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8.6: Long-run production and costs

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    108406
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    The snowboard manufacturer we portray produces a relatively low level of output; in reality, millions of snowboards are produced each year in the global market. Black Diamond Snowboards may have hoped to get a start by going after a local market—the "free-ride" teenagers at Mont Sainte Anne in Quebec or at Fernie in British Columbia. If this business takes off, the owner must increase production, take the business out of his garage and set up a larger-scale operation. But how will this affect his cost structure? Will he be able to produce boards at a lower cost than when he was producing a very limited number of boards each season? Real-world experience would indicate yes.

    Production costs almost always decline when the scale of the operation initially increases. We refer to this phenomenon simply as economies of scale. There are several reasons why scale economies are encountered. One is that production flows can be organized in a more efficient manner when more is being produced. Another is that the opportunity to make greater use of task specialization presents itself; for example, Black Diamond Snowboards may be able to subdivide tasks within the laminating and packaging stations. With a larger operating scale the replacement of labor with capital may be economically efficient. If scale economies do define the real world, then a bigger plant—one that is geared to produce a higher level of output—should have an average total cost curve that is "lower" than the cost curve corresponding to the smaller scale of operation we considered in the example above.

    Average costs in the long run

    Figure 8.5 illustrates a possible relationship between the ATC curves for four different scales of operation. img259.png is the average total cost curve associated with a small-sized plant; think of it as the plant built in the entrepreneur's garage. img260.png is associated with a somewhat larger plant, perhaps one she has put together in a rented industrial or commercial space. The further a cost curve is located to the right of the diagram the larger the production facility it defines, given that output is measured on the horizontal axis. If there are economies associated with a larger scale of operation, then the average costs associated with producing larger outputs in a larger plant should be lower than the average costs associated with lower outputs in a smaller plant, assuming that the plants are producing the output levels they were designed to produce. For this reason, the cost curve img260.png and the cost curve img261.png each have a segment that is lower than the lowest segment on img259.png. However, in Figure 8.5 the cost curve img262.png has moved upwards. What behaviours are implied here?

    Figure 8.5 Long-run and short-run average costs
    img263.png
    The long-run ATC curve, LATC, is the lower envelope of all short-run ATC curves. It defines the least cost per unit of output when all inputs are variable. Minimum efficient scale is that output level at which the LATC is a minimum, indicating that further increases in the scale of production will not reduce unit costs.

    In many production environments, beyond some large scale of operation, it becomes increasingly difficult to reap further cost reductions from specialization, organizational economies, or marketing economies. At such a point, the scale economies are effectively exhausted, and larger plant sizes no longer give rise to lower (short-run) ATC curves. This is reflected in the similarity of the img260.png and the img261.png curves. The pattern suggests that we have almost exhausted the possibilities of further scale advantages once we build a plant size corresponding to img260.png. Consider next what is implied by the position of the img262.png curve relative to the img260.png and img261.png curves. The relatively higher position of the img262.png curve implies that unit costs will be higher in a yet larger plant. Stated differently: If we increase the scale of this firm to extremely high output levels, we are actually encountering diseconomies of scale. Diseconomies of scale imply that unit costs increase as a result of the firm's becoming too large: Perhaps co-ordination difficulties have set in at the very high output levels, or quality-control monitoring costs have risen. These coordination and management difficulties are reflected in increasing unit costs in the long run.

    The terms increasing, constant, and decreasing returns to scale underlie the concepts of scale economies and diseconomies: Increasing returns to scale (IRS) implies that, when all inputs are increased by a given proportion, output increases more than proportionately. Constant returns to scale (CRS) implies that output increases in direct proportion to an equal proportionate increase in all inputs. Decreasing returns to scale (DRS) implies that an equal proportionate increase in all inputs leads to a less than proportionate increase in output.

    Increasing returns to scale implies that, when all inputs are increased by a given proportion, output increases more than proportionately.

    Constant returns to scale implies that output increases in direct proportion to an equal proportionate increase in all inputs.

    Decreasing returns to scale implies that an equal proportionate increase in all inputs leads to a less than proportionate increase in output.

    These are pure production function relationships, but, if the prices of inputs are fixed for producers, they translate directly into the various cost structures illustrated in Figure 8.5. For example, if a 40% increase in capital and labour use allows for better production flows than when in the smaller plant, and therefore yields more than a 40% increase in output, this implies that the cost per snowboard produced must fall in the new plant. In contrast, if a 40% increase in capital and labour leads to say just a 30% increase in output, then the cost per snowboard in the new larger plant must be higher. Between these extremes, there may be a range of relatively constant unit costs, corresponding to where the production relation is subject to constant returns to scale. In Figure 8.5, the falling unit costs output region has increasing returns to scale, the region that has relatively constant unit costs has constant returns to scale, and the increasing cost region has decreasing returns to scale.

    Increasing returns to scale characterize businesses with large initial costs and relatively low costs of producing each unit of output. Computer chip manufacturers, pharmaceutical manufacturers, vehicle rental agencies, booking agencies such as booking.com or hotels.com, intermediaries such as airbnb.com, even brewers, all benefit from scale economies. In the beer market, brewing, bottling and shipping are all low-cost operations relative to the capital cost of setting up a brewery. Consequently, we observe surprisingly few breweries in any brewing company, even in large land-mass economies such as Canada or the US.

    In addition to the four short-run average total cost curves, Figure 8.5 contains a curve that forms an envelope around the bottom of these short-run average cost curves. This envelope is the long-run average total cost (LATC) curve, because it defines average cost as we move from one plant size to another. Remember that in the long run both labour and capital are variable, and as we move from one short-run average cost curve to another, that is exactly what happens—all factors of production are variable. Hence, the collection of short-run cost curves in Figure 8.5 provides the ingredients for a long-run average total cost curve1.

    img264.png

    Long-run average total cost is the lower envelope of all the short-run ATC curves.

    The particular range of output on the LATC where it begins to flatten out is called the range of minimum efficient scale. This is an important concept in industrial policy, as we shall see in later chapters. At such an output level, the producer has expanded sufficiently to take advantage of virtually all the scale economies available.

    Minimum efficient scale defines a threshold size of operation such that scale
    economies are almost exhausted.

    In view of this discussion and the shape of the LATC in Figure 8.5, it is obvious that economies of scale can also be defined in terms of the curvature of the LATC. Where the LATC declines there are IRS, where the LATC is flat there are CRS, where the LATC slopes upward there are DRS.

    Table 8.3 LATC elements for two plants (thousands $)
    Q img265.png img266.png img259.png img267.png img268.png img260.png
    20 50 30 80 100 25 125
    40 25 30 55 50 25 75
    60 16.67 30 46.67 33.33 25 58.33
    80 12.5 30 42.5 25 25 50
    100 10 30 40 20 25 45
    120 8.33 30 38.33 16.67 25 41.67
    140 7.14 30 37.14 14.29 25 39.29
    160 6.25 30 36.25 12.5 25 37.5
    180 5.56 30 35.56 11.11 25 36.11
    200 5 30 35 10 25 35
    220 4.55 30 34.55 9.09 25 34.09
    240 4.17 30 34.17 8.33 25 33.33
    260 3.85 30 33.85 7.69 25 32.69
    280 3.57 30 33.57 7.14 25 32.14
    Plant 1 img269.pngm. Plant 2 img270.pngm. For Q<200, img271.png; for Q>200, img272.png; and for Q=200, ATC1=ATC2. LATC defined by data in bold font.

    Long-run costs – a simple numerical example

    Kitt is an automobile designer specializing in the production of off-road vehicles sold to a small clientele. He has a choice of two (and only two) plant sizes; one involving mainly labour and the other employing robots extensively. The set-up (i.e. fixed) costs of these two assembly plants are $1 million and $2 million respectively. The advantage to having the more costly plant is that the pure production costs (variable costs) are less. The cost components are defined in Table 8.3. The variable cost (equal to the marginal cost here) is $30,000 in the plant that relies primarily on labour, and $25,000 in the plant that has robots. The ATC for each plant size is the sum of AFC and AVC. The AFC declines as the fixed cost is spread over more units produced. The variable cost per unit is constant in each case. By comparing the fourth and final columns, it is clear that the robot-intensive plant has lower costs if it produces a large number of vehicles. At an output of 200 vehicles the average costs in each plant are identical: The higher fixed costs associated with the robots are exactly offset by the lower variable costs at this output level.

    The ATC curve corresponding to each plant size is given in Figure 8.6. There are two short-run ATC curves. The positions of these curves indicate that if the manufacturer believes he can produce at least 200 vehicles his unit costs will be less with the plant involving robots; but at output levels less than this his unit costs would be less in the labour-intensive plant.

    Figure 8.6 LATC for two plants in $000
    img273.png

    The long-run average cost curve for this producer is the lower envelope of these two cost curves: ATC1 up to output 200 and ATC2 thereafter. Two features of this example are to be noted. First we do not encounter decreasing returns – the LATC curve never increases. ATC1 tends asymptotically to a lower bound of img274.png, while ATC2 tends towards img275.png. Second, in the interests of simplicity we have assumed just two plant sizes are possible. With more possibilities on the introduction of robots we could imagine more short-run ATC curves which would form the lower-envelope LATC.


    This page titled 8.6: Long-run production and costs is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Douglas Curtis and Ian Irvine (Lyryx) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.