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# Class Note for EconS 452 with Professor Marsh at WSU 06

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This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Washington State University taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15
O ECONS 452 Advanced Business Management Economics Lectures 78 FinnIndustry I Production Analysis Total Product Marginal Product Average Product lsoquants lsocosts Cost Min ll Cost Analys Total Cost Variable Cost Fixed Costs Cubic Cost Function Cost Relations Ill MultiProduct Cost Functions Production Analysis 39 Production Function 39 Q FKL o is quantity of outputproduced K is capital Input L is labor input F is afuncttonal form relatingthe Inputs to output The maximum amount of output that can he produced with K units of capital and L units of labor 39 ShortRun vs LongRun Decisions 39 Fixed vs Variable Inputs quotE Production Function Algebraic Forms Linear production function inputs are perfect substitmes Q FKL aK bL Leontief production function inputs are used in fixed proportions Q FKL minbKcL CobbDouglas production function inputs have a degree of substitutability QFKLK Productivity Measures Total Product Total Product TP maximum output produced with given amounts of inputs Example CobbDouglas Production Function Q FKL K5L5 K is fixed at 16 units Short run CobbDouglass production function a 165 L5 4 L5 Total Product when 100 units oflabor are used a a 11 j mm an units Productivity Measures Average Product of an Input Average Product of an input measure of output produced per unit ofinput I Average Product of Labor APL QIL Measures the output of an average worker Examp Q FKL K5L5 lfthe puts areK 16 and L isthen the average pruduet uf lahnrlsAPrl16quot l16quot 16 1 I Average Product of Capital APK QIK Measures the output of an average umt of capital FK L K5 L5 lfthe puts areK 16 and L s AlK 116quot 1mum1 s then the average pruduet uf Productivity Measures Marginal Product of an Input Marginal Product on an input change intotal output attributable to the last unit of an input I Marginal Product ofLahor MPL AQIAL Measures the output produced by the last worker slope ofthe shortrun productionruncuon Mlth respectoo laborl I Marginal Product of Capital MPK AQIAK Measures the output produced by the last unlt of capital When capital IS allowed to vary Inthe short run MlK IS the slope ofthe production function lwrth respectoo capltalj Increasing Diminishing and Negative Marginal Returns Q imam DH is Margzml Mayan Retms Returns Return w Guiding the Production Process I Produ 39ng on the product39on function 39 ng incentives to induce maximum worker I Employing the right level of inputs When labor or capital vary in the short run to maximize pro t a manager will hire lahor until the value of marginal product of labor equals the wage lMPL w where lMPL P x mm capital until the value orrnarginal product of capital equals the rental rate lMPK r where VMPK P x MPK lsoquant I Illustrates the longrun combinations of inputs K L that yield the producer the same level of output I The shape of an isoquant re ects the ease with which a producer can substitute among inputs while maintaining the same level of output Marginal Rate of Technical Substitution MRTS I The rate at which two inputs are substituted while maintaining the same output level MP L WTSKL K K Capital and lahorare perrect substitutes Q aK hL MRTsKL hla Linear isoguants imply that inputs are substituted at a constant rate independent ofthe input levels employed lmvemmg Leontief lsoquants Capilalandlahnrarepe ed K Q enmnierne Can ai and iairnrare used in Q xedrprnpnninns 0 inh 5 ee cap cansumed there is nn ms 01 lmvemmg 0m K eL ai and iaimr are xed nrnnn nns Inpulsuhslilulinn Inputs are nnl nerieew suhsl uiairie Incmnsmg 0m As less ninne input is used in the prnduclinn nrneess increasingly rnnre nnne niner zlnnu ianuzn39s thencm m7 npul must he emplnyed In MRTSM prnducelhe same nulpul level q KlLb L L l W39 K Nuwlsoeostbm quots inpmsrhm aswciatadwithhighav prnduce 29 en ievei nlnulpul Cquot me n cu C St M39n39m 39Zat39on aune sarne ensi q WL 39K 5 I Marginal product per dollar spent should be equal Rearranging K 100 wrL cw cm L 1 Fnrgiveninpulpricesisncnsts K r ianherirnrn the wig are anlsocostbmfw dwilh ner casts a adacvaasamtha changes in innm nriees change my maclabor Iheslnpenllheisncnslline WagtWJ L nan mu sine rm Cost Minimization K Pom 90 menmnon Optimal Input Substitution A lm Innmly muucvs a K by anthymn e mmhmmmn n nnns yerresents Wrmlm A a a rst n c sunnnse w are In w rne Isncns mm Mares mumemlnckwlse wnm mnmsemslhe sane ens Ian rmnrtn ineware mange In nrnuucelhe sane level quotrunner on me rm w quum an a rm Igumsl line is a a nmm me sinnemmenew isnmsi irne murmms Ihelnwa wane maweln the rmlal rae in canal Types of Costs I ShortRun leed costs we Sunk costs Shortrun vanable costs we Shortrun total costs 170 LongRun All costs are vanable No fixed costs CQ Minimum total cost 3 of producing alternative clt vcm levels ofoutput VCQ CQ VCQ FC VCQ Costs that vary with output w FC Costs that do not vary n Qe with output w w FC coststhatdo rrot eharrge 3 as output changes Sunk cost Aeostthatrs forever 1ost a er rt has been paro Deersrou makers should rguore sunk eosts to clt vcm VCQ maxxmxze pm t or rrururruze I lnsses Average Tntal cost ATc AVC AFC 3 Am CQQ Average Vaname cost Avc VCQQ Average Fured cost AFC FCQ Margrrra1 cost MC ACAQ MC ATC Avc QHKATCrAVC Qn x AFC QnKFCQn anAVC QochltQono1 V CQn AVC MC anATC MC ancQnQn cQn ATC Cubic Cost Function 39C0fa0h02003 I Marginal Cost Memorize mm a 2m 3c02 Calculus dCIdQ a ZhQ 3002 i 52 An Example Total Cost CQ 10 o 02 Variable cost function vqm a o 01 Variable cost of producing 2 units vcmz m1s Fixed cost rc 1n Marginal cost function qu 1 20 Marginal cost of producing 2 units MCiZ1oZiZ5 LongRun Average Costs Economies nfSEale Disecnnnmles nfSEale 2 Q MultiProd uct Cost Function I CQ1 02 Cost ofjointly producing two outputs I General function form CQthfaQiQ2 be 6sz Economies of Scope 39 Clo 0 CW 02 gt 01102 It is cheaper to produce the two outputs jointly instead of separately I Example It is cheaper for TimeWarner to produce Internet connections and Instant Messaging services jointly than separately Cost Com plementarity I The marginal cost of producing good 1 declines as more of good two is produced AMC1Q102 A02 lt o I Example Cow hides and steaks Quadratic MultiProduct Cost Function 39 01102 f aoloz 01V 02 2 I MC1Q1 02 ZQZ 201 I MC2Q1 02 a01 202 I Cost complementarity a lt 0 I Economies of scope f gt a0102 Clol r0 CW 02 f Q1F f 022 01102 f 3 0102 I 01F I 02 l2 f gt a0102 Joint production is cheaper A Numerical Example clo1ozl so 20102 01 2 02 l2 I Cost Complementaritw Ves since a 2 lt 0 mc1lo1 oz 402 201 I Economies of Scope Ves since 90 gt 20102 We Conclusion To maximize profits minimize costs managers must use inputs such that the value of marginal of each input re ects price the rm must pay to employ the input The optimal mix orinputs is achieved when the MRTsKL wr Cost runctions arethefoundationforhelping to determine pro tm axinlizing behavior in future chapters

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