Returns to Scale

The measure of increased output associated with increases in all inputs is fundamental to the long-ran nature of the firm's production process. How does the output of the firm change as its inputs are proportionately increased? If output more than doubles when inputs are doubled, there are increasing returns to scale. This might arise because the larger scale of operation allows managers and workers to specialize in their tasks and make use of more sophisticated, large-scale factories and equipment. The automobile assembly line is a famous example of increasing returns.

The presence of increasing returns to scale is an important issue from a public policy perspective. If there are increasing returns, then it is economically advantageous to have one large firm producing (at relatively low cost) than to have many small firms (at relatively high cost). Because this large firm can control the price that it sets, it may need to be regulated. For example, increasing returns in the provision of electricity is one reason why we have large, regulated power companies.

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 returns to scale, the size of the firm's operation does not affect the productivity of its factors. The average and marginal productivity of the firm's inputs remains constant whether the plant is small or large. With constant returns to scale, one plant using a particular production process can easily be replicated, so that two plants produce twice as much output. 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 travel agency that services fewer clients.

Finally, output may less than double when all inputs double. This case of decreasing returns to scale is likely to apply to any firm with large-scale operations. Eventually, difficulties of management associated with the complexities of organizing and running a large-scale operation may lead to decreased productivity of both labor and capital. Communication between workers and managers can become difficult to monitor and the workplace more impersonal. Thus, the decreasing-returns case is likely to be associated with the problems of coordinating tasks and maintaining a useful line of communication between management and workers. Or it may result because individuals cannot exhibit their entrepreneurial abilities in a large-scale operation.

With the production function given in footnote 6, it is not difficult (using calculus) to show that the marginal rate of technical substitution is given by MRTS = (MPl/MPk) = ^A)K/L). Thus, the MRTS decreases as the capital-to-labor ratio falls. For an interesting study of agricultural production in Israel, see Richard E. Just, David Zilberman, and Eithan Hochman, "Estimation of Multicrop Production Functions," American Journal of Agricultural Economics 65 (1983): 770-780.

The presence or absence of returns to scale is seen graphically in Figure 6.9. The production process is one in which labor and capital are used as inputs in the ratio of 5 hours of labor to 1 hour of machine time. The ray OB from the origin describes the various combinations of labor and capital that can be used to produce output when the input proportions are kept constant.

At relatively low output levels, the firm's production function exhibits increasing returns to scale, as shown in the range from 0 to A. When the input combination is 5 hours of labor and 1 hour of machine time, 10 units of output are produced (as shown in the lowest isoquant in the figure). When both inputs double, output triples from 10 to 30 units. Then when inputs increase by one-half again (from 10 to 15 hours of labor and 2 to 3 hours of machine time), output doubles from 30 to 60 units.

At higher output levels, the production function exhibits decreasing returns to scale, as shown in the range from A to B. When the input combination increases by one-third, from 15 to 20 hours of labor and from 3 to 4 machine hours, output increases only by one-sixth, from 60 to 70 units. And when inputs increase by one-half, from 20 to 30 hours of labor and from 4 to 6 machine hours, output increases by only one-seventh, from 70 to 80 units.

Figure 6.9 shows that with increasing returns to scale, isoquants become closer and closer to one another as inputs increase proportionally. However,

0 5 10 15 20 25 30 Labor


0 5 10 15 20 25 30 Labor


FIGURE 6.9 Returns to Scale. When a firn's production process exhibits increasing returns to scale as shown by a movement from 0 to A along ray OB, the isoquants get closer and closer to one another. However, when there are decreasing returns to scale as shown by a move from A to B, the isoquants get farther apart.

with decreasing returns to scale, isoquants become farther and farther from one another, because more and more inputs are needed. When there are constant returns to scale (not shown in Figure 6.9), isoquants are equally spaced.

Returns to scale vary considerably across firms and industries. Other things equal, the greater the returns to scale, the larger firms in an industry are likely to be. Manufacturing industries are more likely to have increasing returns to scale than service-oriented industries because manufacturing involves large investments in capital equipment. Services are more labor-intensive and can usually be provided as efficiently in small quantities as they can on a large scale.


During most of this century, railroads have grown larger and larger, yet their financial problems have continued to mount? Does this increase in size make good economic sense? If so, why do railroads continue to have difficulty competing with other forms of transportation? We can get some insight into these questions by looking at the economics of rail freight transportation.

To see whether there are increasing returns to scale, we will measure input as freight density, the number of tons of railroad freight that are run per unit of time along a particular route. Output is given by the amount of a particular commodity shipped along this route within the specified time. Then we can ask whether the amount that can be shipped increases more than proportionately as we add to freight tonnage. We might expect increasing returns initially because as more freight is shipped, the railroad management can use its planning and organization to design the appropriate scheduling of the freight system efficiently. However, decreasing returns will arise at some point when there are so many freight shipments that scheduling gets difficult and rail speeds are reduced.

Most studies of the railroad industry indicate increasing returns to scale at low and moderate freight densities, but decreasing returns to scale begin to set in after a certain point (called the efficient density). Only when the density gets quite large is this phenomenon important, however. One study, for example, indicated increasing returns to scale up to the range of 8 to 10 million tons (per year) per route-mile, a very large freight density.

To see the practical importance of these numbers, we have tabulated the 1980 freight densities of major U.S. railroads in Table 6.5. Some railroads such as Colorado & Southern and Union Pacific have reached or surpassed the point of minimum efficient size (the point at which increasing returns to scale disappear). But many railroads operate at freight densities below this.

This example draws on the analysis of railroad freight regulation by Theodore Keeler, Railroads Freight, and Public Policy (Washington D.C.: The Brookings Institution, 1983), Chapter 3, table 6.5 Freight Densities of Major Railroads (Million Tons Per Route-Mile)



Atchison. Topeka & Santa Fc Baltimore & Ohio Burlington Northern Chicago and Northwestern Colorado & Southern Fort Worth & Denver Kansas City Southern Missouri Pacific Southern Pacific Union Pacific Western Pacific

Since most rail companies have not surpassed iheir optimum size, it appears that growth has been economically advantageous. The financial problems of the railroad industry relate more to competition from oiher forms of transportation than to the nature of the production process itself'.

1. A production function describes the maximum output a firm can produce for each specified combination of inputs.

2. An isocquant is a curve thai 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 arc fixed, whereas in the long run all inputs arc potentially variable,

4. Production with one variable input, labo, can be usefully described in terms of the average product of labor (which measures the productivity of'the average worker), and the marginal product of labor (which measures the productivity of the last worker added to the production process).

5. According to the "law of diminishing returns," when one or more inputs arc fixed, a variable input (usually labor) is likely to have a marginal product that eventually 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 technical substitution at each point on the isoquant. The marginal rate of technical substitution of labor for capital (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 country can attain for its citizens is closely related to its level of labor productivity. Recent decreases in the rate of productivity growth in developed countries are due in part to the lack of growth of capital investment.

8. The possibilities for substitution among inputs in the production process range from a production function in which inputs are perfectly substitutable to one in which the proportions of inputs to be used are fixed (a fixed-proportions production function).

9. In the 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, whereas decreasing returns to scale applies when output less than doubles.

Questions for Review

1. What is a production function? How 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 returns 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 assembly line. Are you more concerned with the average product of labor or the marginal product 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?

5. Faced with constantly changing conditions, why would a firm ever keep any factors fixed? What determines whether a factor is fixed or variable?

6. How does the curvature of an isoquant relate to the marginal rate of technical substitution?

7. Can a firm have a production function that exhibits increasing returns to scale, constant returns to scale, and decreasing returns to scale as output increases?Discuss.

8. Give an example of a production process in which the short run involves a day or a week, and the long run any period longer than a week.

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  • zahra
    How isoquant relates with budget line and return to scale?
    2 years ago
  • aulis luusua
    How isoquant relate with budget line return to scale?
    2 years ago

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