes can be purchased for $1 each and that the wage rate of cartoonists' labor is $2, a. Suppose that In the short run, Tbuchle Is stuck with exactly lElD old jokes (for which he paid $1 each) but Is able to hire as much labor as he wishes. How much labor would 0‘”3 v’ V or What Is Touthie’s short-run total cost as a function of h s he have to hire to produce 0 comic books? 204f3+100 J V output? c. His short-run marginal cost function is 301/3/3. J v at His shorteruh average cost function Is 201/3 + 100/0. JV In Gomorrah, New Jersey, there Is only one newspaper; the Deity Caiumny. The demand for the paper depends on the price and the amount of scandal reported. The demand function is number of column inches of scandal reported in the paper. and p is the Dis, p) = 1531f2p_3, where s is the
price. In equilibrium the quantity demanded of newspapers, Dis. .0). Is also the number of issues sold per day, y, or D(Si D) = y. Scandals are not a scarce commodity in Gomorrah. However, it takes resources to write, edit, and print stories of scandal. The cost of reporting 5 units of scandal is 105. These costs are independent of the money to print and deliver the paper. These cost $0.10 per copy, and t number of papers sold. In addition, it costs he cost per unit is independent of the amount of scandal reported in the paper. Therefore, the total cost of printing y copies of the paper with 5 column inches of scandal is 105 + (Hilly. JV Does the price elasticity i a. Calculate he price elasticity ol‘ demand for the Daily Calumne —3
depend on the amount of scandal reported? No J V
Yes J v Is the price elasticity constant over all prlca? ' b. Remember that Mﬁm) = 0(1 + %). To maximize proﬁts, the Daily Calumny will set marginal revenue equal to marginal cost. Solve for the proﬁt-maximizing price for the Caiumny to charge per newspaper. $0.15 JV When the newspaper charges this price, the difference between the price and the marginai cost of printing and JV delivenng each newspaper is $0.05. l c. If the Deity Caiumny charges the proﬁt-maximizing price and prime 100 column inches of scandal, how many copies would it sell? (Round to the nearest integer.) 44,444 J V Select a general expression for the number of copies sold as a function of s: yis] = 4, 4445”2 \l V i d. Assuming that the paper charges the proﬁt-maximizing price, what i
and 5? Proﬁt = 0.05y — 105 J V s an expression for proﬁt as a function of y Using the solution for yis) that you found in the last part, substitute Ms} for y to select an expression for proﬁt as a function of 5‘ alone. Proﬁt =222.2zs‘i'2—105 \/ v i e. If the Daily Eaton-my charges Its proﬁt-maximizing price and prints the proﬁt-maximizing amount of scandal, how many column inches of scandal should it print (rounding to the nearest integer)? Given the 123 inches J v proﬁt-maximizmg number of column inches you just found, how many copies are sold (also rounded to the nearest integer)? 49,286 J v Otto‘s brother Dent Carr is in the auto repair business. Dent fou
cis) = 252 +100. What is the amount of proﬁt for the Daiiy Cai‘umriy’? $1,234.54 J v nd that the total cost or repairing 5 cars is a. This implies that Dent's average cost is #615} = 25 +100/s, ill V his average variable oost is AVGis) = 25, J v and his marginal cost is mots) = 45. J v That is, 3. In Problun 3.8. the supply curve of any firm is 3:01) = p/Z. If a ﬁrm produces 2 units of 7
output, what are its total variable costs. a “It ‘4 C: 1 3 Suppose that In the 3110“ Hill, the Ilm in Problem 20.3 which has production hmctir : = = 2 mm' F(L,M) = llL‘ﬂM'l2 must use 16 machines. If the cost of labor is $11 per unit and the co
5 I": 45 PI?" D P (‘3 oﬁts of machines is $5 per unit. the short-run total cost of producing 80 units of output is ” Slm Mc— alel’) C ( )-_/M(/ M u. 1/; (a) :2 74° 2) v ’5 ‘ ”3 3) (a) m Hing): ‘lL (It) TC: wL+r M (d ’5 m y. 22 f _ 4,2,2 = 21 414; W) (n n... : Ill?" ; f =0I)(2€)+(€)(M) $4 ’3 ﬂ 3 - 0 ‘ (c) $330. T” pﬂ’l‘m" 8" ”ml; FF IV lo”
(a) There in not enough information givm to delermina total: variable m. (d) 8710 50 : léLlh” : 3 if
(d) 3545 WI: .1 " ‘J'ﬂ/ ' 3.1,“
’< $355. —
(e) 1:283 "M4 : 35’
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‘i = a so a 1; _ a. A ﬁlm's production function is mun) : lying“. 1f the price of factor 1 in $14 and the 4' I“ Problem 1919: “h?" ﬁrmer H°glund a} V e: y 3 © :31)?” me' the marginal
price d factor 2 is $7. in what proporm' us should the ﬁrm use factors 1 and 2 if it wants to produot of fertllrner Ii; 1 — (A7200) bushels 3 g g S 2 ".1? $1 per bushel and
mm proﬁts? 4 l , the [more of fertilizer ls $0.30 per pound, l. S . . E 5' § § 'tlllzer per acre should ﬁx] 61""an N E p ’5’ _ J3- C ; P, %J : “-1 lb] Farmer Hoglund use in order to maximize g :3
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112mm. 11.6: 35-” 2 2 1 (b) 230 05: l' [I 2m. gr églLM
(d) We can't tell without luwulug on price of pint? (a) 74 0 DJ 3 Us 3 g- g
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mu 1 " 200 :3 C'A; ll
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1. Suppose um; D311; emu. long-mu total out of repairing , can per M in a“) - 4.2 + 144_ 4. ’Ibuchie MacFeelie‘s production funnl {7/ :32 g the number of old jokes
Ifthe price 119‘er ﬂor rewiring soar in $24. than in the long run. how many cars will he Elsed lindh 1;; is th: Bugger Di hllullTOfl ‘l” V) ~4- 8' lecIlclilwiih :00 Dilad jam:
ﬁxparweohi emnximimproﬂul’.’ 1 orw ic epai arseac . t »4 a arslt entetot
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2)) m $5 2‘] In Hm LK, he CM 64"” (a) 562 dollars. ' 3/4 t? E (2)(400)+(4) (515
(a) n 5 : 3 “(qﬂ‘i‘lﬂ pml‘i‘} =1) SAMTilPé'M/rl (c) 1.686dollars. §4_ 31.5- 1- a" ll 21.;
' (a) 1,173 dollars. ‘27 f L g1 g
3. In Problun 3-8. the supply cum oi any ﬁrm is 5:02) = 212. If a ﬁrm produces 2 units of (a) 231 dollars. 3 : I)” 5?.
output, what are its total variable costs? A I” C 1 ., g
a h = 3 5i ~ L -
1+" 45: PI; => F91”)
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(b) ‘2 SM (l: M C 2 #19) _> C V ('3) :JM ((3)43 soullanh'l’népgand new mm ﬁﬁthgmmohupglist in ableiompracafoperizcnt $53»
" ' ‘ Mia , 'ta total proﬁts will be
.. m 2 . . . ., '“ . mean-u)
:4 V f] ﬂ'D/Zﬂdlj : ’5 lo - 2-5 = .srml. no —42{3z)(£4)
(9) There is not enough information given to determine total variable emu. :3 :2; ‘ l 0 2 1.1
1. In Problem 25.1, the marginal cost ofproducing anotha copy or Ferdinand Sludge’s hook is (a) 81,535. 35 “41% "
$2. If demand in the US is given by Q; = Slam—200;)“ where p1 is the price in the US and if (a) 8256. _
thedanmndinEllglandisgivenby4,Dm—400m.wherepgisthaprioeinEnglnud,thenthe 325 E
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rhﬁ'erenoe banger: the piimadmrged in England and the price charged in the US will be L 32:2,: 3,123,003 pawn ﬁguring??? in minds-Lg Elvixzmmib 0"? a perm: unves at
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5. In Problem 27.4, suppose that the market demand curve for bean sprouts is given by P = , J )( ) >
2,080 — 49, where P is the price and Q is total industry output. Suppose that the industry ' 2(4) (4
has two ﬁrms, a Stlmkleberg leader and a follower. Each ﬁrm has a constant marginal cost 2 8
of $80 per unit of output. In equilibrium, total output by the two ﬁrms will he _ a l
P: Mlle—Lil! 46! lM- Ll *—
L F P a A Q (l 5’ 63
(a) 250. MRF :Zﬂ'w‘qﬂu' Mr :MCML 25 — L 25—0 ' ' é
a” ”5' 3RF: 2040 Jill; 69F =2” 7 - ....§J<a_§l%~ 3; r V
@ 375' Q F ; 15 0 » aL /7_ : l 2 r 5. There are two films in the blastopheme industry. The demand curve for blastophemes is given
,. b =2,7oo—4,Eachﬂ has fcti lat de hﬁmihasncos function
W) 500. Leader! [7: 2480 - «.1 gr, 4 (25—0 5 ﬂit/2) (9r 6?; 4 621- &£):q3,wnnin is enempucgihgnazu'ihe‘llvggnin; foil‘nazzrtelr and arrange :0 split a»
(a) 62.50. _ M 30 _ 2 ‘9'— : 1gg + ,2; lnl industry proﬁts equally. Under this cartel arrangement, they will maximize joint profitsif
TRL= I 931) 9L —?_ d: M 2.: : M M ' 43L :8.” Ill/IL : 3 75/ and only ileuh rum produces 150 unit: in its plant,
‘ "“ ' " ' " ' ‘ ' ‘ ‘ ‘ ' "“ ‘ ‘ ’ ‘ ‘ ' ' (b) they produce a total of 300 units. no mailer which ﬁrm prorluczs them.
a. A ﬁrm has a. long-run cost function, C(q) = liq“ + 144. In the long run, this ﬁrm will supply a (c) and only it they each produce a total of 337.50 units.
1308““? mount of Output. 321ml; 8! the Price ‘5 yea-tel" “In“ (a) they produce a mm or 225 units, no matter which ﬁrm produces them.
(I) M M A'L M C = 3‘ r— (e) may Shh? down one of the two plants, having the other operate as a mnnopoly Ami splitting
. eprq s. . .
(b) 31m. V AC _ L! + It”) EMA 4% la; lVlfﬂ'lll‘nl, lmmly “MW/151.17 mqmn/ 051‘. M44: 2ft
(a) 824. u- — 1- —-—~ To Mike. 1. unl'l)‘ V”; ”ti-Put Eng/l (lrm Mala: g ukc‘g a; out/P471,
@ 548. i“ ‘llu ML .9; Hm Mun-7L a; ouulpuJL I5 241" '9}- all.
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7f - +—- 7.7110 — 0]
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300 : 1;,
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A Q MR4 : SIR: = 25:5 an Ll ’5 Name
if, , 62c ‘ 270 - .9; (arm A
a. In thlsm 27.5,auppnus that Grinch and Gruhh go into the wine lnulnuu in unnall country l'W : 25.; - £€ _ a, M
where wins is difﬁcult to grow. The demand for wine is given by p: anon .20, where p is 2” alpha}, Q ECO sans
the pﬁos and Q is the total quantity sold. The industry comma of just the two Common (96. m LChaptei- ﬂQull
duopollsts, Grind: and Grubb. Imports are prohibited. Grinch has constant marginal costs \— ._ 2 - ‘9‘ A ml: 15 2014
_ Ill; .
of $30 and Grubb has marginal costs of 345. How much in Grinuh's output in equilibrium? l 3 57 5'- 9; 1 2M 1?”
9’5 (£5001? annual” 1&0.me 04ml M12;— “R; Q: Limo " ‘25 h
(5)1350 MR l - - l3|2 ‘ s thnthed mmmlms: lel 271i dmnm' it)
(c) «31.50 Emmi ~ 600 —.Ll ﬂﬁnﬂp 2 ﬂ ‘ ; ﬁi a...” 1' 1)??le Etta; ’11:” 200— 44:09, whkam Orggnth: €215?ng nﬁlﬁm In.» ﬁnish“ th:
. . 1 ._ t F t ion l . t r t r taut
(d) I’m” ”M?" 5—70 '2 awn“ wnrl, - 5- mnnlnm of $1.26,?“ alulﬂinpzln nim. If cm believes um Elmo-r: l: :lEugm
Til 2! l . .
(2) 2,925 62 a) r. MI, = IL] 2;. QAM“ 3 ‘ produce 0, pumpkin this yaar, than the reunion funchou tolls us how many pumpkins Carl M
K‘Wl'h W0 «,Zagnnu. 'KLlQG-mlab = qu
0‘” aurull:555 -.2 a - «mull amerL: 5337,; - unnnu. should produce hr order to mnximiis his proﬁts. Carl’s reunion function in Roma) = 4.300 — 042. 5:6 r:
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- Supply And Demand, comic books, JV, COLONEL TOM