# The structure of costs in the long run

## Key points

• A production technology is the specific combination of labor, physical capital, and technology that makes up a particular method of production.
• In the long run, firms can choose their production technology, so all costs become variable costs.
• Economies of scale refers to a situation where the average cost decreases as the level of output increases.

## The structure of costs in the long run

Generally speaking, the long run is the period of time when all costs are variable. It is not a precise period of time because it depends on the specifics of each firm.
If you have a one-year lease on your factory, then the long run is any period longer than a year since after a year, you are no longer bound by the lease. No costs are fixed in the long run. A firm can build new factories and purchase new machinery, or it can close existing facilities. In planning for the long run, a firm can compare alternative production technologies or processes.
In this context, technology refers to all alternative methods of combining inputs to produce outputs. It does not refer to a specific new invention like the tablet computer. Firms search for the production technology that will allow them to produce the desired level of output at the lowest cost. After all, lower costs lead to higher profits—at least if total revenues remain unchanged. In addition, each firm knows that if it does not seek out the lowest-cost methods of production, it may lose sales to competitor firms that find a way to produce and sell for less.

## Choice of production technology

Many tasks can be performed with a range of combinations of labor and physical capital. For example, a firm can have human beings answering phones and taking messages, or it can invest in an automated voicemail system. A firm can hire file clerks and secretaries to manage a system of paper folders and file cabinets, or it can invest in a computerized record-keeping system that will require fewer employees. A firm can hire workers to push supplies around a factory on rolling carts, it can invest in motorized vehicles, or it can invest in robots that carry materials without a driver. Firms often face a choice between buying many small machines, which need a worker to run each one, or buying one larger and more expensive machine, which requires only one or two workers to operate it. In short, physical capital and labor can often substitute for each other.
Let's look at an example—a private firm that is hired by local governments to clean up public parks. In the table below, there are three different possible combinations of labor and physical capital for cleaning up a single average-sized park. The first production technology is heavy on workers and light on machines; the next two technologies substitute machines for workers. Since all three of these production methods produce the same thing—one cleaned-up park—a profit-seeking firm will choose the production technology that is least expensive, given the prices of labor and machines.
Three ways to clean a park
Production technology A10 workers2 machines
Production technology B7 workers4 machines
Production technology C3 workers7 machines
Production technology A uses the most labor and least machinery. Production technology C uses the least labor and the most machinery. The table below outlines three examples of how the total cost changes with each production technology as the cost of labor changes. Why do you think that as the cost of labor rises from example one to two to three, the firm will choose to substitute away from labor and use more machinery?
Total cost with rising labor costs
Example one: workers cost $40, machines cost$80
Labor costMachine costTotal cost
Cost of technology A10 × $40 =$4002 × $80 =$160$560 Cost of technology B7 ×$40 = $2804 ×$80 = $320$600
Cost of technology C3 × $40 =$1207 × $80 =$560$680 Example two: workers cost$55, machines cost $80 Labor costMachine costTotal cost Cost of technology A10 ×$55 = $5502 ×$80 = $160$710
Cost of technology B7 × $55 =$3854 × $80 =$320$705 Cost of technology C3 ×$55 = $1657 ×$80 = $560$725
Example three: workers cost $90, machines cost$80
Labor costMachine costTotal cost
Cost of technology A10 × $90 =$9002 × $80 =$160$1,060 Cost of technology B7 ×$90 = $6304 ×$80 = $320$950
Cost of technology C3 × $90 =$2707 × $80 =$560$830 Example one shows the firm’s cost calculation when wages are$40 and machine costs are $80. In this case, technology A is the lowest-cost production technology. In example two, wages rise to$55, while the cost of machines does not change. In this case, technology B is the lowest-cost production technology. If wages keep rising up to $90—while the cost of machines remains unchanged—then technology C becomes the lowest-cost form of production, as shown in example three. These examples show that as an input becomes more expensive—in this case, the labor input—firms will attempt to conserve on using that input and will instead shift to other inputs that are relatively less expensive. This pattern helps to explain why the demand curve for labor, or any input, slopes down; as labor becomes relatively more expensive, profit-seeking firms will seek to substitute the use of other inputs. When a multinational employer like Coca-Cola or McDonald’s sets up bottling plants or restaurants in high-wage economies like the United States, Canada, Japan, or Western Europe, it is likely to use production technologies that conserve on the number of workers and focus more on machines. However, that same employer is likely to use production technologies with more workers and less machinery when producing in lower-wage countries like Mexico, China, or South Africa. ## Economies of scale Once a firm has determined the least costly production technology, it can consider the optimal scale of production, or quantity of output, to produce. Many industries experience economies of scale—as the quantity of output goes up, the cost per unit goes down. This is the idea behind so-called warehouse stores like Costco or Walmart. In everyday language—a larger factory can produce at a lower average cost than a smaller factory. The diagram below illustrates the idea of economies of scale; it shows the average cost of producing an alarm clock falling as the quantity of output rises. For a small-sized factory like $\text{S}$—with an output level of 1,000—the average cost of production is$12 per alarm clock. For a medium-sized factory like $\text{M}$—with an output level of 2,000—the average cost of production falls to $8 per alarm clock. For a large factory like $\text{L}$—with an output of 5,000—the average cost of production declines still further to$4 per alarm clock.
The graph shows a downward sloping line that represents how large-scale production leads to a decrease in average costs.
Image credit: Figure 1 in "The Structure of Costs in the Long Run" by OpenStaxCollege, CC BY 4.0
The average cost curve above may may appear similar to the short-run average cost curves you've seen in other Khan Academy tutorials, but there is one major difference. The economies of scale curve is a long-run average cost, or LRAC, curve; it allows all factors of production to change. Short-run average cost curves assume the existence of fixed costs, and only variable costs are allowed to change.
A great example of economies of scale is the chemical industry. Chemical plants have a lot of pipes. The cost of the materials for producing a pipe is related to the circumference of the pipe and its length. However, the volume of chemicals that can flow through a pipe is determined by the cross-section area of the pipe. The table below shows that a pipe which uses twice as much material to make—as shown by the circumference of the pipe doubling—can actually carry four times the volume of chemicals because the cross-section area of the pipe rises by a factor of four—as you can see in the area column.
Comparing pipes: economies of scale in the chemical industry
Circumference, $2\pi r$Area, $\pi r^{2}$
4-inch pipe12.5 inches12.5 square inches
8-inch pipe25.1 inches50.2 square inches
16-inch pipe50.2 inches201.1 square inches
A doubling of the cost of producing the pipe allows the chemical firm to process four times as much material. This pattern is a major reason for economies of scale in chemical production, which uses a large quantity of pipes. Of course, economies of scale in a chemical plant are more complex than this simple calculation suggests, but the chemical engineers who design these plants have long used what they call the six-tenths rule—a rule of thumb which holds that increasing the quantity produced in a chemical plant by a certain percentage will increase total cost by only six-tenths as much.

## Shifting patterns of long-run average cost

New developments in production technology can shift the LRAC curve in ways that alter the size distribution of firms in an industry.
For much of the 20th century, the most common change has been to see alterations in technology—like the assembly line or the large department store—where large-scale producers seemed to gain an advantage over smaller ones. These innovations caused the downward-sloping economies of scale portion of the LRAC curve to stretch over a larger quantity of output.
However, new production technologies do not inevitably lead to a greater average size for firms. For example, in recent years some new technologies for generating electricity on a smaller scale have appeared. Traditional coal-burning electricity plants needed to produce 300 to 600 megawatts of power to exploit economies of scale fully, but high-efficiency turbines used to produce electricity from burning natural gas can produce electricity at a competitive price while producing a smaller quantity of 100 megawatts or less. This new technology created the possibility for smaller companies or plants to generate electricity as efficiently as large ones.
Another example of a technology-driven shift to smaller plants may be taking place in the tire industry. A traditional mid-size tire plant produces about six million tires per year. However, in 2000, the Italian company Pirelli introduced a new tire factory that uses many robots. The Pirelli tire plant produced only about one million tires per year, but it does so at a lower average cost than a traditional mid-sized tire plant.
Controversy has simmered in recent years over whether new information and communications technologies will increase or decrease the size of firms. On one hand, the new technology may make it easier for small firms to reach out beyond their local geographic area and find customers across a state, the nation, or even across international boundaries. This factor might seem to predict a future with a larger number of small competitors.
On the other hand, new information and communications technology might create winner-take-all markets where one large company will tend to command a large share of total sales—as Microsoft has done in the production of software for personal computers or Amazon has done in online bookselling. Additionally, improved information and communication technologies might make it easier to manage many different plants and operations across the country or around the world, which could encourage larger firms.
How developing technologies affect firm size is of great interest to economists, businesspeople, and policymakers.

## Summary

• A production technology is the specific combination of labor, physical capital, and technology that makes up a particular method of production.
• In the long run, firms can choose their production technology, so all costs become variable costs.
• Economies of scale refers to a situation where the average cost decreases as the level of output increases.

## Self-check questions

Return to the example in the first section of this article that discusses a hypothetical firm hired by the local government to clean up public parks. If the cost of labor remains at $40, but the cost of a machine decreases to$50, what would be the total cost of each method of production? Which method should the firm use, and why?
The new table should look like this:
Labor costMachine costTotal cost
Cost of technology A10 × $40 =$4002 × $50 =$100$500 Cost of technology B7 ×$40 = $2804 ×$50 = $200$480
Cost of technology C3 × $40 =$1207 × $50 =$350$470 The firm should choose production technology C since it has the lowest total cost. This makes sense—with cheaper machine hours—one would expect a shift in the direction of more machines and less labor. In the same example, suppose the cost of machines increases to$55, while the cost of labor stays at $40. How would these changes affect the total cost of the three methods? Which method should the firm choose now? Labor costMachine costTotal cost Cost of technology A10 ×$40 = $4002 ×$55 = $110$510
Cost of technology B7 × $40 =$2804 × $55 =$220$500 Cost of technology C3 ×$40 = $1207 ×$55 = $385$505
The firm should choose production technology B since it has the lowest total cost. Because the cost of machines increased—relative to the previous question—you would expect a shift toward less capital and more labor.
Automobile manufacturing is an industry subject to significant economies of scale. Suppose there are four domestic auto manufacturers, but the demand for domestic autos is no more than 2.5 times the quantity produced at the bottom of the LRAC curve. What do you expect will happen to the domestic auto industry in the long run?
This is the situation that existed in the United States in the 1970s. Since there is only demand enough for 2.5 firms to reach the bottom of the average cost curve, you would expect one firm to not be around in the long run, and at least one firm will be struggling.

## Review questions

• What is a production technology?
• In choosing a production technology, how will firms react if one input becomes relatively more expensive?
• What is a long-run average cost, or LRAC, curve?

## Critical-thinking questions

• We know that businesses operate in the short run, but do they ever operate in the long run? Discuss.
• How do improvements in technology—like high-efficiency gas turbines or the Pirelli tire plant—affect the LRAC curve of a firm? Can you draw an old curve and a new one on the same axes? How might such an improvement affect other firms in the industry?
• Do you think the taxicab industry in large cities is subject to significant economies of scale? Why or why not?

## Problem

A small company that shovels sidewalks and driveways has 100 homes signed up for its services this winter. It can use various combinations of capital and labor: lots of labor with hand shovels, less labor with snow blowers, and still less labor with a pickup truck that has a snowplow on front.
Method 1: 50 units of labor, 10 units of capital
Method 2: 20 units of labor, 40 units of capital
Method 3: 10 units of labor, 70 units of capital
If hiring labor for the winter costs $100/unit and a unit of capital costs$400, what production method should be chosen? What method should be chosen if the cost of labor rises to \$200/unit?