Cost curve

In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms use these curves to find the optimal point of production (minimizing cost), and profit maximizing firms can use them to decide output quantities to achieve those aims. There are various types of cost curves, all related to each other, including total and average cost curves, and marginal ("for each additional unit") cost curves, which are equal to the differential of the total cost curves. Some are applicable to the short run, others to the long run.

Short-run average variable cost curve (SRAVC)

A U shaped short run Average Cost(AC) curve. AVC is the Average Variable Cost, AFC the Average Fixed Cost, MC the marginal cost crossing the minimum of the Average Cost curve.

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

Short-run average total cost curve (SRATC or SRAC)

The average total cost curve is constructed to capture the relation between cost per unit of output and the level of output, ceteris paribus. A perfectly competitive and productively efficient firm organizes its factors of production in such a way that the factors of production is at the lowest point. In the short run, when at least one factor of production is fixed, this occurs at the output level where it has enjoyed all possible average cost gains from increasing production. This is at the minimum point in the diagram on the right.

Short-run total cost is given by

STC = PKK+PLL,

where PK is the unit price of using physical capital per unit time, PL is the unit price of labor per unit time (the wage rate), K is the quantity of physical capital used, and L 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 and APL = Q/L is the average product of labor.[1]:191

Short run average cost equals average fixed costs plus average variable costs. Average fixed cost continuously falls as production increases in the short run, because K is fixed in the short run. The shape of the average variable cost curve is directly determined by increasing and then diminishing marginal returns to the variable input (conventionally labor).[2]:210

Long-run average cost curve (LRAC)

Typical long run average cost curve

The long-run average cost curve depicts the cost per unit of output in the long runthat is, when all productive inputs' usage levels can be varied. All points on the line represent least-cost factor combinations; points above the line are attainable but unwise, while points below are unattainable given present factors of production. The behavioral assumption underlying the curve is that the producer will select the combination of inputs that will produce a given output at the lowest possible cost. Given that LRAC is an average quantity, one must not confuse it with the long-run marginal cost curve, which is the cost of one more unit.[3]:232 The LRAC curve is created as an envelope of an infinite number of short-run average total cost curves, each based on a particular fixed level of capital usage.[3]:235 The typical LRAC curve is U-shaped, reflecting increasing returns of scale where negatively-sloped, constant returns to scale where horizontal and decreasing returns (due to increases in factor prices) where positively sloped.[3]:234 Contrary to the assertion of Canadian economist Jacob Viner,[4] the envelope is not created by the minimum point of each short-run average cost curve.[3]:235 This mistake is recognized as Viner's Error.

In a long-run perfectly competitive environment, the equilibrium level of output corresponds to the minimum efficient scale, marked as Q2 in the diagram. This is due to the zero-profit requirement of a perfectly competitive equilibrium. This result implies production is at a level corresponding to the lowest possible average cost,[3]:259 does not imply that production levels other than that at the minimum point are not efficient. All points along the LRAC are productively efficient, by definition, but not all are equilibrium points in a long-run perfectly competitive environment.

In some industries, the bottom of the LRAC curve is large in comparison to market size (that is to say, for all intents and purposes, it is always declining and economies of scale exist indefinitely). This means that the largest firm tends to have a cost advantage, and the industry tends naturally to become a monopoly, and hence is called a natural monopoly. Natural monopolies tend to exist in industries with high capital costs in relation to variable costs, such as water supply and electricity supply.[3]:312

Short-run marginal cost curve (SRMC)

Typical marginal cost curve

A short-run marginal cost curve graphically represents the relation between marginal (i.e., incremental) cost incurred by a firm in the short-run production of a good or service and the quantity of output produced. This curve is constructed to capture the relation between marginal cost and the level of output, holding other variables, like technology and resource prices, constant. The marginal cost curve is usually U-shaped. Marginal cost is relatively high at small quantities of output; then as production increases, marginal cost declines, reaches a minimum value, then rises. The marginal cost is shown in relation to marginal revenue (MR), the incremental amount of sales revenue that an additional unit of the product or service will bring to the firm. This shape of the marginal cost curve is directly attributable to increasing, then decreasing marginal returns (and the law of diminishing marginal returns). Marginal cost equals w/MPL.[1]:191 For most production processes the marginal product of labor initially rises, reaches a maximum value and then continuously falls as production increases. Thus marginal cost initially falls, reaches a minimum value and then increases.[2]:209 The marginal cost curve intersects both the average variable cost curve and (short-run) average total cost curve at their minimum points. When the marginal cost curve is above an average cost curve the average curve is rising. When the marginal costs curve is below an average curve the average curve is falling. This relation holds regardless of whether the marginal curve is rising or falling.[3]:226

Long-run marginal cost curve (LRMC)

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

The long-run marginal cost curve is shaped by returns to scale, a long-run concept, rather than the law of diminishing marginal returns, which is a short-run concept. The long-run marginal cost curve tends to be flatter than its short-run counterpart due to increased input flexibility as to cost minimization. The long-run marginal cost curve intersects the long-run average cost curve at the minimum point of the latter.[1]:208 When long-run marginal costs are below long-run average costs, long-run average costs are falling (as to additional units of output).[1]:207 When long-run marginal costs are above long run average costs, average costs are rising. Long-run marginal cost equals short run marginal-cost at the least-long-run-average-cost level of production. LRMC is the slope of the LR total-cost function.

Graphing cost curves together

Cost curves in perfect competition compared to marginal revenue

Cost curves can be combined to provide information about firms. In this diagram for example, firms are assumed to be in a perfectly competitive market. In a perfectly competitive market the price that firms are faced with would be the price at which the marginal cost curve cuts the average cost curve.

Cost curves and production functions

Assuming that factor prices are constant, the production function determines all cost functions.[2] The variable cost curve is the inverted short-run production function or total product curve and its behavior and properties are determined by the production function.[1]:209 [nb 1] Because the production function determines the variable cost function it necessarily determines the shape and properties of marginal cost curve and the average cost curves.[2]

If the firm is a perfect competitor in all input markets, and thus the per-unit prices of all its inputs are unaffected by how much of the inputs the firm purchases, then it can be shown[6][7][8] that at a particular level of output, the firm has economies of scale (i.e., is operating in a downward 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 upward sloping region of the long-run average cost curve) if and only if it has decreasing returns to scale, and has neither economies nor diseconomies of scale if it has constant returns to scale. In this case, with perfect competition in the output market the long-run market equilibrium will involve all firms operating at the minimum point of their long-run average cost curves (i.e., at the borderline between economies and diseconomies of scale).

If, however, the firm is not a perfect competitor in the input markets, then the above conclusions are modified. For example, if there are increasing returns to scale in some range of output levels, but the firm is so big in one or more input markets that increasing its purchases of an input drives up the input's per-unit cost, then the firm could have diseconomies of scale in that range of output levels. Conversely, if the firm is able to get bulk discounts of an input, then it could have economies of scale in some range of output levels even if it has decreasing returns in production in that output range.

Relationship between different curves

Relationship between short run and long run cost curves

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

These statements assume that the firm is using the optimal level of capital for the quantity produced. If not, then the SRAC curve would lie "wholly above" the LRAC and would not be tangent at any point.

U-shaped curves

Both the SRAC and LRAC curves are typically expressed as U-shaped.[9]:211; 226 [14]:182;187–188 However, the shapes of the curves are not due to the same factors. For the short run curve the initial downward slope is largely due to declining average fixed costs.[2]:227 Increasing returns to the variable input at low levels of production also play a role,[17] while the upward slope is due to diminishing marginal returns to the variable input.[2]:227 With the long run curve the shape by definition reflects economies and diseconomies of scale.[14]:186 At low levels of production long run production functions generally exhibit increasing returns to scale, which, for firms that are perfect competitors in input markets, means that the long run average cost is falling;[2]:227 the upward slope of the long run average cost function at higher levels of output is due to decreasing returns to scale at those output levels.[2]:227

Cost curves in reality

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

Alan Blinder, former vice president of the American Economics Association, conducted the same type of survey in 1998, which involved 200 US firms in a sample that should be representative of the US economy at large. He found that about 40% of firms reported falling variable or marginal cost, and 48.4% reported constant marginal/variable cost.[19]

See also

Notes

  1. The slope of the short-run production function equals the marginal product of the variable input, conventionally labor. The slope of the variable cost function is marginal costs. The relationship between MC and the marginal product of labor MPL is MC = w/MPL. Because the wage rate w is assumed to be constant the shape of the variable cost curve is completely dependent on the marginal product of labor. The short-run total cost curve is simply the variable cost curve plus fixed costs.

References

  1. 1.0 1.1 1.2 1.3 1.4 1.5 Perloff, J. Microeconomics, 5th ed. Pearson, 2009.
  2. 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Perloff, J., 2008, Microeconomics: Theory & Applications with Calculus, Pearson. ISBN 978-0-321-27794-7
  3. 3.0 3.1 3.2 3.3 3.4 3.5 3.6 Lipsey, Richard G. (1975). An introduction to positive economics (fourth ed.). Weidenfeld & Nicolson. pp. 57–8. ISBN 0-297-76899-9.
  4. Viner, Jacob (1931). "Costs Curves and Supply Curves". 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., "Returns to 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 Production and Distribution, London: Cambridge Univ. Press, 1969.
  9. 9.0 9.1 9.2 9.3 9.4 Pindyck, R., and Rubinfeld, D., Microeconomics, 5th ed., Prentice-Hall, 2001.
  10. Nicholson: Microeconomic Theory 9th ed. Page 238 Thomson 2005
  11. Kreps, D., A Course in Microeconomic Theory, Princeton Univ. Press, 1990.
  12. 12.0 12.1 12.2 12.3 12.4 12.5 12.6 Binger, B., and Hoffman, E., Microeconomics with Calculus, 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. 14.0 14.1 14.2 14.3 Melvin & Boyes, Microeconomics, 5th ed., Houghton Mifflin, 2002
  15. Perloff, J. Microeconomics Theory & Application with Calculus Pearson (2008) p. 231.
  16. Nicholson: Microeconomic Theory 9th ed. Page Thomson 2005
  17. Boyes, W., The New Managerial Economics, Houghton Mifflin, 2004.
  18. Wilford J. Eiteman and Glenn E. Guthrie, The Shape of the Average Cost Curve, American Economic Review, 42.5: 832–838
  19. Alan Stuart Blinder, Asking about Prices: A New Approach to Understanding Price Stickiness, Russell Sage Foundation, New York, 1998