Cost curve

In economics, a cost curve is a graph of the costs of pro-duction as a function of total quantity produced. In a freemarket economy, productively efficient firms use thesecurves to find the optimal point of production (minimiz-ing cost), and profit maximizing firms can use them todecide output quantities to achieve those aims. There arevarious types of cost curves, all related to each other, in-cluding total and average cost curves, and marginal (“foreach additional unit”) cost curves, which are equal to thedifferential of the total cost curves. Some are applicableto the short run, others to the long run.

1 Short-run average variable costcurve (SRAVC)

A U shaped short run Average Cost(AC) curve. AVC is the Aver-age Variable Cost, AFC the Average Fixed Cost, MC the marginalcost crossing the minimum of the Average Cost curve.

Average variable cost (which is a short-run concept) isthe variable cost (typically labor cost) per unit of output:SRAVC = wL / Q where w is the wage rate, L is thequantity of labor used, and Q is the quantity of outputproduced. The SRAVC curve plots the short-run averagevariable cost against the level of output and is typicallydrawn as U-shaped.

2 Short-run average total costcurve (SRATC or SRAC)

The average total cost curve is constructed to capture therelation between cost per unit of output and the level ofoutput, ceteris paribus. A perfectly competitive and pro-ductively efficient firm organizes its factors of production

in such a way that the factors of production is at the lowestpoint. In the short run, when at least one factor of produc-tion is fixed, this occurs at the output level where it hasenjoyed all possible average cost gains from increasingproduction. This is at the minimum point in the diagramon the right.Short-run total cost is given bySTC = PK .K + PL.L ,where PK is the unit price of using physical capital perunit time, PL is the unit price of labor per unit time (thewage rate), K is the quantity of physical capital used, andL is the quantity of labor used. From this we obtain short-run average cost, denoted either SATC or SAC, as STC /Q:

SRATC or SRAC = PKK/Q + PLL/Q = PK /APK + PL / APL,

where APK = Q/K is the average product of capital andAPL = Q/L is the average product of labor.[1]:191

Short run average cost equals average fixed costs plus av-erage variable costs. Average fixed cost continuously fallsas production increases in the short run, because K is fixedin the short run. The shape of the average variable costcurve is directly determined by increasing and then di-minishing marginal returns to the variable input (conven-tionally labor).[2]:210

3 Long-run average cost curve(LRAC)

LRAC

Price

QuantityQ1 Q2

Typical long run average cost curve

1

2 5 LONG-RUN MARGINAL COST CURVE (LRMC)

The long-run average cost curve depicts the cost per unitof output in the long run—that is, when all productiveinputs’ usage levels can be varied. All points on the linerepresent least-cost factor combinations; points above theline are attainable but unwise, while points below areunattainable given present factors of production. The be-havioral assumption underlying the curve is that the pro-ducer will select the combination of inputs that will pro-duce a given output at the lowest possible cost. Giventhat LRAC is an average quantity, one must not con-fuse it with the long-run marginal cost curve, which isthe cost of one more unit.[3]:232 The LRAC curve is cre-ated as an envelope of an infinite number of short-runaverage total cost curves, each based on a particular fixedlevel of capital usage.[3]:235 The typical LRAC curve is U-shaped, reflecting increasing returns of scale where neg-atively sloped, constant returns to scale where horizontaland decreasing returns (due to increases in factor prices)where positively sloped.[3]:234 Contrary to the assertion ofCanadian economist Jacob Viner,[4] the envelope is notcreated by the minimum point of each short-run averagecost curve.[3]:235 This mistake is recognized as Viner’s Er-ror.In a long-run perfectly competitive environment, theequilibrium level of output corresponds to the minimumefficient scale, marked as Q2 in the diagram. This is dueto the zero-profit requirement of a perfectly competitiveequilibrium. This result implies production is at a levelcorresponding to the lowest possible average cost,[3]:259does not imply that production levels other than that atthe minimum point are not efficient. All points along theLRAC are productively efficient, by definition, but not allare equilibrium points in a long-run perfectly competitiveenvironment.In some industries, the bottom of the LRAC curve is largein comparison to market size (that is to say, for all in-tents and purposes, it is always declining and economiesof scale exist indefinitely). This means that the largestfirm tends to have a cost advantage, and the industry tendsnaturally to become a monopoly, and hence is called anatural monopoly. Natural monopolies tend to exist inindustries with high capital costs in relation to variablecosts, such as water supply and electricity supply.[3]:312

4 Short-run marginal cost curve(SRMC)

A short-run marginal cost curve graphically representsthe relation between marginal (i.e., incremental) cost in-curred by a firm in the short-run production of a good orservice and the quantity of output produced. This curve isconstructed to capture the relation between marginal costand the level of output, holding other variables, like tech-nology and resource prices, constant. The marginal costcurve is usually U-shaped. Marginal cost is relatively high

MC

Price

Quantity

MR

Typical marginal cost curve

at small quantities of output; then as production increases,marginal cost declines, reaches a minimum value, thenrises. The marginal cost is shown in relation to marginalrevenue (MR), the incremental amount of sales revenuethat an additional unit of the product or service will bringto the firm. This shape of the marginal cost curve is di-rectly attributable to increasing, then decreasing marginalreturns (and the law of diminishing marginal returns).Marginal cost equals w/MPL.[1]:191 For most productionprocesses the marginal product of labor initially rises,reaches a maximum value and then continuously falls asproduction increases. Thus marginal cost initially falls,reaches a minimum value and then increases.[2]:209 Themarginal cost curve intersects both the average variablecost curve and (short-run) average total cost curve at theirminimum points. When the marginal cost curve is abovean average cost curve the average curve is rising. Whenthe marginal costs curve is below an average curve theaverage curve is falling. This relation holds regardless ofwhether the marginal curve is rising or falling.[3]:226

5 Long-run marginal cost curve(LRMC)

The long-run marginal cost curve shows for each unit ofoutput the added total cost incurred in the long run, thatis, the conceptual period when all factors of productionare variable so as minimize long-run average total cost.Stated otherwise, LRMC is the minimum increase in to-tal cost associated with an increase of one unit of outputwhen all inputs are variable.[5]

The long-run marginal cost curve is shaped by returns toscale, a long-run concept, rather than the law of diminish-ing marginal returns, which is a short-run concept. Thelong-run marginal cost curve tends to be flatter than itsshort-run counterpart due to increased input flexibility asto cost minimization. The long-run marginal cost curveintersects the long-run average cost curve at theminimumpoint of the latter.[1]:208 When long-run marginal costsare below long-run average costs, long-run average costs

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are falling (as to additional units of output).[1]:207 Whenlong-run marginal costs are above long run average costs,average costs are rising. Long-run marginal cost equalsshort run marginal-cost at the least-long-run-average-costlevel of production. LRMC is the slope of the LR total-cost function.

6 Graphing cost curves together

MCPrice

Quantity

MR

ATC

Cost curves in perfect competition compared to marginal revenue

Cost curves can be combined to provide informationabout firms. In this diagram for example, firms are as-sumed to be in a perfectly competitive market. In a per-fectly competitive market the price that firms are facedwith would be the price at which the marginal cost curvecuts the average cost curve.

7 Cost curves and production func-tions

Assuming that factor prices are constant, the produc-tion function determines all cost functions.[2] The vari-able cost curve is the inverted short-run production func-tion or total product curve and its behavior and proper-ties are determined by the production function.[1]:209 [nb 1]

Because the production function determines the vari-able cost function it necessarily determines the shape andproperties of marginal cost curve and the average costcurves.[2]

If the firm is a perfect competitor in all input markets, andthus the per-unit prices of all its inputs are unaffected byhow much of the inputs the firm purchases, then it canbe shown[6][7][8] that at a particular level of output, thefirm has economies of scale (i.e., is operating in a down-ward sloping region of the long-run average cost curve)if and only if it has increasing returns to scale. Likewise,it has diseconomies of scale (is operating in an upwardsloping region of the long-run average cost curve) if andonly if it has decreasing returns to scale, and has neither

economies nor diseconomies of scale if it has constantreturns to scale. In this case, with perfect competition inthe output market the long-run market equilibrium willinvolve all firms operating at the minimum point of theirlong-run average cost curves (i.e., at the borderline be-tween economies and diseconomies of scale).If, however, the firm is not a perfect competitor in the in-put markets, then the above conclusions aremodified. Forexample, if there are increasing returns to scale in somerange of output levels, but the firm is so big in one ormore input markets that increasing its purchases of an in-put drives up the input’s per-unit cost, then the firm couldhave diseconomies of scale in that range of output levels.Conversely, if the firm is able to get bulk discounts ofan input, then it could have economies of scale in somerange of output levels even if it has decreasing returns inproduction in that output range.

8 Relationship between differentcurves

• Total Cost = Fixed Costs (FC) + Variable Costs(VC)

• Marginal Cost (MC) = dC/dQ; MC equals the slopeof the total cost function and of the variable costfunction

• Average Total Cost (ATC) = Total Cost/Q

• Average Fixed Cost (AFC) = FC/Q

• Average Variable Cost (AVC) = VC/Q.

• ATC = AFC + AVC

• The MC curve is related to the shape of the ATCand AVC curves:[9]:212

• At a level of Q at which the MC curve is abovethe average total cost or average variable costcurve, the latter curve is rising.[9]:212

• If MC is below average total cost or averagevariable cost, then the latter curve is falling.

• If MC equals average total cost, then averagetotal cost is at its minimum value.

• If MC equals average variable cost, then aver-age variable cost is at its minimum value.

9 Relationship between short runand long run cost curves

Basic: For each quantity of output there is one cost mini-mizing level of capital and a unique short run average costcurve associated with producing the given quantity.[10]

4 10 U-SHAPED CURVES

• Each STC curve can be tangent to the LRTC curveat only one point. The STC curve cannot cross (in-tersect) the LRTC curve.[2]:230[9]:228–229 The STCcurve can lie wholly “above” the LRTC curve withno tangency point.[11]:256

• One STC curve is tangent to LRTC at the long-runcost minimizing level of production. At the point oftangency LRTC = STC. At all other levels of pro-duction STC will exceed LRTC.[12]:292–299

• Average cost functions are the total cost function di-vided by the level of output. Therefore, the SATCcurveis also tangent to the LRATC curve at the cost-minimizing level of output. At the point of tan-gency LRATC = SATC. At all other levels of pro-duction SATC>LRATC[12]:292–299 To the left of thepoint of tangency the firm is using too much capi-tal and fixed costs are too high. To the right of thepoint of tangency the firm is using too little capitaland diminishing returns to labor are causing costs toincrease.[13]

• The slope of the total cost curves equals marginalcost. Therefore, when STC is tangent to LTC, SMC= LRMC.

• At the long run cost minimizing level of outputLRTC = STC; LRATC = SATC and LRMC =SMC,.[12]:292–299

• The long run cost minimizing level of output may bedifferent from minimum SATC,.[9]:229[14]:186

• With fixed unit costs of inputs, if the productionfunction has constant returns to scale, then at theminimal level of the SATC curve we have SATC =LRATC = SMC = LRMC.[12]:292–299

• With fixed unit costs of inputs, if the productionfunction has increasing returns to scale, the min-imum of the SATC curve is to the right of thepoint of tangency between the LRAC and the SATCcurves.[12]:292–299 Where LRTC = STC, LRATC =SATC and LRMC = SMC.

• With fixed unit costs of inputs and decreasing re-turns the minimum of the SATC curve is to theleft of the point of tangency between LRAC andSATC.[12]:292–299 Where LRTC = STC, LRATC =SATC and LRMC = SMC.

• With fixed unit input costs, a firm that is experienc-ing increasing (decreasing) returns to scale and isproducing at its minimum SAC can always reduceaverage cost in the long run by expanding (reduc-ing) the use of the fixed input.[12]:292–99 [14]:186

• LRATC will always equal to or be less thanSATC.[1]:211

• If production process is exhibiting constant returnsto scale then minimum SRAC equals minimum longrun average cost. The LRAC and SRAC intersectat their common minimum values. Thus under con-stant returns to scale SRMC = LRMC = LRAC =SRAC .

• If the production process is experiencing decreas-ing or increasing, minimum short run average costdoes not equal minimum long run average cost. Ifincreasing returns to scale exist long run minimumwill occur at a lower level of output than SRAC. Thisis because there are economies of scale that havenot been exploited so in the long run a firm couldalways produce a quantity at a price lower than min-imum short run average cost simply by using a largerplant.[15]

• With decreasing returns, minimum SRAC occurs ata lower production level than minimum LRAC be-cause a firm could reduce average costs by simplydecreasing the size or its operations.

• The minimum of a SRAC occurs when the slope iszero.[16] Thus the points of tangency between theU-shaped LRAC curve and the minimum of theSRAC curve would coincide only with that portionof the LRAC curve exhibiting constant economiesof scale. For increasing returns to scale the point oftangency between the LRAC and the SRAc wouldhave to occur at a level of output below level associ-ated with the minimum of the SRAC curve.

These statements assume that the firm is using the optimallevel of capital for the quantity produced. If not, thenthe SRAC curve would lie “wholly above” the LRAC andwould not be tangent at any point.

10 U-shaped curves

Both the SRAC and LRAC curves are typically expressedas U-shaped.[9]:211; 226 [14]:182;187–188 However, the shapesof the curves are not due to the same factors. For theshort run curve the initial downward slope is largely dueto declining average fixed costs.[2]:227 Increasing returnsto the variable input at low levels of production also playa role,[17] while the upward slope is due to diminishingmarginal returns to the variable input.[2]:227 With the longrun curve the shape by definition reflects economies anddiseconomies of scale.[14]:186 At low levels of productionlong run production functions generally exhibit increasingreturns to scale, which, for firms that are perfect competi-tors in input markets, means that the long run average costis falling;[2]:227 the upward slope of the long run averagecost function at higher levels of output is due to decreas-ing returns to scale at those output levels.[2]:227

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11 Cost curves in reality

The U-shaped cost curves have no basis in fact. In a sur-vey by Wilford J. Eiteman and Glenn E. Guthrie in 1952managers of 334 companies were shown a number of dif-ferent cost curves, and asked to specify which one bestrepresented the company’s cost curve. 95% of managersresponding to the survey reported cost curves with con-stant or falling costs.[18]

Alan Blinder, former vice president of the American Eco-nomics Association, conducted the same type of sur-vey in 1998, which involved 200 US firms in a sam-ple that should be representative of the US economy atlarge. He found that about 40% of firms reported fallingvariable or marginal cost, and 48.4% reported constantmarginal/variable cost.[19]

12 See also• Cost

• Economic cost

• General equilibrium

• Joel Dean (economist)

• Partial equilibrium

• Point of total assumption

13 Notes[1] The slope of the short-run production function equals the

marginal product of the variable input, conventionally la-bor. The slope of the variable cost function is marginalcosts. The relationship between MC and the marginalproduct of labor MPL is MC = w/MPL. Because the wagerate w is assumed to be constant the shape of the variablecost curve is completely dependent on the marginal prod-uct of labor. The short-run total cost curve is simply thevariable cost curve plus fixed costs.

14 References[1] Perloff, J. Microeconomics, 5th ed. Pearson, 2009.

[2] Perloff, J., 2008,Microeconomics: Theory & Applicationswith Calculus, Pearson. ISBN 978-0-321-27794-7

[3] Lipsey, Richard G. (1975). An introduction to positive eco-nomics (fourth ed.). Weidenfeld & Nicolson. pp. 57–8.ISBN 0-297-76899-9.

[4] Viner, Jacob (1931). “Costs Curves and SupplyCurves”. Zeitschrift für Nationalökonomie 3 (1): 23–46.doi:10.1007/BF01316299. Reprinted in Emmett, R. B.,ed. (2002). The Chicago Tradition in Economics, 1892–1945 6. Routledge. pp. 192–215.

[5] Sexton, Robert L., Philip E. Graves, and Dwight R. Lee,1993. “The Short- and Long-Run Marginal Cost Curve:A Pedagogical Note”, Journal of Economic Education,24(1), p. 34. [Pp. 34-37 (press +)].

[6] Gelles, Gregory M., and Mitchell, Douglas W., “Returnsto scale and economies of scale: Further observations,”Journal of Economic Education 27, Summer 1996, 259-261.

[7] Frisch, R., Theory of Production, Drodrecht: D. Reidel,1965.

[8] Ferguson, C. E., The Neoclassical Theory of Productionand Distribution, London: Cambridge Univ. Press, 1969.

[9] Pindyck, R., and Rubinfeld, D., Microeconomics, 5th ed.,Prentice-Hall, 2001.

[10] Nicholson: Microeconomic Theory 9th ed. Page 238Thomson 2005

[11] Kreps, D., A Course in Microeconomic Theory, PrincetonUniv. Press, 1990.

[12] Binger, B., and Hoffman, E.,Microeconomics with Calcu-lus, 2nd ed., Addison-Wesley, 1998.

[13] Frank, R., Microeconomics and Behavior 7th ed. (Mc-Graw-Hill) ISBN 978-0-07-126349-8 at 321.

[14] Melvin&Boyes,Microeconomics, 5th ed., HoughtonMif-flin, 2002

[15] Perloff, J. Microeconomics Theory & Application withCalculus Pearson (2008) p. 231.

[16] Nicholson: Microeconomic Theory 9th ed. Page Thom-son 2005

[17] Boyes, W., The New Managerial Economics, HoughtonMifflin, 2004.

[18] Wilford J. Eiteman and Glenn E. Guthrie, The Shapeof the Average Cost Curve, American Economic Review,42.5: 832–838

[19] Alan Stuart Blinder, Asking about Prices: A New Ap-proach to Understanding Price Stickiness, Russell SageFoundation, New York, 1998

6 15 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

15 Text and image sources, contributors, and licenses

15.1 Text• Cost curve Source: https://en.wikipedia.org/wiki/Cost_curve?oldid=676242021 Contributors: Charles Matthews, WhisperToMe, Bearcat,

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