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Unformatted text preview: Consider a firm with cost function 1800 ifq : 0
C(q) = where q is the firm’s output.
5000 +3092 + 2q’ ifq > 0 SUPPDQC the ﬁrm Herc n: :1. Competitive pricotnkcr Find it: Gimp!) function and it:
producer’s surplus as a function of the price. 0 or L{O {£P=iqo ‘30 .
fag 1’? P>i90 producer’s surplus PS(p) :— O ic P E {=1 .. (so? ﬂlﬂoo Answer: supply function 5(1)) : 8 :41 p>l‘10
Show your workfexplain:
i800 ES Sunk J Sbooqgw: 3200 is auoidabfe Gaeﬂcort
Average nowsunk (109+ iS ACTan 322,0 4 30 +029 mavgincd cosi a"; mug): 30+4Q Solve ACCQ): MUG) £0» CQ: 3320 +30 +20. 3 30%“)?
or Q :40 wiHA ACWO) 2 mcCW: 190 For P>ici0’ 9oiue (“Cf/62):? govai Boa'40:? 0v : Pal{30
9L?) For [)7 [0L0]
9.
[33: (3359—)— ~3200
~30 40
or 2' _;cio('1T '3‘
_———————""——""" z: The long—run competitive equilibrium fora market in which firms have cost function
(“(61) = 80000 + 25f for q > 0 and C(O) : 0, where q is the firm’s output. and aggregate demand is
D(p) : 94:000 i 1000, where p is the per—unit price. is p* = 800 and Q* = 14,000 with 70 active
firms producing cf“ : 200 each. Suppose the 80000 in the cost function represents the salary paid to a manager needed to
coordinate production The number of potential managers with this skill level is unlimited. and
all have the option of working in a different industry in which they could obtain wage 80.000 per
period Starting from the longiruu equilibrium specified :iboxc. suppose that :1 new group of
potential managers becomes available. All the new potential managers are identical. and identical
to the original managers, in their abilities outside this industry and all but two are identical to the
original managers in terms of their skills in this industry as well. However, two ofthe new
potential managers. Melba and Nora, are known to have a different level of skill when
organizing production in this industry. When Melba runs a firm in this industry, its cost function
(ignoring the manager—salary portion) is 500q + 0.3756}2 while the corresponding cost when Nora
runs a firm is 2004: + 0.75972. in the new longrun equilibrium, where do Melba and Nora work and what are their salaries?
Answer: Melba works i“ ‘1 d'g'gere“+ for salary: 80, 000
twins—fry
Noraworks Ivi. HmiS MAME? forsalary: [$10,000
I A .13ng w'.‘i"ln Nova al'Saiﬂwy Showyourwork/explain: : S 'paCI‘Vlj Price P: 800 A “Firm valPk Menace a'i' ‘ P: 800.; Mg = 200 44.562
Quint?! S 43cm: price p: 800 t atsctoo p: 800 2 me, = 600+ 07552 phi 625L100) revauue—Cos'i‘ is of = Lloo 1 @ml Lion)——[QZooIqoo)+ (9.7§(Lloo)1+ 5'] A4. Q*=L[oo) revenue. —€‘.0$+ iS L800) (lino) — [QtTooxclw) 4 0.3750400)? +Sj ( = [20,000 S
Firms Compe‘l‘e hahure
: £30,000 “S l Nara uwvlril her Salary
The Ltvm Camelot “0+ {myvive I “(5 {10,000 ahd +ke ﬁrm
Paw“i Melba! 801000 . Thus “it”? imm st+ breaks
Sh?— wavl’ss elsewhere ‘pov‘ i even. Site rePlaLes o? of
gqtary Eozdgo 5 'P'te Y‘ejvtlav manage/cg, Consider a competitive market with aggregate demand function mm = 1400 7 [Up for p
5 I40 [and D(p) = 0 forp > I40].
Each firm has supply function $(p) : U for p < 50
5(50) 2 0 or [0 and
(in) : p 40 far In ‘> V]
a. If there are 15 firms. what are the shorterun competitive equilibrium price. aggregate
quantitv. concumerc‘ anplus. and omrlucerq’ QUIT‘lIIQq Answer: price 2 O aggregate quantity = (00 O producers” surplus : {lgo Show your work/explain: Asquime 50<P< HO. We“ «agreﬁa‘ie ‘5“?le lg
lsiPr‘r‘Dl ‘3 (SP 600 curl Supply ts egucql +0
Cleft/Laon wlteu igpvéoo '= i400“iOP 0*“ $380 . Male 50 <Pi< Wt)) 30 +lte
Cormulag ucecx “For 5&5)le awe (Lamamoi are.
Corree‘l". Q‘k = DCSO) : 600 as : (42) (Ho —Bo)(c,oo) ~_ [8000 Pg : (80~§0)( Eggﬂ? : llJ§O b. In the long run. with free entry and exit. what are the competitive equilibrium price.
aggregate quantity. consumers‘ surplus. and producers surplus? Answer: price = [50
aggregate t'lurmtity f C“? O
t'ﬂttsttmei's‘ sttrplw 7 producers surpius = Show your work/explain: {leg Qw‘li‘v'y) Price; (Lani/10+ be IAVJEY‘ HQ“ (:05 par‘i‘CQB) DOS—O) 7 O ) So [’34: (5—0. (Q44? 3. Suppose the demand function for chicken can be expressed (in the relevant region) as
Q 2 I 10+ IOM—70p+ 20])?
where Q is the quantity of Chicken demanded (in millions of kilograms per year). M is average
household income in thousands ot‘doilars per year.p is the price of chicken in dollars per
kilogram. and p3 is the price of beef in dollars per kilogram Calculate the own—price elasticity of
LlCllliillLl lot thlL‘le‘ll \\llCil.l1r: 4H1,” 2 —i_ and ,H: = (S. Show )titti' nullh . . ‘1
Answer: Elasticity: '“ O‘. E) Show your work/explain: m.
H 3.29;
c? 9? ll L! (llwa 5: L (70) z _ 0.8 b. Suppose the own price elasticity of demand for beef is — 0.8 and the cross price (chicken
price) elasticity of demand for beef is 0.4. Starting from a beef price of $6 per kilogram, a
chicken price of $4 per kilogram. and a quantity demanded of 30 million kilograms per month, if
the price of chicken decreases in $3 per kilogram. does the quantity of beef demanded increase or decrease. and by how much? .  _ : I" 7'»!
.XHDHL‘L iiiciedn, m LlLJLlL'slbl‘. Hpuvcuﬁ‘ﬁ 3 “ﬂiuiou Per Mei1+“ SiZe of change : Show your i\'0rkfexplaiilz The ci'ii‘cicevi price 25 damaging} so +llie + e
I " (— cu‘ (9M l
aim99 Price elggii‘Ciiyj (DJlJ is ‘l'ixe, eev W A92 13f
T 1’ (OLD P AQ: @H) (so) : “3 0‘ 190/5; diacreqSe Tm Ha firch dJ‘F {3 0T
0 Elie/ken leach c1 (OJ(7(ch78 '3 [0
(JCCIFECUSe ?V\, 1"qu 5Mkn+f+y all bee£4
demawﬂecq j wlxcek [S q olecrque c3 3 Each of two firms uses labor. L. and capital. K. to produce the same output good. The
first firm has production function ftLi‘ K1) and the second firm has production function gal. KZ)‘
where each production function has strictly diminishing marginal rate of technicat substitution. At input bundle (Ll. K,) = (5., ll). the first firm’s production function has output 87 and
its marginal products are 2 for labor and 3 for capital. At input bundle (Ii. K} = (7. Q). the second firni‘s production function has output on
and its marginal products are e for labor and 9 for capital. Throughout this problem. the total amount of resources available to he split
between the two ﬁrms is (13“, R“) = (S, 11) + (7, 9) = (12, 20). at What does the statement that a firm‘s “production function has strictly diminishing
marginal rate of technical substitution" mean? For any pogf‘Ht/i? ow‘l‘pu‘f’ level) as
we move (dawn «hang ‘HtQ I'Sogwan'i' Correspovwhwo? ‘i‘e ‘H'ue‘t' ow‘i—pwd’ level
‘H'LQ iSo guani becomes «Hathear ‘iGeru‘l' . l'vie‘;
C the Slope of a line +aw3en‘i ‘l‘o ‘
_________________________
. L.
the (Saguayd' % exi—S those» +0 'z—exo]
b. Decide whether the following statement is true, or false, or uncertain, and explain. It is not possibte to produce more than 6l2 + 87 = 699 in total using the two firms. Answer: True or false or uncertain? i: al. 5 6 Explain: Bo‘l‘lﬁ labor CLKA Capi'i‘ﬁi are. mice. Prodwc‘l‘ive rt». +ke Secouo‘ {lirm 1
EMF; = a < c, = me: wt WPL“r 3L ‘12 Wk
11 ULS Movivij 0x SWLOL“ QMOULVL+ O'i' {ulnar 0v Cupi‘i‘al 4:chqu yttrm 1 "F0 fiYm l boole
increase. +o‘i‘ai ou‘l‘abu‘l'. (3. Decide whether the foliowing statement is true. or false. or uncertain. and explain.
It is not possibie to produce more than 612 in firm 2 if firm 1 is required to produce 87'. Answer: True or false or uncertain? [ R“ E. Explain: ! \
NETSIC §_ MPLKSM) _ E“
g’ H F MP; (9,10 3 mngC‘m) : “PLmtg) .3 9. z 1
thft'm) ‘1 3 AW inktvfov saiu‘i—EOM 4‘0 Mme 3(Lz,l<z) sawed“ 1L0 £(flL1’10K75=87
L13l<z I
("S C/LWY‘QC‘I’ETE'EcJ MRTSZCL'LJI‘CL): (ll‘L'L/ZO’KQ') [1+ 1% a» mandvm’terr because new ﬁrm
have. (Jamimm? men] The Covwii‘i'i‘ou WMQ a‘i' LL24 Kw] 3" bf”)
gum.— awe rs +1"; Ws+ Admin!
be Mamet by {cm 1 wkew Cimi ...
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This note was uploaded on 04/02/2012 for the course ECON 340 taught by Professor Mostafabeshkar during the Spring '08 term at Purdue University.
 Spring '08
 MOSTAFABESHKAR

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