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1、Chapter FourProducer Behavior Theory(3)生产者行为理论1学院Chapter Four includes:2学院n 4.1 Introductionn 4.2 Production Functionn 4.3 Cost Theory4.3 Cost Theory 4.3.1 Characteristics of Cost 4.3.2 From Cost Minimization to the Cost Function 4.3.3 Cost Functions In the Short Run 4.3.4 Cost Functions In the Long

2、 Run3学院n Zhang(2007): Chapter 6,P199-229n Nicholson: Chapter 12, P297-3304学院Readings about the part of this chapter4.3 Cost Theory 4.3.1 Characteristics of Cost 4.3.2 From Cost Minimization to the Cost Function 4.3.3 Cost Functions In the Short Run 4.3.4 Cost Functions In the Long Run5学院1.Measuring

3、Cost: Which Costs Matter?n Accounting Cost(会计成本)n Actual expenses plus depreciation charges(折旧费) for capital equipmentn Economic Cost（成本）n Cost which a firm utilize all economic resources inproduction, including opportucost6学院Economic Cost vs. Accounting CostWhat is OpportuCost?n The Opportucost of

4、using some resourcein a particular way is defined as the value ofthat resource in its next best alternative use .7学院What is OpportuCost?n An Examplen A firm owns its own building and pays no rent for office spacen Does this mean the cost of office space is zero?n Answer: No8学院n Sunk Cost（沉没成本）n Expe

5、nditure that has been made and cannot be recoveredn Should not influence a firms decisions.9学院2.Explicit and Implicit Costsn A firms cost of production include explicit costs and implicit costs.Explicit costs（显性成本） involve a direct money outlay for factors of production which are bought from input m

6、arkets.Implicit costs（隐性成本） are those costs associated with the use of the firms own resources and reflect the fact that these resources could be employed elsewhere.10学院3.Economic Profit versus Accounting Profitu Economists measure a firms economic profit利润）as total revenue minus all the（opportucost

7、s (explicit and implicit).u Accountants measure the accounting profit（会计利润） as the firms total revenue minus only the firms explicit costs. In other words, they ignore the implicit costs.11学院Economic Profit versus Accounting Profit12学院When total revenue exceeds both explicit and implicit costs, the

8、firm earns economic profit.u Economic profit is smaller than accounting profit.Economic Profit versus Accounting ProfitHow an Economist Views a FirmHow an Accountant Views a FirmRevenueRevenueTotal opportu costs13学院Accounting profitExplicit costsEconomic profitImplicit costsExplicit costs4.Definitio

9、n of Cost Functionn Cost Functionn shows the relation between the minimum cost to produce a given level of output and output level,C = C(q)14学院5.Short-Run and Long-Run Cost Functionsn In the short run, some factors of production are fixed: short-run cost function gives the minimum cost to produce a

10、given level of output, only adjusting the variable factors of production.n In the long run all factors are variable: long run cost function gives the minimum cost to produce a given level of output, adjusting all factors of production.15学院4.3 Cost Theory 4.3.1 Characteristics of Cost 4.3.2 From Cost

11、 Minimization to the Cost Function 4.3.3 Cost Functions In the Short Run 4.3.4 Cost Functions In the Long Run16学院From Cost Minimization to the Cost Functionn Cost-minimizing firmn produces q ³ 0 at min total costn Min cost for each q yields:n The Total cost function - c(q)n With input prices w

12、= (w1,w2,wn),n The Total cost function isC=c(w1,wn,q)17学院The Cost-Minimization Problemn Consider a firm using 2 inputs to make 1 outputn Production function isq = f(x1,x2)n Take output level q ³ 0 as given.n Given input prices w1 and w2,n Total cost of input bundle (x1,x2) isw1x1 + w2x218学院The

13、Cost-Minimization Problemn So, for given w1, w2 and q, firms cost- minimization problem is to solvemin w1x1 + w2 x2x1 ,x2 ³0S. t.f (x1,x2) = q19学院The Cost-Minimization Problemn Solution x1*(w1,w2,q) and x2*(w1,w2,q) are firms conditional demands for inputs 1, 2n Smallest possible total cost for

14、 producing q isc(w1 , w2 , q) = w x* (w1 , w2 , q)11+ w x* (w, w, q)221220学院The Cost-Minimization Problem: GraphCost min bundle that will produce q:x2x2*f(x1,x2) º qx1*x121学院The Cost-Minimization Problem: GraphAt an interior cost-min input bundle:(a) f(x1*,x2*) = q(b) slope of isocost = slope o

15、f isoquantx2-w1w2MP1 MP2at (x* , x* )=MRTS=12x2*f(x1,x2) º qx1*x22学院Cobb-Douglas Example of Cost Min./3x2/3qfn Production function is12n Input prices are w1 and w2w1 = ¶ q/¶ x1¶ q/¶ x2w2x*(1/3)(=2 x*(2/3)(123学院A Cobb-Douglas Ex. of Cost Minimizationx*w1= 2 (a)q=(x ) (x2)(b)*

16、 1/3* 2/32x*w211= 2w1x*x*From (b),21w 2Now substitute into (a) to get2/32w ö2/3x*q1wèøè2 ø2ö 2 / 3æwSo=conditional demand学院x * 2÷qç12 wè1 ø24A Cobb-Douglas Ex. of Cost Minimizationö2/3 æw= 2w1 x*x*= ç2 ÷x*qSinceand2112wè

17、1 øw2Firms conditional demand for input 2 isö2/31/32w æ w2x =*q 1 2 ç÷2w2w2 è1 øè2 ø25学院A Cobb-Douglas Ex. of Cost MinimizationSo, cost min input bundle for y units of output()*x (w , w , q),x (w , w , q)112212ææöö2/ 3w ö1/ 3wq

18、47;= çç÷èè 2w1 øw2èøø26学院Conditional Input Demand Curves(条件投入需求曲线)Fixed w1and w2x2q3q2q1x127学院Conditional Input Demand Curvesx2q3q2q1x*x*(q3)*1x2 (q )22x*(q2 )*3x2 (q )2x*(q2 )3q32*q1x2 (q )q2q1q2q1x1x*(q1)x*(q3)111*x128x*(q2)*1x*(q3)x (q )111*2x1(q )学院Co

19、nditional Input Demand CurvesCond. demand for input 2x2q3q2q1output expansion pathx*x*(q3)x*(q1)222x*(q2 )*3x2 (q )Cond. demand for input 12x*(q2 )3q32*q1x2 (q )q2q1q2q1x1x*(q1)x*(q3)111*x129x*(q2)*1x*(q3)x (q )111*2x1(q )学院Cobb-Douglas Example of Cost MinSo the firms long run total cost function is

20、c(w1 , w 2 , q) = w x* (w1 , w 2 , q) + wx* (w1 , w 2 , q)1122ö2 / 3ö1 / 3øææ 2ww= w1 ç2 q + w 2 ç1qè 2w1 øw 2è2 / 3= æ 1 ö1 / 32 / 31 / 31 / 32 / 3q + 2w1w 2w1w 2qç 2èøw 2 ö1 / 3æ w= 3ç12q4è30学院4.3 Cost T

21、heory 4.3.1 Characteristics of Cost 4.3.2 From Cost Minimization to the Cost Function 4.3.3 Cost Functions In the Short Run 4.3.4 Cost Functions In the Long Run31学院Introduction: Cost function in the Short Runn In the short run, there are some variable inputs and some fixed inputs in the production.n

22、 So cost function isC = w · L(w, r, q) + r · K (w, r, q)32学院1.Family of Total Costs in the Short Runn Fixed Cost（固定成本）n those costs that do not vary with the quantity of output producedn Variable Cost（变动成本）u those costs that do change as the firm alters the quantity of output produced.33学院

23、Fixed and Variable Costs1.Family of Total Costs in the Short Run34学院u Total Fixed Costs (TFC)（总固定成本）u Total Variable Costs (TVC)（总变动成本）u Total Costs (TC) （总成本）TC = TFC + TVCFrom TPL to TVC35学院Cost Curves for a FirmTCCost($ per year)400TVC30020010050TFCOutput01234567891011121336学院Fixed cost does not

24、vary with outputVariable cost increases with production andthe rate varies with increasing & decreasing returns.Total cost is the verticalsum of FC and VC.Family of Total CostsQuantity012345678910Total Cost$ 3.003.303.804.505.406.507.809.3011.0012.9015.00Fixed Cost$3.00 3.003.003.003.003.003.003

25、.003.003.003学.院0Variable Cost$ 0.000.300.801.502.403.504.806.308.009.9012.00371.Family of Total Costs in the Short Run$16.00TC$14.00TVC$12.00$10.00$8.00$6.00TFC$4.00$2.00$0.00246810120Quantity of Output学na院d(glashour)38Total Cost2.Family of Average Costs in the Short Run39学院u Average Fixed Costs (AF

26、C)（平均固定成本）u Average Variable Costs (AVC)（平均变动成本）u Average Total Costs (ATC)（平均成本）ATC = AFC + AVC2.Family of Average CostsF i x e dc o s tF CA F C=Q u a n tity qVa r i a b l ec o s tT VCAV C =Q u a n tity qT o t a lc o s tT CA T C =Q u a n tity q40学院2.Family of Average Costs41QuantityAFCAVCATC01$3.00

27、$0.30$3.30231.501.000.400.501.901.50450.750.600.600.701.351.3060.500.801.30780.430.380.901.001.331.389100.330.3031.50学院Average-Cost and Marginal-Cost Curves.$3.50$3.00$2.50MC$2.00ATCAVC$1.50$1.00$0.50AFC$0.00246810120Quantity of Output学ad院e(glassour)42Costs3.Marginal Cost（边际成本）u Marginal c

28、ost (MC) measures the amount total cost rises when the firm increases production by one unit.43学院3.Marginal CostMC= (Change in total cost)(Change in quantity)= DTC DqDTCdTCMC =limDqdqDq ® ¥44学院Marginal Cost45学院QuantityTotal CostMarginal CostQuantityTotal CostMarginal Cost0$3.0013.30$0.306$

29、7.80$1.3023.800.5079.301.5034.500.70811.001.7045.400.90912.901.9056.501.101015.002.104.Relationship Between Marginal Cost and Average Total Cost$3.50$3.00$2.50$2.00ATCAVC$1.50$1.00$0.50AFC$0.00246810120Quantity of Output学ad院e(glassour)46CostsM C4.Relationship Between Marginal Cost and Average Total

30、Costu Whenever marginal cost is less than average total cost, average total cost is falling.u Whenever marginal cost is greater than average total cost, average total cost is rising.47学院4.Relationship Between Marginal Cost and Average Total Cost48学院n The marginal-cost curve crosses the average-total

31、-cost curve at the efficient scale.Efficient scale is the quantitythat minimizes average total cost.C>MC (q) = AC (q)<>dAC ( q ) = 0asdq<MC(q)AC(q)q49学院Proof of Relationship between MC and AC( q )SinceAC ,dAC(q) = d æ TC÷ = ´ MC(q) - 1´ TC(q) .q2dqTherefore,dø>

32、;q ´ MC (q) = TC ( q).<>dAC ( q ) = 0as¶ q<>>MC(q) = AC(q).<dAC (q) = 0asdq<50学院Relationship Between Marginal Cost and Average Variable CostMC(q) = AVC(q) Þ dAVC(q) =0CdqMC(q)AVC(q)q 51学院The short-run MC curve intersects the short-run AVC curve from below at the A

33、VC curvesminimum.Proof of Relationship between MC and AVC( q )SinceAVC ,dAVC(q) = d æ VC÷ = ´ MC(q) - 1´VC(q) .q2dqTherefore,dø>q ´ MC (q) = VC ( q).<>dAVC ( q ) = 0as¶ q<>>MC(q) = AVC(q).<dAVC (q) = 0asdq<52学院Summary: Marginal & Average

34、 Cost Functionsn The short-run MC curve intersects the short- run AVC curve from below at the AVC curves minimum.n And, similarly, the short-run MC curve intersects the short-run ATC curve from below at the ATC curves minimum.53学院CMC(q)AC(q)AVC(q)q54学院Summary:Three Important Properties of Cost Curve

35、su Marginal cost eventually rises with the quantity of output.u The average-total-cost curve is U- shaped.u The marginal-cost curve crosses the average-total-cost curve at the minimum of average total cost.55学院Summary: TC TVC AC、AVC and MC56学院5.Product Curves and Cost CurvesHow are the product curve

36、s related to the cost curves?57学院5.Product Curves and Cost Curvesn For Example: Assume the wage rate (w) is fixed relative to the number of workers hired. Then:58学院TVC = w · L5.Product Curves and Cost Curvesn Continuing:AVC = TVCw · L11LMC = dTVC = dw · L = w · dL = w ·1dq1=

37、 w ·dqdqdqMPLdL59学院5.Product Curves and Cost CurvesAPMP01.52.0Labor60学院Average product and marginal productand d64R2ising MP andfalling MC: rising AP and falling AVCFalling MP rising MC: falling AP an rising AVCFalling MP and rising MC: rising AP and falling AVC5.Product Curves and Cost Curves129MC6AVC306.510学院Labor61Average product and marginal productum AP andminimum AVCum MP andminimum MC5.Product Curves and Cost Curves62学院6. An algebra examplesIn our example, the short-run