1、Chapter 7The Cost of ProductionChapter 1Slide 2Topics to be DiscussednMeasuring Cost: Which Costs Matter?nCost in the Short RunnCost in the Long RunnLong-Run Versus Short-Run Cost CurvesChapter 1Slide 3Topics to be DiscussednProduction with Two Outputs-Economies of ScopenDynamic Changes in Costs-The
2、 Learning CurvenEstimating and Predicting CostChapter 1Slide 4IntroductionnThe production technology measures the relationship between input and output.nGiven the production technology, managers must choose how to produce.Chapter 1Slide 5IntroductionnTo determine the optimal level of output and the
3、input combinations, we must convert from the unit measurements of the production technology to dollar measurements or costs.Chapter 1Slide 6Measuring Cost:Which Costs Matter?nAccounting CostlActual expenses plus depreciation charges for capital equipmentnEconomic CostlCost to a firm of utilizing eco
4、nomic resources in production, including opportunity costEconomic Cost vs. Accounting CostChapter 1Slide 7nOpportunity cost.lCost associated with opportunities that are foregone when a firms resources are not put to their highest-value use.Measuring Cost:Which Costs Matter?Chapter 1Slide 8nAn Exampl
5、elA firm owns its own building and pays no rent for office spacelDoes this mean the cost of office space is zero?Measuring Cost:Which Costs Matter?Chapter 1Slide 9nSunk CostlExpenditure that has been made and cannot be recoveredlShould not influence a firms decisions.Measuring Cost:Which Costs Matte
6、r?Chapter 1Slide 10nAn ExamplelA firm pays $500,000 for an option to buy a building.lThe cost of the building is $5 million or a total of $5.5 million.lThe firm finds another building for $5.25 million.lWhich building should the firm buy?Measuring Cost:Which Costs Matter?Chapter 1Slide 11Choosing th
7、e Locationfor a New Law School BuildingnNorthwestern University Law School1) Current location in downtown Chicago2) Alternative location in Evanston with the main campusChapter 1Slide 12nNorthwestern University Law School3) Choosing a SiteuLand owned in ChicagouMust purchase land in EvanstonuChicago
8、 location might appear cheaper without considering the opportunity cost of the downtown land (i.e. what it could be sold for)Choosing the Locationfor a New Law School BuildingChapter 1Slide 13nNorthwestern University Law School3) Choosing a SiteuChicago location chosen-very costly uJustified only if
9、 there is some intrinsic values associated with being in ChicagouIf not, it was an inefficient decision if it was based on the assumption that the downtown land was “free”Choosing the Locationfor a New Law School BuildingChapter 1Slide 14nTotal output is a function of variable inputs and fixed input
10、s. nTherefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or VC FC TCMeasuring Cost:Which Costs Matter?Fixed and Variable CostsChapter 1Slide 15nFixed CostlDoes not vary with the level of outputnVariable
11、 Cost lCost that varies as output variesMeasuring Cost:Which Costs Matter?Fixed and Variable CostsChapter 1Slide 16nFixed CostlCost paid by a firm that is in business regardless of the level of outputnSunk Cost lCost that have been incurred and cannot be recoveredMeasuring Cost:Which Costs Matter?Ch
12、apter 1Slide 17nPersonal Computers: most costs are variable lComponents, labornSoftware: most costs are sunklCost of developing the softwareMeasuring Cost:Which Costs Matter?Chapter 1Slide 18nPizzalLargest cost component is fixedMeasuring Cost:Which Costs Matter?A Firms Short-Run Costs ($)050 050-15
13、0501005050501002507812828253964350981482016.732.749.34501121621412.52840.555013018018102636650150200208.32533.3750175225257.12532.1850204254296.325.531.8950242292385.626.932.4105030035058530351150385435854.53539.5Rate ofFixedVariableTotalMarginalAverageAverageAverageOutputCostCostCostCostFixedVariab
14、leTotal(FC)(VC)(TC)(MC)CostCostCost(AFC)(AVC)(ATC)Chapter 1Slide 20Cost in the Short RunnMarginal Cost (MC) is the cost of expanding output by one unit. Since fixed cost have no impact on marginal cost, it can be written as:QTCQVC MCChapter 1Slide 21Cost in the Short RunnAverage Total Cost (ATC) is
15、the cost per unit of output, or average fixed cost (AFC) plus average variable cost (AVC). This can be written:QTVCQTFC ATCChapter 1Slide 22Cost in the Short RunnAverage Total Cost (ATC) is the cost per unit of output, or average fixed cost (AFC) plus average variable cost (AVC). This can be written
16、:QTCor AVC AFC ATCChapter 1Slide 23Cost in the Short RunnThe Determinants of Short-Run CostlThe relationship between the production function and cost can be exemplified by either increasing returns and cost or decreasing returns and cost.Chapter 1Slide 24Cost in the Short RunnThe Determinants of Sho
17、rt-Run CostlIncreasing returns and costuWith increasing returns, output is increasing relative to input and variable cost and total cost will fall relative to output.lDecreasing returns and costuWith decreasing returns, output is decreasing relative to input and variable cost and total cost will ris
18、e relative to output.Chapter 1Slide 25Cost in the Short RunnFor Example: Assume the wage rate (w) is fixed relative to the number of workers hired. Then:QVC MCL VCwChapter 1Slide 26Cost in the Short RunnContinuing:L VCwQL MCwChapter 1Slide 27Cost in the Short RunnContinuing:L MPLQLMP1QL Qunit 1 afor
19、 LChapter 1Slide 28Cost in the Short RunnIn conclusion:nand a low marginal product (MP) leads to a high marginal cost (MC) and vise versa.LMP MCwChapter 1Slide 29Cost in the Short RunnConsequently (from the table):lMC decreases initially with increasing returns u0 through 4 units of outputlMC increa
20、ses with decreasing returnsu5 through 11 units of outputA Firms Short-Run Costs ($)050 050-150501005050501002507812828253964350981482016.732.749.34501121621412.52840.555013018018102636650150200208.32533.3750175225257.12532.1850204254296.325.531.8950242292385.626.932.4105030035058530351150385435854.5
21、3539.5Rate ofFixedVariableTotalMarginalAverageAverageAverageOutputCostCostCostCostFixedVariableTotal(FC)(VC)(TC)(MC)CostCostCost(AFC)(AVC)(ATC)Chapter 1Slide 31Cost Curves for a FirmOutputCost($ peryear)100200300400012345678910111213VCVariable costincreases with production andthe rate varies withinc
22、reasing &decreasing returns.TCTotal costis the verticalsum of FC and VC.FC50Fixed cost does notvary with outputChapter 1Slide 32Cost Curves for a FirmOutput (units/yr.)Cost($ perunit)25507510001234567891011MCATCAVCAFCChapter 1Slide 33Cost Curves for a FirmnThe line drawn from the origin to the tange
23、nt of the variable cost curve:lIts slope equals AVClThe slope of a point on VC equals MClTherefore, MC = AVC at 7 units of output (point A)OutputP100200300400012345678910111213FCVCATCChapter 1Slide 34Cost Curves for a FirmnUnit CostslAFC falls continuouslylWhen MC AVC or MC AVC or MC ATC, AVC & ATC
24、increaseOutput (units/yr.)Cost($ perunit)25507510001234567891011MCATCAVCAFCChapter 1Slide 35Cost Curves for a FirmnUnit CostslMC = AVC and ATC at minimum AVC and ATClMinimum AVC occurs at a lower output than minimum ATC due to FCOutput (units/yr.)Cost($ perunit)25507510001234567891011MCATCAVCAFCChap
25、ter 1Slide 36Operating Costs for Aluminum Smelting ($/Ton - based on an output of 600 tons/day)Variable costs that are constant at all output levelsElectricity$316Alumina369Other raw materials125Plant power and fuel10 Subtotal$820Chapter 1Slide 37Operating Costs for Aluminum Smelting ($/Ton - based
26、on an output of 600 tons/day)Variable costs that increase when output exceeds 600 tons/dayLabor$150Maintenance120Freight50 Subtotal$320Total operating costs$1140Chapter 1Slide 38The Short-Run VariableCosts of Aluminum SmeltingOutput (tons/day) Cost($ per ton)1100120013003006009001140MCAVCChapter 1Sl
27、ide 39Cost in the Long RunnUser Cost of Capital = Economic Depreciation + (Interest Rate)(Value of Capital)The User Cost of CapitalChapter 1Slide 40Cost in the Long RunnExamplelDelta buys a Boeing 737 for $150 million with an expected life of 30 yearsuAnnual economic depreciation = $150 million/30 =
28、 $5 millionuInterest rate = 10%The User Cost of CapitalChapter 1Slide 41Cost in the Long RunnExamplelUser Cost of Capital = $5 million + (.10)($150 million depreciation)uYear 1 = $5 million + (.10)($150 million) = $20 millionuYear 10 = $5 million + (.10)($100 million) = $15 millionThe User Cost of C
29、apitalChapter 1Slide 42Cost in the Long RunnRate per dollar of capitallr = Depreciation Rate + Interest RateThe User Cost of CapitalChapter 1Slide 43Cost in the Long RunnAirline ExamplelDepreciation Rate = 1/30 = 3.33/yrlRate of Return = 10%/yrnUser Cost of Capitallr = 3.33 + 10 = 13.33%/yrThe User
30、Cost of CapitalChapter 1Slide 44Cost in the Long RunnAssumptionslTwo Inputs: Labor (L) & capital (K)lPrice of labor: wage rate (w)lThe price of capitaluR = depreciation rate + interest rateThe Cost Minimizing Input ChoiceChapter 1Slide 45Cost in the Long RunnQuestionlIf capital was rented, would it
31、change the value of r ?The User Cost of CapitalThe Cost Minimizing Input ChoiceChapter 1Slide 46Cost in the Long RunnThe Isocost LinelC = wL + rKlIsocost: A line showing all combinations of L & K that can be purchased for the same costThe User Cost of CapitalThe Cost Minimizing Input ChoiceChapter 1
32、Slide 47Cost in the Long RunnRewriting C as linear:lK = C/r - (w/r)LlSlope of the isocost: uis the ratio of the wage rate to rental cost of capital.uThis shows the rate at which capital can be substituted for labor with no change in cost.rwLKThe Isocost LineChapter 1Slide 48Choosing Inputs nWe will
33、address how to minimize cost for a given level of output.lWe will do so by combining isocosts with isoquantsChapter 1Slide 49Producing a GivenOutput at Minimum CostLabor per yearCapitalperyearIsocost C2 shows quantity Q1 can be produced withcombination K2L2 or K3L3.However, both of theseare higher c
34、ost combinationsthan K1L1.Q1Q1 is an isoquantfor output Q1.Isocost curve C0 showsall combinations of K and Lthat can produce Q1 at thiscost level.C0C1C2CO C1 C2 arethreeisocost linesAK1L1K3L3K2L2Chapter 1Slide 50Input Substitution When an Input Price ChangeC2This yields a new combinationof K and L t
35、o produce Q1.Combination B is used in placeof combination A.The new combination represents the higher cost of labor relativeto capital and therefore capital is substituted for labor.K2L2BC1K1L1AQ1If the price of laborchanges, the isocost curvebecomes steeper due to the change in the slope -(w/L).Lab
36、or per yearCapitalperyearChapter 1Slide 51Cost in the Long RunnIsoquants and Isocosts and the Production FunctionKLMPMP- MRTSLKrwLK lineisocost of SloperwMPMPKL andChapter 1Slide 52Cost in the Long RunnThe minimum cost combination can then be written as:lMinimum cost for a given output will occur wh
37、en each dollar of input added to the production process will add an equivalent amount of output.rwKLMPMPChapter 1Slide 53Cost in the Long RunnQuestionlIf w = $10, r = $2, and MPL = MPK, which input would the producer use more of? Why?Chapter 1Slide 54The Effect of EffluentFees on Firms Input Choices
38、nFirms that have a by-product to production produce an effluent.nAn effluent fee is a per-unit fee that firms must pay for the effluent that they emit.nHow would a producer respond to an effluent fee on production?Chapter 1Slide 55nThe Scenario: Steel Producer1) Located on a river: Low cost transpor
39、tation and emission disposal (effluent).2) EPA imposes a per unit effluent fee to reduce the environmentally harmful effluent.The Effect of EffluentFees on Firms Input ChoicesChapter 1Slide 56nThe Scenario: Steel Producer3) How should the firm respond?The Effect of EffluentFees on Firms Input Choice
40、sChapter 1Slide 57The Cost-MinimizingResponse to an Effluent FeeWaste Water(gal./month)Capital(machine hours permonth)Output of 2,000Tons of Steel per MonthA10,00018,00020,000012,000Slope of isocost = -10/40 = -0.252,0001,0004,0003,0005,0005,000Chapter 1Slide 58The Cost-MinimizingResponse to an Effl
41、uent FeeOutput of 2,000Tons of Steel per Month2,0001,0004,0003,0005,00010,00018,00020,000012,000Capital(machine hours permonth)E5,0003,500Slope of isocost = -20/40= -0.50BFollowing the impositionof the effluent fee of $10/gallonthe slope of the isocost changeswhich the higher cost of water tocapital
42、 so now combination B is selected.APrior to regulation the firm chooses to produce an output using 10,000 gallons of water and 2,000machine-hours of capital at A.CFWaste Water(gal./month)Chapter 1Slide 59nObservations:lThe more easily factors can be substituted, the more effective the fee is in redu
43、cing the effluent.lThe greater the degree of substitutes, the less the firm will have to pay (for example: $50,000 with combination B instead of $100,000 with combination A)The Effect of EffluentFees on Firms Input ChoicesChapter 1Slide 60nCost minimization with Varying Output LevelslA firms expansi
44、on path shows the minimum cost combinations of labor and capital at each level of output.Cost in the Long RunChapter 1Slide 61A Firms Expansion PathLabor per yearCapitalperyearExpansion PathThe expansion path illustratesthe least-cost combinations oflabor and capital that can be used to produce each
45、 level ofoutput in the long-run.25507510015010050150300200A$2000Isocost Line200 UnitIsoquantB$3000 Isocost Line300 Unit IsoquantCChapter 1Slide 62A Firms Long-Run Total Cost CurveOutput, Units/yrCostperYearExpansion Path100010030020020003000DEFChapter 1Slide 63Long-Run VersusShort-Run Cost CurvesnWh
46、at happens to average costs when both inputs are variable (long run) versus only having one input that is variable (short run)?Chapter 1Slide 64Long-RunExpansion PathThe long-run expansionpath is drawn as before.The Inflexibility ofShort-Run ProductionLabor per yearCapitalperyearL2Q2K2DCFEQ1ABL1K1L3
47、PShort-RunExpansion PathChapter 1Slide 65nLong-Run Average Cost (LAC)lConstant Returns to ScaleuIf input is doubled, output will double and average cost is constant at all levels of output.Long-Run VersusShort-Run Cost CurvesChapter 1Slide 66nLong-Run Average Cost (LAC)lIncreasing Returns to ScaleuI
48、f input is doubled, output will more than double and average cost decreases at all levels of output.Long-Run VersusShort-Run Cost CurvesChapter 1Slide 67nLong-Run Average Cost (LAC)lDecreasing Returns to ScaleuIf input is doubled, the increase in output is less than twice as large and average cost i
49、ncreases with output.Long-Run VersusShort-Run Cost CurvesChapter 1Slide 68nLong-Run Average Cost (LAC)lIn the long-run:uFirms experience increasing and decreasing returns to scale and therefore long-run average cost is “U” shaped.Long-Run VersusShort-Run Cost CurvesChapter 1Slide 69nLong-Run Average
50、 Cost (LAC)lLong-run marginal cost leads long-run average cost:uIf LMC LAC, LAC will riseuTherefore, LMC = LAC at the minimum of LACLong-Run VersusShort-Run Cost CurvesChapter 1Slide 70Long-Run Averageand Marginal CostOutputCost($ per unitof outputLACLMCAChapter 1Slide 71nQuestionlWhat is the relati
