# 12.3: Diffusion and Technical Change

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The Theory of the Firm is a highly abstracted model of a real-world firm, yet there are fundamental ideas that can be applied to observed firm behavior. This section does exactly that, applying the Shutdown Rule to explain differing rates of diffusion of new technology.

The Shutdown Rule, $$P < AVC$$, says that firms will not produce when price is below average variable cost because profits are maximized (and losses minimized) by shutting down instead of producing at the best of the positive output choices (at $$MR = MC$$).

Diffusion of new technology is the process by which new methods of production are adopted by firms. The speed of diffusion is criticalthe faster firms upgrade and modernize, the richer the society. We will see that some industries have fast and others slow diffusion with the Shutdown Rule playing a key role.

#### Setting the Table

Consider two thoughts that are both wrong:

1. Always upgrade to have the best equipment or to use "best practice" techniques.

2. Never throw working machinery away or abandon a process that can produce output.

The first statement is wrong because firms would always be replacing almost new machinery, tools, and plant to have the very latest equipment. The second statement is the polar opposite of the first: Now you keep using ancient machinery that was long ago superseded by better technology just because it is still functioning.

There has to be a middle ground between these two extremes and a logical way to determine when to replace equipment.

Consider these two words that are accepted as synonymous in common usage, but are different in the language of the specialized literature of diffusion:

1. Outmoded: machinery that is not the best at the time, but is still used.

2. Obsolete: machinery that is scrapped (thrown away) yet still functions.

Your phone is outmoded if it is not the latest, greatest available version. When you replace your phone with a new one, the old one becomes obsolete. At any point in time, a few people have the newest, fanciest model; the rest have versions of outmoded models still in use; and there are many obsolete models that are no longer being used. As time goes by, the newest model becomes outmoded and, eventually, obsolete.

The distinction between outmoded and obsolete sharpens our focus on this question: When does machinery go from being outmoded to obsolete?

Another important idea is labor productivity: the ability of labor to make output. This is measured in two ways, output per hour or labor required to produce one unit of output.

The output per hour version is simply the average product of labor, $$\frac{q}{L}$$. The bigger this ratio, the more productive is labor. You can take the reciprocal and ask, “How much labor is needed to make one unit of output?” This measure, called the unit labor requirement, gets smaller as labor productivity improves.

There are two ways of increasing labor productivity:

1. Better labor: increasing education.

2. Better machinery: technical (or technological) change.

Most people only think of the first way. More educated and skilled labor obviously will be more effective in translating labor input into output. But holding labor quality constant, if workers have better technology, such as computers or power tools, then labor productivity rises.

So, if you want to increase ditch digging productivity, you can improve the worker (think ditch digging classes) or you can improve the technology. A worker with a shovel digs a ditch a lot faster than one without. But the explosion in productivity and output really occurs when you give the worker a backhoe.

But here’s the curious thing, after backhoes are invented and brought online, if you look at the entire industry of ditch digging, you will see many different methods being used. Not everyone will instantly adopt the backhoe.

The question we are interested in boils down to explaining the rate of diffusion: how rapidly do the latest, best machinery and methods spread?

The mere existence of a new machine (e.g., a backhoe) is not enough to spur economy-wide increases in labor productivity. If the machine is not adopted rapidly, it will have little effect on the economy. We want fast diffusion so new methods spread quickly. This will boost productivity and economic growth.

The rate of diffusion is like adding a drop of red dye in a bucket of water. How rapidly will the water turn red? What factors affect the rate of diffusion? If we stir, the rate of diffusion rocketshow can we "stir" the economy to speed up diffusion?

It turns out that the rate of diffusion of technical change in an economy varies across industries and depends on specific characteristics. We are not searching for an unknown constant, but for the factors that explain wide variation in rates of diffusionsometimes backhoes are rapidly adopted and other times not.

The rate of diffusion depends on whether machinery is determined to be outmoded versus obsolete. If machines are scrapped and replaced with the latest technology fairly quickly, then the rate of diffusion of technical change will be fast. If old technology is kept online and in production for a long time, then the rate of diffusion of technical change will be slow.

Before we see how the Shutdown Rule plays a critical role in deciding whether machinery is outmoded or obsolete, we review data used by W. E. G. Salter (1960) to support the claim that the rate of diffusion varies across industries. We also introduce a new graph that captures the idea of a distribution of methods or vintages of machinery.

#### On the Variation of Methods Used Across Industries

Salter presents data on a variety of goods. He focuses on the methods of production used at any point in time. It is quite obvious that there is always a mix of technologies being used. As new plants come online and new machinery is installed, older plants with older machinery remain in operation.

For example, Salter’s Table 5, reproduced as Figure 12.9, shows a mix of technologies used in pig-iron production. Notice that the labor productivity of the best-practice plants (the latest technology) rises from 1911 to 1926. The industry average, however, lags behind because the latest technology is not immediately adopted by every manufacturer. The machine charged and cast method (the right most column) is the best technology, but even by 1926, 30.6% of the firms are not using it. These firms remain in operation with older technology. This slow diffusion hampers industry-wide labor productivity.

Figure 12.10 (Salter’s Table 6) focuses on the production of five-cent cigars. Salter keeps constant the quality and type of cigar, the five-cent variety, to focus on an apples-to-apples comparison of production methods. Because the measure of productivity is the labor required to make 1,000 five-cent cigars, the lower the hours required, the greater the labor productivity. The two-operator machine is the best practice, but three other methods are also used. Once again, the point is that a mix of methods are used and all of them combined determines industry-wide productivity.

Figure 12.11 offers a final example of Salter’s point that an economy’s labor productivity depends on the technology actually being utilized to make output. The Range of all plants column shows substantial variation in output from the best-practice firms to the least productive methods still being used. Notice that lower numbers are higher productivity because, as the title says, we are measuring "labour content per unit of output."

For bricks, with 17 plants in operation, the middle 50% range is from a best 0.93 hours to make 1,000 bricks to 1.75 hours. That is a huge difference and it is just the middle 50%. Take a moment to look at the ranges of the other products in Figure 12.11.

The Ratio of range to mean columns measure the rate of diffusion. If somehow every plant adopted the best-practice method, this ratio would be zero. Thus, houses and men’s shoes are industries with much faster diffusion than the others.

Pig-iron, five-cent cigars, and products in Figure 12.11 are examples of a widespread phenomenon that was of great interest to Salter. The rate of diffusion of new technology is neither constant nor instantaneously fast. Salter wanted to know what diffusion depends on in the hope of manipulating it. After all, if there is a policy or lever we can pull to speed up diffusion, we would improve productivity and increase output.

#### A Graph is Born

Salter used an uncommon graph, an ordered histogram, to show how an industry incorporated various technologies in production.

Figure 12.12 (Salter’s original Fig. 5) uses rectangles to indicate each method or vintage of machinery. We call this a Salter graph.

The greater the base of each rectangle in Figure 12.12, the greater the share of the industry’s output for that particular technology. So, in the middle of the graph, the wider rectangle has a bigger share of the output than the narrower one right next to it. The sum of lengths of the bases have to add up to 100% of the industry output.

The height of each rectangle tells you how much labor is needed to make one unit with that technology. The lower the height (because the y axis shows the labor required to make one unit of output), the greater the labor productivity for that technology.

The Salter graph has to have a stair-step structure because the rectangles are ordered according to when they came online. The oldest technology is to the right and the newest is to the left. The left-most rectangle is the best-practice technology at that time and all of the other rectangles are at different stages of outmodedness.

The Salter graph in Figure 12.12 is actually a single frame of a motion picture. As time goes by, and new techniques are invented and brought online, some of the right most rectangles will “fall over” and be replaced by a new shorter rectangle coming in from the left. Figure 12.13 shows a possibility for the next frame in the movie.

The base of the rectangle of the newest technology in Figure 12.13 equals the sum of the widths of the three rectangles representing obsolete technologies, which fall off the graph because they are no longer used.

The wider the base of the newest technology, the better in terms of fast diffusion of technological change and rapid increases in industry-wide productivity. If a new technology swept through an industry like wildfire, the Salter graph would show it as having a very long base, indicating it was producing a large share of industry output.

Another, less favorable possibility is that the newest technology has a small width. This would mean that few firms have adopted the best-practice method and industry-wide productivity will not improve by much. The industry will remain dominated by outmoded methods.

Consider the two Salter graphs in Figure 12.14 (Salter’s original Fig. 12). They are enhanced by a strip in the middle, the height of which represents the industry average productivity.

We would much prefer the industry on the left in Figure 12.14 because it has a lower industry average unit labor requirement, which means it has higher productivity. This is a result of much more rapid diffusion of newer, higher productivity technology.

The industry average shaded bar is a weighted average of all of the technologies in existence at any point in time. This statistic is the correct way to add up the rectangles with differing widths into a single measure of industry productivity. To understand how to do this, we turn to a concrete example in Excel.

STEP Open the Excel workbook DiffusionTechChange.xls, read the Intro sheet, then go to the IndustryAverage sheet to see how a weighted average is computed and how the Salter graph works.

Cells C9 and C10 show how two technologies contribute to the industry output. Initially, Methods A and B produce 50% of the total output. Because A (the superior, best-practice technology) requires only 1 hour of labor to make a unit of output, whereas B (an outmoded technology) requires 2 hours, the industry average productivity is 1.5 hours per unit of output.

STEP Click on the scroll bar a few times to increase A’s share of total output to 90%. Notice how the Salter graph changes as you manipulate the scroll bar.

The Salter graph now shows A’s share as a much wider rectangle (indicating much faster diffusion) and the red, industry (weighted) average rectangle is much shorter. Although the simple average does not change, the weighted average falls because more of the output is being generated by the more productive A technology. The weighted average computation (implemented in the formula for cell M10) is: $WeightedAverage=\frac{Output_A}{TotalOutput}UnitLReq_A+\frac{Output_B}{TotalOutput}UnitLReq_B$

STEP Click on the scroll bar to decrease A’s share of total output to 10%.

This time, the industry (weighted) average is 1.9 because only 10% of the output is produced with the best-practice technology. This would be an example of slow diffusion.

The contributions of each technology to industry output, weighted by the share of total output, is a good way to show how the rate of diffusion affects industry-wide productivity.

Having seen data that there is substantial variation in the rate of diffusion and that a Salter graph displays this variation, we are ready to explain why we see industries with mixes of technologies. We answer two questions:

1. Why is a machine that works sometimes kept (so it is outmoded) and other times scrapped (so it is obsolete)?

2. What determines the rate of diffusion of technical change?

#### 1. Outmoded versus Obsolete?

We assume that new technologies are being constantly generated in all industries, but some are adopted more quickly. Why is that? Why are some factories and technologies quickly replaced while others remain online? Salter’s work pointed to an easily overlooked element: the cost structure of the firms in an industry.

STEP Proceed to the Output sheet. The opening situation is depicted in Figure 12.15.

The graph shows two firms, one that is labor intensive and the other capital intensive. The capital intensive firm has a larger gap between ATC and AVC because it has higher fixed (capital) costs. The much lower AVC curve will prove to be critical.

Both firms in Figure 12.15 are earning small, but positive economic profits. As time goes by, however, new technologies are introduced and incorporated in newly built factories with shiny, modern equipment. The products from firms with the newest factories with their best-practice methods (the left-most rectangle in a Salter graph) can be made more cheaply so competitive pressure drives the price down.

STEP Click on the scroll bar to lower the price.

Since you know the Shutdown Rule, it is easy to see that the L-intensive firm will shut down first. As soon as you make $$P < AVC$$, the factory is obsolete and taken offline. The factory on the left will survive as an outmoded technology that is still in operation for much longer. You will have to keep driving the price down for much longer to see it shut its doors.

All firms use the same Shutdown Rule, but differing cost structures is what makes some factories stay in production while others close down.

So, to directly answer the question, Why is a machine that works sometimes kept (so it is outmoded) and other times scrapped (so it is obsolete)? Because the Shutdown Rule, $$P < AVC$$, determines the difference between outmoded and obsolete technology. Old plants that are kept online, using outmoded machines, operate in an environment in which profits may be negative, but $$P > AVC$$. These plants will remain in operation as long as revenues cover variable costs. Once $$P < AVC$$, we know the machines will be scrapped and become obsolete as the factory is closed down.

#### 2. What Does the Rate of Diffusion Depend On?

Figure 12.15 shows that the firm’s cost structure is one of the factors which determine the rate of diffusion of technical change. Industries with capital intensive production and low variable costs will have slow rates of diffusion because plants and technologies will remain online until $$P < AVC$$.

Steel is a good example of such an industry. Old factories remain in production alongside modern mini-mills. The Salter graph looks like the right panel in Figure 12.14 and the cost structure is given by the left panel in Figure 12.15.

On the other hand, industries who produce in a way that labor is dominant and fixed costs are low will see rapid rates of diffusion of new methods. Legal services are a good example. Cost curves look like the right panel in Figure 12.15 so when new computers and information systems (such as LexisNexis) are developed, they are rapidly adopted and old ways are discarded. Thus, the Salter graph looks like the left panel in Figure 12.14.

Another factor affecting the rate of diffusion is the speed at which price falls. Competition among firms can be intense or muted. If, for example, the government protects an industry from foreign competition with trade barriers, preventing price from falling, the rate of diffusion of new technology and growth of labor productivity are retarded. This has certainly played a role in the rate of diffusion in the steel industry.

So, what determines the rate of diffusion of technical change? There are three factors:

1. New ideas and inventions from research and development (R&D): This is the creativity of the society. Curiosity and willingness to experiment produce a stream of better methods. The faster the flow, the better.

2. The cost structure of the firm: Capital intensive industry with high fixed and low variable costs retards diffusion of new technology. The new ideas are there, but the old ways stay online.

3. The speed at which price falls: If it is slow, we get slow diffusion. We want to encourage competition so price puts pressure on outmoded methods and drives them to be obsolete.

The first factor is the obvious one that everyone thinks of when explaining why technology affects labor productivity and economic growth. Innovation is the implementation of inventionnew ideas are the raw material which expand the production function.

But Salter identified another crucial factor: Even if new technology exists, it will be mixed with existing technology and the rate at which it is adopted will depend on the Shutdown Rule. Highly capital intensive industries with low AVC will feel the drag of old technology for a long time because the gap between ATC and AVC will be great. Old methods will stay outmoded as long as $$P > AVC$$.

The Shutdown Rule compares average variable cost to price. Both matter. Low AVC will keep old methods around, but so will slow decline in P. Although economists usually defend free trade policies on the basis of comparative advantage, this analysis points to another reason for allowing foreign competition in domestic markets. As price is pushed down, firms are forced to modernize, taking old methods offline and investing in the newest technology. Steel tariffs are an example.

You might be confused about the claim that competition makes price fall as time goes by. It seems like inflation, prices rising, is the usual state of affairs. The explanation lies in the difference between real and nominal price.

In nominal terms, also known as current prices, the price of a light bulb is definitely higher today than 10 years ago and much higher than 100 years ago.

But in this application, the correct price to consider is the real price, in terms of actual input use. In real terms, the price of lighting is incredibly lower today. Figure 12.16, created by Nobel Prize winner William Nordhaus, tells an amazing story. In terms of the number of hours of work needed to buy 1,000 lumen hours, the price of light went from incredibly expensive for thousands of years to a free fall since the 1800s. In terms of input use, as technology improves, costs and, therefore, price of the output fall over time.

Nordhaus argues that "price indexes can capture the small, run-of-the-mill changes in economic activity, but revolutionary jumps in technology are simply ignored by the indexes" (Bresnahan and Gordon, eds., 1997, p. 55). Thus, the real price of lighting, in terms of the labor used, keeps falling and falling as time goes by.

#### It Is Diffusion, not Discovery, that Really Matters

Wilfred Edward Graham Salter was an Australian economist born in 1929. His promising career was tragically cut short when he died in 1963 after battling heart disease. His dissertation, finished in 1960, was published by Cambridge University Press as Productivity and Technical Change and was met with wide acclaim.

Salter was amazed by the ability of markets to incorporate new technology to increase output per person. He realized that scientific knowledge, technology "on the shelf," is not the only or even the most important driver of rapid growth. The new technology has to be implemented, actually used in production, and the faster it is adopted, the faster the economy grows.

Salter’s primary contribution was in showing that the rate of diffusion varies tremendously and depends on the cost structures of firms. Industries with high fixed and low variable costs have large $$ATC - AVC$$ gaps that imply long time spans for outmoded technology.

We want nimble, adaptive firms and startups that challenge established titans. Replacing old with new machinery is necessary for rising productivity. Economies with ossified, rigid institutions are stagnant. There was a silver lining after Germany and Japan’s factories were destroyed during World War II. The latest, greatest technology could be used to make all of an industry’s output and productivity increased rapidly.

## Exercises

1. Sometimes a best practice investment is quickly leapfrogged by newer technology. Google "fiber optic overinvestment" to see an example. Briefly describe what happened and cite at least one web source.

2. Automobile emissions requirements are stricter in Japan than in the United States (where many areas have no vehicle inspection at all). In both countries, newer cars pass inspection (if required) easily, but older cars are more likely to fail inspection and be removed from the operating car fleet. Draw hypothetical Salter graphs, with emissions on the y axis, for the car fleets of Japan and the United States that reflect the stricter emissions standards in Japan.

3. What happens to a late model year Toyota or Honda that has failed an emissions inspection in Japan and, therefore, cannot be used there? Google "Japan used engines" to find out. What effect does this have on the United States Salter graph that you drew above?

4. The National Highway and Traffic Safety Administration maintains a data base of car characteristics by model year. For miles per gallon (MPG) performance, they show the following:

These data cannot be used to show a Salter graph (with MPG on the y axis) of the US car fleet. Why not? What additional information is needed?

#### References

The epigraph is from page 183 of Jared Diamond, Guns, Germs, and Steel: The Fates of Human Societies (W. W. Norton & Company, originally published in 1997). Diamond argues that geography determines historical development. It is not the people, but fortunate geographical circumstances that guaranteed that western Eurasian societies would become disproportionately powerful. It is geography that enabled the rapid diffusion of technology and knowledge. Diamond, like Salter, is concerned with a point that is easily misseddiffusion is more important than discovery. Visit www.pbs.org/gunsgermssteel for the documentary.

The primary source for the application in this chapter is W. E. G. Salter, Productivity and Technical Change (Cambridge University Press; 1st edition, 1960; 2nd edition, 1966; 1st paperback edition, 1969).

For more on technological change and the spread of new ideas, see Timothy F. Bresnahan and Robert J. Gordon, The Economics of New Goods (The University of Chicago Press, 1997) and David Warsh, Knowledge and the Wealth of Nations: A Story of Economic Discovery (W. W. Norton & Company, 2006).

Richard Preston’s American Steel (Simon and Schuster, 1991) tells the story of a mini-mill in rural Indiana that uses German cold-casting technology. It is an entertaining tale of entrepreneurshipa billion dollar gambleand an introduction to the exciting world of business management.

This page titled 12.3: Diffusion and Technical Change is shared under a CC BY-SA license and was authored, remixed, and/or curated by Humberto Barreto.