Daniel l. Rubinfeld

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234 Part 2 Producers, Consumers, and Competitive Markets Chapter 7 The Cost of Production 235 Figure 7.12 shows a learning curve for the production of machine tools. The horizontal axis measures the cUlIlulative number of lots of machine tools (groups of approximately 40) that the firm has produced. The vertical axis shows the nulUbel' of hours of labor needed to produce each lot Labor input per unit of output directly affects the production cost because the fewer the hours of labor needed, the Imver the marginal and average cost of production. The learning curve in Figure 7.12 is based on the relationship (dollars per unit of output) / Economies of Scale L = A + BN-(3 (7.8) where N is the cumulative units of output produced and L the labor input per unit of output. A, B, and 13 are constants, with A and B positive, and 13 behveen o and 1. When N is equal to I, L is equal to A + B, so that A + B measures the labor input required to produce the first l.mit of output When 13 equals 0, labor input per unit of output remains the same as the cumulative le\'el of output increases; there is no learning. When 13 is positive and N gets larger and larger, L becomes arbitrarily close to A. A, therefore, represents the minimum labor input per unit of output after all learning has taken place. The larger is 13, the more important is the learning effect. With 13 equal to 0.5, for example, the labor input per l.mit 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 13 is 0.31. For this particular learning curve, every doubling in cumulative output causes the input requirement (less the minimum attainable input requirement) to fall by about 20 percent. lO As Figure 7.12 shows, the learning curve drops sharply as the cumulatiye number of lots increases to about 20. Beyond an output of 20 lots, the cost saYings are relatively smalL Learning versus Economies of Scale Once the firm has produced 20 or more machine lots, the entire effect of the learning curve 'would be complete, and we could use the usual analysis of cost. If, however, the production process were relatively new, relatively high cost at low levels of output (and relatively low cost at higher levels) would indicate learning effects, not economies of scale. With learning, the cost of production for a mature firm is relatively low regardless of the scale of the firm's operation. 1£a firm that produces machine tools in 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 1o"\\'er its cost by scheduling the production of many lots regardless of the individual lot size. Figure 7.13 shows this phenomenon. AC 1 represents the long-run average cost of production of a firm that enjoys economies of scale in production. Thus the change in production from A to B along AC 1 leads to lower cost due to economies of scale. However, the move from A on AC 1 to C on ACe leads to lower cost due to learning, which shifts the average cost curve dm".'l1\vard. 10 Because (L - A) BN-.31, we can check that O.8(L - A) is approximately equal to B(2\T.31 Learning Output 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 AC j ), or it can decline because there is a leaming curve (a move from A on curve AC j to C on curve AC 2 )· The learning CLUTe 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 13 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 CUMULATIVE OUTPUT PER· UNIT LABOR REQUIREMENT TOTAL LABOR (N) FOR EACH 10 UNITS OF OUTPUT (L)* 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 .51 53.4 (48.3 + 5.1) 'The numbers in this column were calculated from the equation log(L) = - 0.322 log(N/IO), where L is the unit labor input and N is cumulative output
236 Part 2 Producers, Consumers, and Competitive Markets :h, ... "jr",~ 7 The Cost of Production 237 firm looking only at the high initial labor requirement -will obtain an m"erly pessimistic vie-w of the business. Suppose the firm plans to be in bus~ness for "a long time, producing 10 units per year. Suppose the total labor reqUlrement tor the first year's production is 10. In the first year of production, the firm's cost v"ill be high as it learns the business. But once the learning effect has taken place, production costs will falL After 8 years, the labor required to produce 10 units will be only 5.1, and per-unit cost will be roughly half what it was in the first year of production_ Thus the learning curve can be important for a firm deciding whether it is profitable to enter an industry. 100 Production Hours per Aircraft 80 60 JO Awrage for First 100 Aircraft 20 Suppose that as the manager of a firm that has just entered the chemical processing indush,)" you face the following problem: Should you produce a relatively Im'\' 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 appealing if there is a learning CUIye in this industry In that case, 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. For example, a study of 37 chemical products reveals that cost reductions in the chemical processing industry are directly tied to the growth of cumulative indush'Y output, to inveshnent in improved capital equipment, and, to a lesser extent, to economies of scale ll In fact, for the entire sample of chemical products, average costs of production fall at 5.5 percent per yeaL The Shldy reveals that for each doubling of plant scale, the average cost of production falls by 11 percent For each doubling of cumulative output, however, 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 industryY The learning curve has also been shown to be important in the semiconductor indushy A study of seven generations of dynamic random-access memory (DRAM) semiconductors from 1974 to 1992 fOlmd that the learning rates averaged about 20 percent; thus a 10-percent increase in cumulative production OL-______ L-____ ~ ______ -L ______ ~ ____ ~ __ _ o 100 200 300 400 500 Number of Aircraft Produced The learning curve relates the labor requirement per aircraft to the cumulative number of aircraft produced. As the production process becomes better organized and workers familiarity with their jobs, labor requirements fall dramatically would lead to a 2-percent decrease in cost,u The study also compared learning bv firms in Japan to firms in the United States and found that there was no dis ~guishable difference in the speed of learning. Another example is the aircraft industry, where studies have fOlmd learning rates that are as high as 40 percent This is illustrated in Figure 7_14, which shows the labor requirements for production of aircraft by Airbus Industrie. Obsen"e that the first 10 or 20 airplanes require far more labor to produce than the hundredth or two hundredth airplane. Also note how the learning cun'e flattens out after a certain point; in this case, nearly all learning is complete after 200 airplanes have been built. Learning curve effects can be important in determining the shape of longrun cost curves and can thus help guide managem_ent decisions. Managers can use learning CUITe information to decide whether a production operation is profitable and, if it is, how to plan how large the plant operation and the volume of cumulative output need be to generate a positive cash flow. 11 The studv was conducted by MaITin Lieberman, "The Learning Cun"e and Pricing in the Chemical Processing"Industries," RAND JOllmal of Economics 15 (198J): 213-28_ 12 The author used the average cost AC of the chemical products, the cumulati\:e industry output X, and the a\-erage scale of a production plant Z. He then estimated the relatlOnshlp log (AC) - 0387 log (X) - OJ73 log (Z). The - 0387 coefficient on cumulative output tells us that f~~ e\"ery I-percent increase in cumulative output, average cost decreases 0387 percent. The - 0.1/~ coefficient on plant size tells us that for e\-ery I-percent increase in plant size, cost decreases 0.17J percent By interpreting the two coefficients in lio-ht of the output and plant-size variables, we can allocate about 15 percent of the cost reduction to i~creases in the average scale of plants and 85 percent to increases in cumulative industry output. Suppose plant scale doubled while cumulati\-e output increased by a factor of 5 during the study. In that case, costs would fall by 11 percent from the increased scale and by 62 percent from the increase in cumulati\"e output A business that is expanding or contracting its operation must predict how costs will change as output changes. Estimates of future costs can be obtained from a cost function, which relates the cost of production to the level of output and other variables that the firm can control. 13The study \,-as conducted by D A. Irwin and P J Kleno,,", "Learning-by-Doing Spillo\-ers in the Semiconductor Industry," Journal of Political Eco1l01I1I/102 (December 199J): 1200-27 cost function Function relating cost of production to le\'el of output and other variables that the firm can controL
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Daniel l. Rubinfeld

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