11.3 Short-Run versus Long-Run Costs

Up to this point, we have treated fixed cost as completely outside the control of a firm because we have focused on the short run. But as we noted earlier, all inputs are variable in the long run: this means that in the long run fixed cost may also be varied. In the long run, in other words, a firm’s fixed cost becomes a variable it can choose. For example, given time, Selena’s Gourmet Salsas can acquire additional food-preparation equipment or dispose of some of its existing equipment. In this section, we will examine how a firm’s costs behave in the short run and in the long run. We will also see that the firm will choose its fixed cost in the long run based on the level of output it expects to produce.

Let’s begin by supposing that Selena’s Gourmet Salsas is considering whether to acquire additional food-preparation equipment. Acquiring additional machinery will affect its total cost in two ways. First, the firm will have to either rent or buy the additional equipment; either way, that will mean higher fixed cost in the short run. Second, if the workers have more equipment, they will be more productive: fewer workers will be needed to produce any given output, so variable cost for any given output level will be reduced.

The table in Figure 11-13 shows how acquiring an additional machine affects costs. In our original example, we assumed that Selena’s Gourmet Salsas had a fixed cost of $108. The left half of the table shows variable cost as well as total cost and average total cost assuming a fixed cost of $108. The average total cost curve for this level of fixed cost is given by ATC1 in Figure 11-13. Let’s compare that to a situation in which the firm buys additional food-preparation equipment, doubling its fixed cost to $216 but reducing its variable cost at any given level of output. The right half of the table shows the firm’s variable cost, total cost, and average total cost with this higher level of fixed cost. The average total cost curve corresponding to $216 in fixed cost is given by ATC2 in Figure 11-13.

Figure11-13Choosing the Level of Fixed Cost for Selena’s Gourmet Salsas There is a trade-off between higher fixed cost and lower variable cost for any given output level, and vice versa. ATC1 is the average total cost curve corresponding to a fixed cost of $108; it leads to lower fixed cost and higher variable cost. ATC2 is the average total cost curve corresponding to a higher fixed cost of $216 but lower variable cost. At low output levels, at 4 or fewer cases of salsa per day, ATC1 lies below ATC2: average total cost is lower with only $108 in fixed cost. But as output goes up, average total cost is lower with the higher amount of fixed cost, $216: at more than 4 cases of salsa per day, ATC2 lies below ATC1.

From the figure you can see that when output is small, 4 cases of salsa per day or fewer, average total cost is smaller when Selena forgoes the additional equipment and maintains the lower fixed cost of $108: ATC1 lies below ATC2. For example, at 3 cases per day, average total cost is $72 without the additional machinery and $90 with the additional machinery. But as output increases beyond 4 cases per day, the firm’s average total cost is lower if it acquires the additional equipment, raising its fixed cost to $216. For example, at 9 cases of salsa per day, average total cost is $120 when fixed cost is $108 but only $78 when fixed cost is $216.

Why does average total cost change like this when fixed cost increases? When output is low, the increase in fixed cost from the additional equipment outweighs the reduction in variable cost from higher worker productivity—that is, there are too few units of output over which to spread the additional fixed cost. So if Selena plans to produce 4 or fewer cases per day, she would be better off choosing the lower level of fixed cost, $108, to achieve a lower average total cost of production. When planned output is high, however, she should acquire the additional machinery.

In general, for each output level there is some choice of fixed cost that minimizes the firm’s average total cost for that output level. So when the firm has a desired output level that it expects to maintain over time, it should choose the level of fixed cost optimal for that level—that is, the level of fixed cost that minimizes its average total cost.

Now that we are studying a situation in which fixed cost can change, we need to take time into account when discussing average total cost. All of the average total cost curves we have considered until now are defined for a given level of fixed cost—that is, they are defined for the short run, the period of time over which fixed cost doesn’t vary. To reinforce that distinction, for the rest of this chapter we will refer to these average total cost curves as “short-run average total cost curves.”

For most firms, it is realistic to assume that there are many possible choices of fixed cost, not just two. The implication: for such a firm, many possible short-run average total cost curves will exist, each corresponding to a different choice of fixed cost and so giving rise to what is called a firm’s “family” of short-run average total cost curves.

At any given point in time, a firm will find itself on one of its short-run cost curves, the one corresponding to its current level of fixed cost; a change in output will cause it to move along that curve. If the firm expects that change in output level to be long-standing, then it is likely that the firm’s current level of fixed cost is no longer optimal. Given sufficient time, it will want to adjust its fixed cost to a new level that minimizes average total cost for its new output level. For example, if Selena had been producing 2 cases of salsa per day with a fixed cost of $108 but found herself increasing her output to 8 cases per day for the foreseeable future, then in the long run she should rent or purchase more equipment and increase her fixed cost to a level that minimizes average total cost at the 8-cases-per-day output level.

The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost for each level of output.

Suppose we do a thought experiment and calculate the lowest possible average total cost that can be achieved for each output level if the firm were to choose its fixed cost for each output level. Economists have given this thought experiment a name: the long-run average total cost curve. Specifically, the long-run average total cost curve, or LRATC, is the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost for each level of output. This means that the long-run average total cost curve touches the lowest values of all the possible short-run average cost curves (for every possible fixed cost configuration).1 In the long run, a firm generally has greater flexibility and thus can do at least as well as in the short run, and possibly much better. If there are many possible choices of fixed cost, the long-run average total cost curve will have the familiar, smooth U shape, as shown by LRATC in Figure 11-14.

Figure11-14Short-Run and Long-Run Average Total Cost Curves Short-run and long-run average total cost curves differ because a firm can choose its fixed cost in the long run. If Selena has chosen the level of fixed cost that minimizes short-run average total cost at an output of 6 cases, and actually produces 6 cases, then she will be at point C on LRATC and ATC6. But if she produces only 3 cases, she will move to point B. If she expects to produce only 3 cases for a long time, in the long run she will reduce her fixed cost and move to point A on ATC3. Likewise, if she produces 9 cases (putting her at point Y) and expects to continue this for a long time, she will increase her fixed cost in the long run and move to point X.

We can now draw the distinction between the short run and the long run more fully. In the long run, when a producer has had time to choose the fixed cost appropriate for its desired level of output, that producer will be at some point on the long-run average total cost curve. But if the output level is altered, the firm will no longer be on its long-run average total cost curve and will instead be moving along its current short-run average total cost curve. It will not be on its long-run average total cost curve again until it readjusts its fixed cost for its new output level.

Figure 11-14 illustrates this point. The curve ATC3 shows short-run average total cost if Selena has chosen the level of fixed cost that minimizes average total cost at an output of 3 cases of salsa per day. This is confirmed by the fact that at 3 cases per day, ATC3 touches LRATC, the long-run average total cost curve. Similarly, ATC6 shows short-run average total cost if Selena has chosen the level of fixed cost that minimizes average total cost if her output is 6 cases per day. It touches LRATC at 6 cases per day. And ATC9 shows short-run average total cost if Selena has chosen the level of fixed cost that minimizes average total cost if her output is 9 cases per day. It touches LRATC at 9 cases per day.

Suppose that Selena initially chose to be on ATC6. If she actually produces 6 cases of salsa per day, her firm will be at point C on both its short-run and long-run average total cost curves. Suppose, however, that Selena ends up producing only 3 cases of salsa per day. In the short run, her average total cost is indicated by point B on ATC6; it is no longer on LRATC. If Selena had known that she would be producing only 3 cases per day, she would have been better off choosing a lower level of fixed cost, the one corresponding to ATC3, thereby achieving a lower average total cost. Then her firm would have found itself at point A on the long-run average total cost curve, which lies below point B.

Suppose, conversely, that Selena ends up producing 9 cases per day even though she initially chose to be on ATC6. In the short run her average total cost is indicated by point Y on ATC6. But she would be better off acquiring more equipment and incurring a higher fixed cost in order to reduce her variable cost and move to ATC9. This would allow her to reach point X on the long-run average total cost curve, which lies below Y.

The distinction between short-run and long-run average total costs is extremely important in making sense of how real firms operate over time. A company that has to increase output suddenly to meet a surge in demand will typically find that in the short run its average total cost rises sharply because it is hard to get extra production out of existing facilities. But given time to build new factories or add machinery, short-run average total cost falls.

Returns to Scale

There are increasing returns to scale when long-run average total cost declines as output increases.

What determines the shape of the long-run average total cost curve? The answer is that scale, the size of a firm’s operations, is often an important determinant of its long-run average total cost of production. Firms that experience scale effects in production find that their long-run average total cost changes substantially depending on the quantity of output they produce. There are increasing returns to scale (also known as economies of scale) when long-run average total cost declines as output increases. As you can see in Figure 11-14, Selena’s Gourmet Salsas experiences increasing returns to scale over output levels ranging from 0 up to 6 cases of salsa per day—the output levels over which LRATC is declining. In contrast, there are decreasing returns to scale (also known as dis-economies of scale) when long-run average total cost increases as output increases. For Selena’s Gourmet Salsas, decreasing returns to scale occur at output levels greater than 6 cases, the output levels over which its long-run average total cost curve is rising. There is also a third possible relationship between long-run average total cost and scale: firms experience constant returns to scale when long-run average total cost is constant as output increases. In this case, the firm’s long-run average total cost curve is horizontal over the output levels for which there are constant returns to scale. As you can see in Figure 11-14, Selena’s Gourmet Salsas has constant returns to scale when it produces 6 cases of salsa per day. (You may notice from the high fixed cost table in Figure 11-13 that, since their average cost curve is fairly flat near 6 cases of output, Selena’s Gourmet Salsas almost has constant returns to scale for levels of production anywhere from 5 to 7 cases of salsa per day.)

There are decreasing returns to scale when long-run average total cost increases as output increases.

There are constant returns to scale when long-run average total cost is constant as output increases.

What explains these scale effects in production? The answer ultimately lies in the firm’s technology of production. Increasing returns often arise from the increased specialization that larger output levels allow—a larger scale of operation means that individual workers can limit themselves to more specialized tasks, becoming more skilled and efficient at doing them. Another source of increasing returns is very large initial set-up cost; in some industries—such as auto manufacturing, electricity generating, or petroleum refining—incurring a high fixed cost in the form of plant and equipment is necessary to produce any output. A third source of increasing returns, found in certain high-tech industries such as software development, is network externalities, a topic covered in Chapter 16. As we’ll see in Chapter 13, where we study monopoly, increasing returns have very important implications for how firms and industries interact and behave.

Decreasing returns—the opposite scenario—typically arise in large firms due to problems of coordination and communication: as the firm grows in size, it becomes ever more difficult and so more costly to communicate and to organize its activities. Although increasing returns induce firms to get larger, decreasing returns tend to limit their size. And when there are constant returns to scale, scale has no effect on a firm’s long-run average total cost: it is the same regardless of whether the firm produces 1 unit or 100 000 units.

Summing Up Costs: The Short and Long of It

If a firm is to make the best decisions about how much to produce, it has to understand how its costs relate to the quantity of output it chooses to produce. Table 11-3 provides a quick summary of the concepts and measures of cost you have learned about.

TABLE11-3 Concepts and Measures of Cost

THERE’S NO BUSINESS LIKE SNOW BUSINESS

Cities with higher average annual snowfall maintain larger snowplow fleets.

Anyone who has lived both in a snowy city, like Montreal, and in a city that only occasionally experiences significant snowfall, like Victoria, is aware of the differences in total cost that arise from making different choices about fixed cost.

In Victoria, even a minor snowfall—say, 4 or 5 centimetres overnight—is enough to create chaos during the next morning’s commute. The same snowfall in Montreal has hardly any effect at all. The reason is not that Victorians are wimps and Montrealers are made of sterner stuff; it is that Victoria, where it rarely snows, has only a fraction as many snowplows and other snowclearing equipment as cities where heavy snow is a fact of life.

In this sense Victoria and Montreal are like two producers who expect to produce different levels of output, where the “output” is snow removal. Victoria, which rarely has significant snow, has chosen a low level of fixed cost in the form of snow-clearing equipment. This makes sense under normal circumstances but leaves the city unprepared when major snow does fall. Montreal, which knows that it will face lots of snow, chooses to accept the higher fixed cost that leaves it in a position to respond effectively.

Quick Review

  • In the long run, firms choose fixed cost according to expected output. Higher fixed cost reduces average total cost when output is high. Lower fixed cost reduces average total cost when output is low.

  • There are many possible short-run average total cost curves, each corresponding to a different level of fixed cost. The long-run average total cost curve, LRATC, shows average total cost over the long run, when the firm has chosen fixed cost to minimize average total cost for each level of output.

  • A firm that has fully adjusted its fixed cost for its output level will operate at a point that lies on both its current short-run and long-run average total cost curves. A change in output moves the firm along its current short-run average total cost curve. Once it has readjusted its fixed cost, the firm will operate on a new short-run average total cost curve and on the long-run average total cost curve.

  • Scale effects arise from the technology of production. Increasing returns to scale tend to make firms larger. Decreasing returns to scale tend to limit their size. With constant returns to scale, scale has no effect.

Check Your Understanding 11-3

CHECK YOUR UNDERSTANDING 11-3

Question 11.3

The accompanying table shows three possible combinations of fixed cost and average variable cost. Average variable cost is constant in this example (it does not vary with the quantity of output produced).

  1. For each of the three choices, calculate the average total cost of producing 12 000, 22 000, and 30 000 units. For each of these quantities, which choice results in the lowest average total cost?

  2. Suppose that the firm, which has historically produced 12 000 units, experiences a sharp, permanent increase in demand that leads it to produce 22 000 units. Explain how its average total cost will change in the short run and in the long run.

  3. Explain what the firm should do instead if it believes the change in demand is temporary.

  1. The accompanying table shows the average total cost of producing 12 000, 22 000, and 30 000 units for each of the three choices of fixed cost. For example, if the firm makes choice 1, the total cost of producing 12 000 units of output is $8000 + 12 000 × $1.00 = $20 000. The average total cost of producing 12 000 units of output is therefore $20 000/12 000 = $1.67. The other average total costs are calculated similarly.

    So if the firm wanted to produce 12 000 units, it would make choice 1 because this gives it the lowest average total cost. If it wanted to produce 22 000 units, it would make choice 2. If it wanted to produce 30 000 units, it would make choice 3.

  2. Having historically produced 12 000 units, the firm would have adopted choice 1. When producing 12 000 units, the firm would have had an average total cost of $1.67. When output jumps to 22 000 units, the firm cannot alter its choice of fixed cost in the short run, so its average total cost in the short run will be $1.36. In the long run, however, it will adopt choice 2, making its average total cost fall to $1.30.

  3. If the firm believes that the increase in demand is temporary, it should not alter its fixed cost from choice 1 because choice 2 generates higher average total cost as soon as output falls back to its original quantity of 12 000 units: $1.75 versus $1.67.

Question 11.4

In each of the following cases, explain what kind of scale effects you think the firm will experience and why.

  1. A telemarketing firm in which employees make sales calls using computers and telephones

  2. An interior design firm in which design projects are based on the expertise of the firm’s owner

  3. A diamond-mining company

  1. This firm is likely to experience constant returns to scale. To increase output, the firm must hire more workers, purchase more computers, and pay additional telephone charges. Because these inputs are easily available, their long-run average total cost is unlikely to change as output increases.

  2. This firm is likely to experience decreasing returns to scale. As the firm takes on more projects, the costs of communication and coordination required to implement the expertise of the firm’s owner are likely to increase.

  3. This firm is likely to experience increasing returns to scale. Because diamond mining requires a large initial set-up cost for excavation equipment, long-run average total cost will fall as output increases.

Question 11.5

Draw a graph like Figure 11-14 and insert a short-run average total cost curve corresponding to a long-run output choice of 5 cases of salsa per day. Use the graph to show why Selena should change her fixed cost if she expects to produce only 4 cases per day for a long period of time.

The accompanying diagram shows the long-run average total cost curve (LRATC) and the short-run average total cost curve corresponding to a long-run output choice of 5 cases of salsa (ATC5). The curve ATC5 shows the short-run average total cost for which the level of fixed cost minimizes average total cost at an output of 5 cases of salsa. This is confirmed by the fact that at 5 cases per day, ATC5 touches LRATC, the long-run average total cost curve.

If Selena expects to produce only 4 cases of salsa for a long time, she should change her fixed cost. If she does not change her fixed cost and produces 4 cases of salsa, her average total cost in the short run is indicated by point B on ATC5; it is no longer on the LRATC. If she changes her fixed cost, though, her average total cost could be lower, at point A.

Kiva Systems’ Robots versus Humans

When you order a product such as a book online, your order is likely packed and shipped by humans and robots working together as a team. E-commerce retailers can see their sales quadruple during the run-up to the Christmas holidays. So in North America, online retailers such as Amazon, Crate & Barrel, Toys “R” Us, Gap, and others have been increasingly using robots in their order fulfillment. According to the Business News Network (BNN), with the help of greater use of mobile robots, online sales in the United States rose by 17.3% on Thanksgiving and Black Friday in 2013, outpacing sales growth at brick-and-mortar stores.

The leader in these technological advances in warehouse automation is Kiva Systems. The Kiva robots receive orders via a computer system and deliver the products from the warehouse to human employees who pack the products for shipping. According to Canadian Business, the online shoe retailer Zappos.com found that its productivity doubled and its energy cost was cut in half less than a year after adopting the Kiva system. With the help of its Kiva robots, Zappos.com was still guaranteeing Christmas Eve delivery to U.S. customers on the morning of December 23rd.

Behind these technological advances in warehouse automation, however, lies a debate: people versus robots. The use of robots definitely boosts productivity and reduces labour requirements, but it might also reduce job security. Also, why don’t we observe all online retailers using more robots to fulfill their orders? The answer is simple: it is not cheap to install a robotic system. According to Kiva, it can install a robotic system for as little as a few million dollars, but some installations have cost as much as $20 million. Yet hiring workers has a cost, too: during the 2013 holiday season, Amazon, the world’s largest online retailer, hired about 70 000 temporary workers at its distribution centres around the globe.2

And as one industry analyst noted, an obstacle to the adoption of a robotic system for many e-commerce retailers is that it doesn’t make economic sense: it’s too expensive to buy sufficient robots for the busiest time of the year because they would be idle at other times. Kiva is now testing a program to rent out its robots seasonally so that retailers can “hire” enough robots to handle their holiday orders just like Amazon hires more humans.

Canadian retailers wishing to capture the benefits of Kiva without the costs of installing the system can choose to outsource their warehouse management to a logistic company. Based in Vaughan, Ontario, Think Logistics uses Kiva Systems robots to fill online orders for several companies. By serving multiple companies, Think Logistics can more fully utilize the benefits of their Kiva system all year round and is less prone to seasonal fluctuations in sales revenue.

QUESTIONS FOR THOUGHT

Question 11.6

Assume that a firm can sell a robot, but that the sale takes time and the firm is likely to get less than what it paid. Other things equal, which system, human-based or robotic, will have a higher fixed cost? Which will have a higher variable cost? Explain.

46O/GvlXlao=
Assume that a firm can sell a robot, but that the sale takes time and the firm is likely to get less than what it paid. Other things equal, which system, human-based or robotic, will have a higher fixed cost? Which will have a higher variable cost? Explain.

Question 11.7

Predict the pattern of off-holiday sales versus holiday sales that would induce a retailer to keep a human-based system. Predict the pattern that would induce a retailer to move to a robotic system. Explain how Kiva’s “robot-for-hire” program would affect your answers.

46O/GvlXlao=
Predict the pattern of off-holiday sales versus holiday sales that would induce a retailer to keep a human-based system. Predict the pattern that would induce a retailer to move to a robotic system. Explain how Kiva’s “robot-for-hire” program would affect your answers.

Question 11.8

Explain why the adoption of the Kiva robotic system could allow a company like Think Logistics to expand and hire additional workers.

46O/GvlXlao=
Explain why the adoption of the Kiva robotic system could allow a company like Think Logistics to expand and hire additional workers.