Daniel l. Rubinfeld

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198 Part 2 Producers, Consumers, and Competitive Markets Chapter 6 Production 199 returns to scale Rate at which output increases as inputs are increased proportionately increasing returns to scale Output more than doubles when all inputs are doubled. constant returns to scale Output doubles when all inputs are doubled. decreasing returns to scale Output less than doubles when all inputs are doubled. 100 bushels of wheat, what will happen to output if we put two farmers to work "with two machines on two acres of land Output "",ill almost certainly increase, but will it double, more than double, or less than double Returns to scale is the rate at which output increases as inputs are increased proportio~ately. 'I'Ve will examine three different cases: increasing, constant, and decreasmg returns to (machine hours) 6 scale. Increasing Scale If output more than doubles when inputs are doubled, there are i.ncreasing 2 returns to scale. This might arise because the larger scale of operatlOn allows manaaers and workers to specialize in their tasks and to make use of more sophi~ticated, large-scale factories and equipment. The automobile assembly o line is a famous example of increasing returns. The prospect of increasing returns to scale is an important issue from a public policy perspective. If there are increasing retilrns, then it is economically advantaaeous to have one larae firm producing (at relatively low cost) rather than to h:ve many small firms (at relatively high cost). Because this large fir~ can cntral the price that it sets, it may need to be regulated. For example, mcreasmg returns in the provision of electricity is one reason why we have large, regulated power companies. Constant Returns to Scale A second possibility with respect to the scale of production is that output may double when inputs are doubled. In this case, we say there are constant returns to scale. With constant retilrns to scale, the size of the firm's operation does not affect the productivity of its factors-one plant using a partic.ular production process can easily be replicated, so that two plants produce tWIce ~s much ~utput. For example, a large travel agency might provide the same serVIce per clIent and use the same ratio of capital (office space) and labor (travel agents) as a small agency that services fewer clients. Decreasing Returns to Scale Finally, output may less than double when all inputs double. This ca~e of decreasing returns to scale applies to some firms with large-scale op~ratlOns. Eventually, difficulties in organizing and running a large.-scale operatIOn n~ay lead to decreased productivity of both labor and capItal. CommumcatlOn between workers and manaaers can become difficult to monitor as the workplace becomes more imperso~aL Thus the decreasing-rehl~ns ~a~e is likely to.be associated with the problems of coordinating tasks and mamtammg a usetullme 1 of communication behveen management and workers. Describing Returns to Scale The presence or absence of returns to scale is seen graphically ~ the hvo part: of Figure 6.11. The line OA from the origin in each panel descnbes a ~roductlOn process in which labor and capital are used as inputs to pro~uce .vanous l~vels of output in the ratio of 5 hours of labor to 2 hours of machme time. In ~Igur~ 6.11(21), the firm's production function exhibits constant returns to scale. When J 30 (machine I hours) 5 10 15 5 10 Labor (hours) (a) 2 30 O"'--~--..L.------ (b) A Labor (hours) When a firm's production process exhibits constant retilffiS to scale as shown by a movement alona ray OA in part (a) the isoquants are equally spaced as output increases proportionally. However, when there are in~reasina returns t~ scale as shown in (b), the isoquants move closer together as are increased along the ray. 0 hours of labor and 2 hours of machine time are used, an output of 10 units is produced. When both inputs double, output doubles from 10 to 20 units; when both inputs triple, output triples, from 10 to 30 units. Put differently, hvice as much of both inputs is needed to produce 20 units, and three times as"much is needed to produce 30 units. In Figure 6. l1(b), the firm's production function exhibits increasina returns to scale. Now the isoquants become closer toaether as we mO\"e away fl~m the orio ~ gin along OA As a result, less than twice the amount of both inputs is needed to increase production from 10 units to 20; substantiallY less than three times the inputs are needed to produce 30 units. The re,"el'se w'ould be true if the production function exhibited decreasing returns to scale (not shown here). With decreasing returns, the isoquants become increasinalv distant from one another 0_ as output le,"els proportionally increase. .Returns to scale ,,"ary considerably across finns and industries. Other things bemg equal, the greater the returns to scale, the laraer firms in an industry are likely" to be. ~ecause manufacturing ilWoh"es large il~vestments in capital equipment, manutacturing industries are more like Iv to have increasina returns to "0 sea ethan sen"ice-oriented industries. Services are more labor-intensive and can usually be pro,,"ided as efficiently in small quantities as they can on a large scale. T he carpet industry in the United States centers around the town of Dalton in northern Georgia. From a relati,"elv small industry "with many small firms in the first half of the twentieth century, it gre"w rapidly and b~came a
200 Part 2 Producers, Consumers, and Competitive Markets Chapter 6 Production CARPET SHIPMENTS, 1996 (MILLIONS OF DOLLARS PER YEAR) 1. Shaw Industries 3,202 6. World Carpets 475 2. Mohawk Industries 1,795 7. Burlington Industries 450 3. Beaulieu of America 1,006 8. Collins & Aikman 418 4. Interface Flooring 820 9. Masland Industries 380 5. Queen Carpet 775 10. Dixie Yarns 280 VVe can therefore characterize the carpet industry as one in 'which there are constant returns to scale for relatively small plants but increasing returns to scale for larger plants. These increasing rehIrns, hOlvever, are limited, and we can expect that if plant size were increased further, there would eventuallv be decreasing rehlrns to scale. . ..... maJ'or industrv with a laro-e number of firms of all sizes. For example, the top ~ 0 ten carpet manufachlrers, ranked by shipments in millions of dollars in 1996, are shovm in Table 6.5. 9 Currently, there are three relatively large manufacturers (Shaw, Mohawk, and Beaulieu) alono- with a number of smaller producers. There are also many , 0 - carpet retailers, wholesale distributors, carpet buying groups, and national retail carpet chains. The carpet industry has grown rapidly for several reasons. Consumer demand for ''\'001, nylon, and polypropylene carpets in commercial and residential uses has skyrocketed. In addition, innovations such as the introd uction of larger, faster, ~ and more efficient carpet-tufting machines have reduced costs and greatly increased carpet production. Along with the increase in production, innovation and competition have worked together to reduce real carpet prices. To what extent, if any, can the growth of the carpet indush'y be explained by the presence of rehmlS to scale There have certainly been substantial improvements in the processing of key production inputs (such as stain-resistant yarn) and in the distribution of carpets to retailers and consumers. But what about the production of carpets Carpet production is capital intensive-manufacturing plants require heavy llweshnents in high-speed tufting machines that hllTI various types of yarn into carpet, as well as machines that put the backings onto the carpets, cut the carpets lllto appropriate sizes, and package, label, and dish'ibute them. Overall, physical capital (including plant and equipment) accounts for.about 77 percent of a typical carpet manufachlrer's costs, while labor accOlmts tor the remaining 23 percent. Over time, the major carpet manufacturers have lllCreased the scale of their operations by putting larger and more efficient hItting machines into larger plants. At the same time, the use of labor in the~e plants has also increased significantly. The result Proportional inCI~eases In inputs have resulted in a more than proportional increase in output tor these larger plants. For example, a doubling of capital and labor inputs might lead to a nO-percent increase in output. This pattern has not, hovvever, been uniform across the industrv. Most smaller carpet manufachlrers have found that small changes in scale 11ave little or no effect on output; i.e., small proportional increases in inputs have only increased output proportionally. 9 Frank O'Neill, "The Focus 100," Foc1I5 (May 1997): 20. 1. A production function describes the maximum output a firm can produce for each specified combination of inputs 2. An iSOqUiliit is a CUITe that shows all combinations of inputs that yield a given level of output. A firm's production function can be represented by a series of isoquants associated with different levels of output 3. In the short run, one or more inputs to the production process are fixed. In the long run, all inputs are potentially variable. 4. Production 'with one variable input, labor, can be usefully described in terms of the Ilvemge prodllct of Illbol (which measures output per lUlit of labor input), and the mllrgillill product of labor (which measures the additional output as labor is increased by 1 unit). 5. According to the law of dimillisizing IIlllrgilllll retunls, when one or more inputs are fixed, a yariable input (usually labor) is likely to haye a marginal product that e\"entually diminishes as the level of input increases. 6. Isoquants always slope downward because the marginal product of all inputs is positive. The shape of each isoquant can be described by the marginal rate of 1. What is a production function HOlY does a long-run production function differ from a short-run production function 2. Why is the marginal product of labor likely to increase and then decline in the short run 3. Diminishing rehlrns to a single factor of production and constant returns to scale are not inconsistent Discuss. 4. You are an employer seeking to fill a vacant position on an assemblv line .. Are vou more concerned with the average pr~duct of lab~r or the marginal product technical substitution at each point on the isoquant. The IIlllrgilllll rllte of tec1l1licllIsllbstitlitioll of lilborfor Cllpitlll (MRTS) is the amount by which the input of capital can be reduced when one extra unit of labor is used so that output remains constant. 7. The standard of living that a cOlmtry can attain for its citizens is closely related to its level of labor productivity. Decreases in the rate of productivity growth in developed countries are due in part to the lack of growth of capital investment. S. The possibilities for substihltion among inputs in the production process range from a production function in which inputs are perfect sllbstitlltes to one in which the proportions of inputs to be used are fixed (a fixedproportiolls productioll fllilction). . 9. In long-run analysis, we tend to focus on the firm's choice of its scale or size of operation. Constant returns to scale means that doubling all inputs leads to doubling output Increasing returns to scale occurs when output more than doubles when inputs are doubled; decreasing returns to scale applies when output less than doubles of labor for the last person hired If you observe that your average product is just beginning to decline, should you hire any more workers What does this situation imply about the marginal product of your last worker hired 3. Faced with constantly changing conditions, why would a firm ever keep lilly factors fixed What criteria determine whether a factor is fixed or variable 6. How does the curvature of an isoquant relate to the marginal rate of tedmical substitution
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Daniel l. Rubinfeld

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