Dynamic Changes in Costs The Learning Curve
Our discussion has suggested one reason a large firm may have a lower long-run average cost than a small firm-increasing returns to scale in production. It is tempting to conclude that firms that enjoy lower average cost over time are growing firms with increasing returns to scale. But this need not be true. In some firms, long-run average cost may decline over time because workers and managers absorb new technological information as they become more experienced at their jdbs.
As management and labor gain experience with production, the firm's marginal and average cost of producing a given level of output falls for four reasons. First, workers often take longer to accomplish a given task the first few times they do it. As they become more adept, their speed increases. Second, managers learn to schedule the production process more effectively, from the flow of materials to the organization of the manufacturing itself. Third, engineers, who are initially very cautious in their product designs, may gain enough experience to be able to allow for tolerances in design that save cost without increasing defects. Better and more specialized tools and plant organization may also lower cost. Fourth, suppliers of materials may learn how to process materials required by the firm more effectively and may pass on some of this advantage to the firm in the form of lower materials cost.
As a consequence, a firm "learns" over time as cumulative output increases. Managers use this learning process to help plan production and to forecast future costs. Figure 7.11 illustrates this process, in the form of a learning curve. A learning curve describes the relationship between a firm's cumulative output and the amount of inputs needed to produce a unit of output.
FIGURE 7.11 The Learning Curve. A firm's cost of production may fall over time as the managers and workers become more experienced and more effective at using the available plant and equipment. The learning curve shows the extent to which the hours of labor needed per unit of output (a machine in this case) fall as the cumulative output (number of machines) produced increases.
10 20 3C 40 50
Cumulative Numbei of Machine Lots Produced
Figure 7.11 shows a learning curve for the production of machine tools by a manufacturer.12The horizontal axis measures the cumulative number of lots of machine tools that the firm has produced (a lot is a group of approximately 40 machines), and the vertical axis the number of hours of labor needed to produce each lot. Labor input per unit of output directly affects the firm's cost of production because the fewer the hours of labor needed, the lower the marginal and average cost of production.
The learning curve in the figure is based on the relationship
where, N is the cumulative units of output produced, L is the labor input per units of output, and A, B, and [3 are constants, with A and B positive, and j3 between 0 and 1. When N is equal to 1, L is equal to A + B, so that A + B measures the labor input required to produce the first unit of output. When p equals 0, labor input per unit of output remains the same as the cumulative level of output increases, so there is no learning. When ยก3 is positive and N gets larger and larger, L becomes arbitrarily close to A, so that A represents the minimum labor input per unit of output after all learning has taken place.
The larger is (3, the more important is the learning effect. With p equal to 0.5, for example, the labor input per unit of output falls proportionally to the square root of the cumulative output. This degree of learning can substantially reduce the firm's production costs as the firm becomes more experienced.
In this machine tool example, the value of (3 is 0.31. For this particular learning curve, every doubling in cumulative output causes the difference between the input requirement and the minimum attainable input requirement to fall by about 20 percent.13 As Figure 7.11 shows, the learning curve drops sharply as the cumulative number of lots produced increases to about 20. Beyond an output of 20 lots, the cost savings are relatively small.
Once the firm has produced 20 or more machine lots, the entire effect of the learning curve would be complete, and the usual analysis of cost could be employed. If, however, the production process were relatively new, then relatively high cost at low levels of output (and relatively low cost at higher levels) would indicate learning effects, and not economies of scale. With learning, the cost of production for a mature firm is relatively low irrespective of the scale of the firm's operation. If a firm that produces machine tools in groups (or "lots") knows that it enjoys economies of scale, it should produce its machines in very large lots to take advantage of the lower cost associated with size. If there is a learning curve, the firm can lower its cost by scheduling the production of many lots irrespective of the individual lot size.
Figure 7.12 shows this phenomenon. ACi represents the long-run average cost of production of a firm that enjoys economies of scale in production. Thus, the change inl production from A to B along ACi leads to lower
See Werner Z. Hirsch, "Manufacturing Progress Functions,"1 Review of Economics and Statistics 34 (May
Because (L- A) = BN-.31, one can check that 0.8(L- A) is approximately equal to B(2N)-.3i.
- Cost ($ per unit of output)
Economies of Scale
AC 2
Output
FIGURE 7.12 Economies of Scale Versus Learning. A firm's average cost of production can decline over time because of growth of sales when increasing returns are present (a move from A to B on curve ACt), or it can decline because there is a learning curve (a move from A on curve ACi to C on curve AC2).
cost due to economies of scale. However, the move from A on ACt to C on ACi leads to lower cost due to learning, which shifts the average cost curve downward.
The learning curve is crucial for a firm that wants to predict the cost of producing a new product. Suppose, for example, that a firm producing machine tools knows that its labor requirement per machine for the first 10 machines is 1.0, the minimum labor requirement A is equal to zero, and fi is approximately equal to 0.32. Table 7.3 calculates the total labor requirement for producing 80 machines.
Because there is a learning curve, the per-unit labor requirement falls with increased production. As a result, the total labor requirement for producing more and more output increases in smaller and smaller increments. Therefore,, a firm looking at the high initial labor requirement will obtain an overly pessimistic view of the business. Suppose the firm plans to be in business for a long time and the total labor requirement for each year's product is 10. In the first year of production, the labor requirement is 10, so the firm's cost will be high as it learns the business. But once the learning effect has taken place, production costs will be lower. After 8 years, the labor requirement will be only 0.51, and per-unit cost will be roughly half what it was in the first year of production. Thus, learning curve effects can be important for a firm deciding whether it is profitable to enter an industry.
TABLE 7.3 Predicting the Labor Requirements of Producing a Given Output
Cumulative Output Per-Unit Labor Requirement Total Labor
(N) for each 10 units of Output (L)14 Requirement
TABLE 7.3 Predicting the Labor Requirements of Producing a Given Output
Cumulative Output Per-Unit Labor Requirement Total Labor
(N) for each 10 units of Output (L)14 Requirement
|
10 |
1.00 |
10.0 |
|
20 |
.80 |
18.0 (10.0 + 8.0) |
|
30 |
.70 |
25.0 (18.0 + 7.0) |
|
40 |
.64 |
31.4 (25.0 + 6.4) |
|
50 |
.60 |
37.4 (31.4 + 6.0) |
|
60 |
.56 |
43.0 (37.4 + 5.6) |
|
70 |
.53 |
48.3 (43.0 + 5.3) |
|
80 and over |
.51 |
53.4 (48.3 + 5.1) |
example 7.5 the learning curve in the chemical processing industry
Suppose that as the manager of a firm that has just entered the chemical processing industry you face the following problem: Should you produce a relatively low level of output (and sell at a high price), or should you price your product lower and increase your rate of sales? The second alternative is particularly appealing if there is a learning curve in this industry. Then the increased volume will lower your average production costs over time and increase the firm's profitability.
To decide what to do, you can examine the available statistical evidence that distinguishes the components of the learning curve (learning new processes by labor, engineering improvements, etc.) from increasing returns to scale. A study of 37 chemical products from the late 1950s to 1972 reveals that cost reductions in the chemical processing industry were directly tied to the growth of cumulative industry output, to investment in improved capital equipment, and to a lesser extent to economies of scale.15 In fact,for the entire sample of chemical products, average costs of production fell at 5.5 percent per year.16 The study reveals that for each doubling of plant scale, the average cost of production falls by 11 percent. For each doubling of cumulative output, how
14The numbers in this column were calculated from the equation log(L) = -0.322 log(AWO), where L is the unit labor input and N is cumulative output.
The study was by Marvin Lieberman, "The Learning Curve and Pricing in the Chemical Processing Industries," RAND Journal of Economics 15 (1984): 213-228.
16The author used the average cost AC of the chemical products, the cumulative industry output X, and the average scale of a production plant Z and estimated the relationship log (AC) = -0.387 log (X) - 0.173 log (Z). The -0.387 coefficient on cumulative output tells us that for every 1 percent increase in cumulative output, average cost decreases 0.387 percent. The -0.173 coefficient on plant size tells us that for every 1 percent increase in plant size,cost decreases 0.173 percent.
ever, the average cost of production falls by 27 percent. The evidence shows clearly that learning effects are more important than economies of scale in the chemical processing industry.17
Learning curve effects can be important in determining the shape of long-run cost curves and can thus help guide the firm's manager. The manager can use learning curve information to decide whether a production operation is profitable, and if it is, to plan how large the plant operation and the volume of cumulative output need be before a positive cash flow will result.
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