生产函数决定成本函数

1、Steven Landsburg, University of RochesterChapter 6Production and CostsCopyright 2005 by Thomson South-Western, part of the Thomson Corporation. All rights reserved.Introduction生產函數決定本钱函數，而(邊際)本钱會影響供給函數；因此，本章先介紹生產函數，然後說明本钱函數。生產函數在說明生產要素與產量之間的關係；生產要素分為兩類，一類是短期即可變動其运用的數量的(以勞工為代表)，另一類是長期才可變動其运用的數量的(以資本為

2、代表) 。產量遭到生產技術與生產要素的影響Where do cost curves come fromDepends on firms available technologyDetermines production processProduction process determines firms costs.Production and Costs in the Short RunLimited options in short run (SR)Initial assumptionFirm can hire more labor.Production in the Short RunT

3、otal product (TP) of labor Quantity of output produced by firm in a given amount of time dependent on labor hiredInformation graphically represented by production functionProduction function slopes upwardProduction function is rule for determining how much output can be produced with a given basket

4、of inputs.Calculating MP and APMarginal product of labor (MPL) Increase in total product based on hiring one additional workerAssume capital fixedSlope of TPAverage product of labor (APL) Total product divided by number of workers.Relation between MP and APNTP.Calculating MP and AP.MPL&APL.EXHIBIT 6

5、.1Total, Marginal and Average Products.Shape of MP and AP CurvesAPIf number of workers large, additional workers cause average product of labor to decreaseInverted U-shapeMPInverted U-shapeAP and MP relationship to one anotherIf MP AP, MP lies above APIf MP AP, MP lies below APIf MP = AP, AP at maxi

6、mum or peak.EXHIBIT 6.2The Stages of Production.Variable Costs in the SRConstructing the firms variable cost curveNeed total product curveNeed wage ratePrice of hiring laborMultiply number of workers by wage rate to get variable cost PLL=VCCurve relates total product, not number of workers, to varia

7、ble cost.Exhibit 6.3 VC CurveNTPQVCTC155156521212308032121459542828601105333375125636369014073737105155.EXHIBIT 6.3Variable Cost Curve.Fixed Costs in the SRCosts of capitalPhysical assets, such as machinery and factoriesEx. handymans van.Total CostTotal cost equal to sum of fixed and variable costs

8、of productionTC=FC+VC=FC+PLLAdditional cost considerations beside totals.Computing Average and Marginal CostsAverage variable cost (AVC): variable cost divided by quantity of outputLabor only variable factor of productionCalculate AVC by taking the wage rate and dividing by APLAverage cost (AC): tot

9、al cost divided by quantity of outputSometimes called average total costMarginal cost (MC): additional cost attributable to the last unit of output producedLabor only variable factor of productionCalculate MC by taking the wage rate and dividing by MPL.Computing Average and Marginal Costs.EXHIBIT 6.

10、4Deriving the Average and Marginal Cost Curves.MC&AC.Shapes of Cost CurvesVC curve always increasingMore output requires more laborHigher costsTC curve determined by sum of FC and VCFC constantHas same shape as VC curveMC, AC, and AVC curves are U-shaped.EXHIBIT 6.5The Geometry of Product Curves and

11、 Cost Curves.Cost Curves RelationsMC relationship to AVC and ACMC below AVC, AVC fallingMC above AVC, AVC risingMC equals AVC, AVC at minimumCan replace AVC with AC, same holds trueShapes of cost curves related to shapes of product curves.Production and Costs in the Long RunIn long run (LR), firm ca

12、n adjust employment of capital and laborAttempts to achieve the least cost method of producing a given quantity of output.IsoquantsGeometry of LR productionLabel vertical axis with K, stands for capitalLabel horizontal axis with L, which stands for laborFixed period of timeWant to use least costly m

13、ethodAvoid technologically inefficient points which are outside the boundaryGeneral observationsSlope downwardFill the planeNever crossConvex.Marginal Rate of Technical SubstitutionAbsolute value of slope of isoquantMPL divided by MPKAmount of capital necessary to replace one unit of labor while mai

14、ntaining a constant level of outputIf much labor and little capital employed to produce a unit of output, MRTSLK is smallGeometrically isoquant is convex.EXHIBIT 6.8The Production Function.Choosing a Production ProcessMinimizing cost important part of maximizing profitIsocost allow to keep track of

15、costsSet of all baskets of inputs that can be employed at a given costSlope: -PL/PKMinimizing cost and maximizing output requires firm choose tangency point between an isocost and an isoquantMeans that MRTS = PL/PKTangencies lie along curve called the firms expansion path.EXHIBIT 6.9Cost Minimizatio

16、n.Long-Run Cost CurvesInformation neededProduction function or isoquantsInput pricesFirms long-run total cost Cost of producing a given amount of output when the firm is able to operate on its expansion pathLong-run average costLong-run total cost divided by quantityLong-run marginal costPart of lon

17、g-run total cost attributable to the last unit produced.EXHIBIT 6.11Deriving Long-Run Total Cost.EXHIBIT 6.12Long-Run Total, Marginal, and Average Costs.Returns to ScaleWhen all input quantities are increased by 1%, does output go up bymore than 1%Increasing returns to scaleOccurs at low levels of o

18、utputLong-run average cost curve is decreasingexactly 1%Constant returns to scale“What a firm can do one, it can do twiceLong-run average cost curve is flatless than 1%Decreasing returns to scaleOccurs at sufficiently high levels of outputLong-run average cost curve is increasing.Relations between the SR and LRDerive SRTC from isoquants and factor pricesDerive LRTC from isoquants and factor pricesSRTC versus LRTCSRTC always at least as great as LRTCMultitude of short run situationsEach has different level of fixed c