sample-midt-solutions-2

sample-midt-solutions-2 - SUPPLV 64055. {2(th 3 TO 3' (whee...

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Unformatted text preview: SUPPLV 64055. {2(th 3 TO 3' (whee GOES FRoD PC To P. (QuAA/TITY Goes PROD (Q0 TO 62, aTflx Q" BOIH GRAPHS ARE @RQEQT_ b P :P5+t PD: {arglcg Pfllb 8‘7 THE CONSu-nére PS: PRICE RECEIVEA 6‘7 THE SELL:Q J.a l BOTH PRODUCER [Anus GONSNIEK becagflse— (63 SURPgU S §UQ,Pau$ bgfib WEIGHT L055 E: —_- A&/Q ‘ 6.6 /o _ __ 6‘6 70 ~‘2 ____.. - _______________ _, .v AP/P (IQ—:8)/18 -'— 3 SUPPogé TH: PK‘CG 3.3 Such T4447. SUPPLV I5 LARGGQ THAN DGDANB lHEN Ftflns CANT SELL fll—L The OUTPU7 TH5<7 Paobuct {*Nb WIGHT Tray TD Law/ea Pryce , IF, l~575n»/ TH€ PRtCE I; SUCfl THWD Sum-17 is SEIALLEK THEN benflmb’ THEN Sofie CDAJSUFLERA htGHT Tray TO OFFER. A HIGHER PQKCE To WP: —-—> A 2“ SmPe, 0Q \ndeEQreche CMVVC '- drab CCbULOC‘Rén Jeor S\OQe. OR o. Una -. AXL (fiSe. <9 ~ ‘ /Mt/ m h an md‘gertnce Curve, ' ‘ 3 W we“ um VQMCUNWS Lavfimrfi ) Wherefore : Ax Mum + MLMMZ = O *1": x. AX; \JAM'I/ bxl 3'AV [‘7‘ 3 fl‘ @ OWmPrL CoNSumeN ?O‘MT * Z?L® “Pi (Z/QD @13- ? L Q. 3’» We») a; V 2,? val : p‘ ___1_ ; ,___Z:— 2,"? 87/ Q‘ L V). dfin‘fig/ 091-1qu LONSLAm'o‘mOU 1H -‘> B L A wm?\1\,afixm QL‘L k I x 2— % w A «#5 : ammm‘o 671F661 ’ 6,5 C : lucomé EFFGCI Answer Key for Part III 1. 1. (a) This is the problem of a short run decision since the amount of bauxite is fixed. The firm chooses the amount of electricity that equates the marginal revenue product of electricity to the price of electricity. The optimal use of electricity can be represented in either way of the two below. (In the following PA denotes the price of one unit of aluminum.) MPE MRPE PE/PA ............................................................ pE :E :E (Grading Policy : A partial credit was given when it was not indicated what the sloped line meant but the graph was right. When one misunderstood the sloped line and mistakenly write PB, P or PA in place of PE , no credit was given.) (b). The firm chooses the optimal level of the two inputs, Bauxite and electricity, such that minimizes the cost incurred by producing the given output level Q. Therefore, the firm will choose an isocost line that is tangent to the isoquant curve of the given output level Q where the slope of the isocost line is determined by the ratio of the price of inputs. Optimal Choice of Inputs 13* Isocost Line : C = E* PE+ B* PB Isoquant at Q E F (c). The tangency implies that two equations hold at the optimal choice of inputs, E* and B :C=E*PE+B PB (orQ=F(E ,B ))andMPflPE=MPB/PB. (Grading policy: A full credit was given to any answer that contains the tangency condition MPE/PE = MPH/PB although one needs one more equation : cost line equation or production function. When only the cost line equation or production function equation was given, I gave a partial credit.) ((1) Since the firm needs to remain at the same level Q, the optimal choice of inputs should be on the same isoquant but at a different tangency point because the relative price of inputs has changed. In order to maintain the same level of output, the firm would increase use of bauxite and decrease use of electricity because the latter has become relatively Cheaper than the former. Graphical representation of this logic is as follows: New Isocost Line : C = E P’E+ B PB Optimal Choice of Inputs After Change in PE Optimal Choice of Inputs Before Change in PE Old Isocost Line : C = E PE + B PB Isoquant at Q =. s E E’ E* (Grading policy: I gave a partial credit that simply says E goes down and B goes up. I gave a full credit to any answer that contains a correct explanation of why B needs to go up, either graphically or verbally.) Part III 9% Given optimal inputs (bauxite and electricity, or labor and capital, etc.) as a function of input prices and output, i.e. B*( p1,,pe, Q) and E *(pb, pg, Q), we know that the total cost as a function of output is: C(Q) =pb' B *( pupa Q) We E *(pwe, Q)- Marginal cost is then just the slope of the total cost function, i.e. the cost of producing one more unit: MC= AC(Q) = _AB*(pb,pe,Q)+pe_AE*(pb,pe,Q) AQ AQ AQ Note that finding marginal cost does not depend on the P=MC profit—maximizing rule for a perfectively competitive firm. This rule is used to determine the optimum output level. b om: Cost function a+bQ+dQ2 (a) Fixed cost is all costs that must be incurred regardless of how much output is produced. Fixed cost is a. (b) Variable cost is total costs minus fixed costs. So variable costs are bQ+dQZ. (c) Average cost is total costs divided by output: 2 Ac=E=M=g+b+dQ Q Q Q cm This question asks you to express profits in terms of price, average cost, and output. We know that profits are defined to be total revenues (P- Q) minus total costs (TC). Since total cost is simply average cost (AC) times output, we have the following relationship between profits, average cost, and output: PROFITS = P-Q— AC - Q = Q(P—AC). \WVE Qw/s’h‘m :1 \ W [47?) q at)" Méx‘Q—WQ Law/4's) (Ls QWM badges ‘. 7w, _’ Qwshm ji’z, \ \ * (a) 999%.”; WWrtW») ow:qu \s Q wmmn Sou/w, Arne, Q“=”> aim 9=ML 51> Q=Q*2 =9 (3mm uwk Q > Q? m wavx Wk’es MSW»; \omvhfivwd. UMH—s 8246?") the '1'»qu he, {-wa m)be {AMA “Aule Mm vua‘k— pmlww “Ase WW3- P%~h LP>ML). Twew ) m {JV‘M WM MQMVJ“ 0AA “9M4 mew FNM- Agrer gas/U: 9=Hc, mJ‘W W3 aubL WW4»: firm; pesflkejg LMNFBMQ, +19 :55 Wear WMM W659 "cmgagw‘fip “VF-“ML 2“ E'WIS Qwfiuh AV‘QI‘M‘EW‘L (in ? max—m4 3 U9 ufive saw“ 9% M W qc: quad-b”ch Qno&uw& ‘0‘ my 0W1 WKMACl-CL ed ang. T = vq- cam WK“ =PQ—ecm Q P61- 7 V'- VLLLfiflsc ‘17 PtrvLLCQ') K aux LNFHM‘ 0“ §Ammz>s1 W\.&r\ Fran, " w \ WKLt’T \QM; “(gm on 3% \N‘s‘LQ \z firm“ J ad» Guam QH‘LQ. P2ML. : 7— i. on ?2_ ME‘DEI— ANSUJER (“KL IFLTB Th; wwm W «s x“? x1 o—rc. somfi‘wc: so IQ __ x L R) xLxI/ We“. 13 o\ "Waugh/Q. stv 091M. no» bnnbu‘dgcfi” “‘M‘l- a?“ '\b TANCri NT +0 “(AL or; ‘moA \nckicCoKncL, vac. . /t\4\s Ks KM. ‘mm (“1. Cgkc’r‘ 3+ "\6 Wmswhi SWhicJflla hut. - (DKQWLL ‘0va l ’9'“. VngA qubg‘r \irv.’ 1 mg, “ng‘x’ fPoLc’r I V C13 Mob EL. ANSwCK sunk C03’VS ‘ arc, m {xywdx'tW-L fixed- has beg,“ muck. Wodr commfv \oc. ucovuad- BC.ch 'I’r \AKB n0 cA-‘pcvxa-‘MC. \bL, \‘\”$ OQPDVMKW (.53? i$ 200). 19 Sunk Lush \ALKOKSQ.’ Wm. Cum oazH bt. LCZSS \qujqu ’11) cxi’c. ’n/xib \b bccm; ’ML, ogp§qu C°$\~ a? boqu \n ’\\ML_. kaifiCSS ‘5 new \Qmer. (Swfik QOSX‘S 4‘ =3 6?? ash 473‘ cm mow fictovu \e, 53 065035 when ex'x‘rj Anew; use/3&0 aea/ Unéqrsw M’v L1th We”; Wk SLNL Cir-3T Maw) (CL'toQLh-E % WWW “re—M l 041‘ . 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This note was uploaded on 04/08/2008 for the course ECON 115 taught by Professor Stevenberry during the Fall '07 term at Yale.

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sample-midt-solutions-2 - SUPPLV 64055. {2(th 3 TO 3' (whee...

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