Exam 1 Solution - Consider a firm with cost function 1800...

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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 i-c 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 now-sunk (109+ iS ACTan 322,0 4 30 +029 mavgincd cos-i a"; mug): 30+4Q Solve ACCQ): MUG) £0»- CQ: 3320 +30 +20. 3 30%“)? or Q :40 wi-HA 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 long-run 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: [$10,000 I A .13ng w'.‘i"ln Nova al'Saiflwy Showyourwork/explain: : S 'paC-I‘Vlj Price P: 800 A “Firm val-Pk Menace a'i' ‘ P: 800.; Mg = 200 44.562 Quint?! S 43cm: price p: 800 t atsctoo p: 800 2 me, = 600+ 0-7552 phi 625L100) revauue—Cos'i‘ is of = Lloo 1 @ml Lion)——[QZooIqoo)+ (9.7§(Lloo)1+ 5'] A4. Q*=L[oo) revenue. —€‘.0$+ iS L800) (lino) —- [Qt-Tooxclw) 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 (Lama-moi are. Corree‘l". Q‘k =- DCSO) : 600 as : (42-) (Ho —Bo)(c,oo) ~_ [8000 Pg : (80~§0)( Egg-fl? :- 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 = [5-0 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' null-h . . ‘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 Mei-1+“ SiZe of change : Show your i\'0rkfexplaiilz The ci'ii‘cicevi price 25 damaging} so +llie + e I " (— cu‘ (9M l aim-99 Price elggii‘Cii-yj (DJ-lJ 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 «Hath-ear ‘iG-eru‘l' . l'vie‘; C the Slope o-f 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 boo-le 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) : “PL-mtg) .3 9. z 1 thft'm) ‘1 3 AW inktvfov saiu‘i—EOM 4‘0 Mme 3(Lz,l<z) sawed“ 1L0 £(fl-L1’10-K75=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. (Jami-mm? 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.

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Exam 1 Solution - Consider a firm with cost function 1800...

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