Increasing Returns to Scale in “Components” and in “Systems:”

An Essay

by

Jeffrey L. Funk

Associate Professor

National University of Singapore

7 Engineering Drive 1

Block E3A, 4th Floor

Singapore 129793

etmfjl@nus.edu.sg

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Increasing Returns to Scale in “Components” and in “Systems:”

An Essay

Abstract

This paper provides one of the first full-length overviews of “increasing returns to scale”

in technologies. Using the concept of “nested hierarchy of subsystems,” it shows how

increasing returns to scale in a higher level “system” depends on the performance and cost of

lower level “components” (along with advances in science) and increasing returns to scale in

a lower level “component” can drive large improvements in the performance and cost of a

higher level “system” even when increasing returns to scale does not exist in the system itself.

Following a presentation of examples from the existing literature, it applies the concept of

increasing returns to scale to wind and solar energy.

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1. Introduction

An increasing demand for technologies that can help the world deal with energy,

environmental, health and other problems increases the need for a better understanding of

where long-term improvements in performance and cost come from. The conventional

wisdom is that these improvements come from advances in science (Balconia et al,

forthcoming), a change from product to process innovation (Utterback, 1994), and increases

in production volumes (Argote and Epple, 1990). The fact that there is a long time lag

between advances in science and the commercialization of them (Kline and Rosenberg, 1986;

Klevorick et al, 1995; Mansfield, 1991) and the fact that some technologies have experienced

much greater improvements or what some call “exponential” improvements in cost and

performance (Kurzweil, 2005: Kressel and Lento, 2007) suggests that these three factors are

by themselves inadequate explanations.

Another literature suggests that increasing returns to scale (IRtS) (Nelson and Winter,

1982; Rosenberg, 1982; Rosenberg, 1994; Freeman and Louca, 2001; Lipsey et al, 2005;

Winter, 2008) provides a better explanation for long-term improvements, including

exponential improvements (Kurzweil, 2005), in the cost and performance of technologies

than do the above-mentioned reasons. While economy of scale refers to a situation in which

increases in production volume at a single point in time leads to lower cost, IRtS refers to a

situation in which large increases in an input over long periods of time lead to larger

increases in an output than in the input and it can apply to both larger (e.g., production,

energy systems, transportation equipment) and smaller (e.g., semiconductors) scale. For

example, IRtS in some production equipment has led to dramatic increases in the scale of this

equipment and thus the emergence of large economies of scale in this equipment.

A key aspect of this IRtS is the notion of so-called geometrical scaling (Sahal, 2005) in

which the “scale effects are permanently embedded in the geometry and the physical nature

of the world in which we live” (Lipsey et al, 2005). In technologies that display geometrical

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scaling, cost is roughly proportional to one dimension (e.g., length squared or area) less than

is the output (e.g., length cubed or volume) thus leading to IRtS. For example, the output

from a steam or jet engine roughly rises with its volume while the cost rises with its surface

area (Lipsey et al, 2005). Similarly, the carrying capacity of trains, ships, automobiles, and

aircraft roughly rises with the volume (i.e., cube of a dimension) while the cost of them rises

with the surface area (i.e., square of a dimension) (Sahal, 1985; Winter, 2008).

In spite of the many anecdotal examples of IRtS, however, our theoretical and practical

understanding is severely limited (Winter, 2008). Most papers merely provide examples of

IRtS and do not attempt to organize them in any way. Without such an organization, how can

we understand what technologies have or might benefit the most from IRtS and why?

Similarly, how do limits to scale emerge and how can we recognize and overcome them?

These questions are relevant to firms, universities, governments, and other organizations

when they search for and evaluate the potential of new systems. In fact, understanding these

questions is an essential part of any solution to the world’s energy and environmental

problems.

This paper focuses on these questions and makes three contributions. First, it shows how

IRtS of systems depends on improvements in “components” and how a lack of sufficient

improvements in components may prevent further increases in scale. In doing so it uses the

notion of a nested hierarchy of subsystems to examine the relationship between components

and systems and thus more finely examine the aspects of a “technology” (Lipsey et al, 2005)

that enable one to realize and benefit from IRtS. Second, building on the first point, it shows

how the existence of IRtS in components can contribute to IRtS in systems. Third, it argues

that IRtS in components can drive long-term improvements in system performance and cost

even when the system itself does not exhibit IRtS.

This paper is organized in the following way. First, it places the issue of IRtS within the

literature on technological change and in particular within Dosi’s (1982) notion of technology

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paradigms. Second, it discusses the relationship between IRtS in “systems” and in

“components” and it organizes these historical examples of IRtS in terms of: 1) production;

2) energy; 3) transportation; and 4) electronics. Third, it applies the concept of IRtS to the

future of wind turbines and solar cells. Fourth, it uses these examples to discuss ideas for

future research.

2. Research Literature

IRtS refers to a situation where the output of a technology increases faster than does an

input(s) such as labor, capital, materials, and energy. It is different from economies of scale

(noted above), increasing returns to scale in demand (i.e., network effects), and learning.

Increasing returns to scale in demand refers to a situation when the value of a technology

depends on the number of users or complementary products (Katz and Shapiro, 1985; Arthur,

1994; Katz and Shapiro, 1994). The literature on learning focuses on the organizational

processes that are involved with reducing costs or improving performance (Arrow, 1962;

Huber, 1991; March, 1991) while IRtS focuses on the characteristics of a technology that

determine the potential for learning (Gold, 1981). Thus, while the literature on learning

suggests that solving energy and environmental problems is primarily an organizational issue,

the literature on IRtS suggests that IRtS can tell us where an organization’s learning efforts

should be focused.

IRtS is an important aspect in Dosi’s (1982) concept of a “technology paradigm.” Such a

paradigm is associated with a specific technological discontinuity (Abernathy and Utterback,

1978; Tushman and Anderson, 1986; Anderson and Tushman, 1990; Utterback, 1994) where

such a discontinuity is typically defined and classified by the extent to which a new product,

when compared to previous ones, involves changes in the concepts or architectures that form

the basis of a product or key component (Henderson and Clark, 1990; Murmann and Frenken,

2006). New concepts, and to a lesser extent new architectures, are the result of advances in

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science and they define new technology paradigms (Dosi, 1982). For example, electric

vehicles are based on a different concept for propulsion than are gasoline powered ones just

as solar cells (and wind turbines) and light-emitting diodes (LEDs) are based on different

concepts for creating electricity and light respectively than are existing technologies. Each of

these new concepts was based on advances in science (Balconia et al, forthcoming) and each

of them defines a new technology paradigm.

A technology paradigm determines the tradeoffs between various dimensions of

technological performance and cost and between various design choices, and the potential

directions of advance within these tradeoffs (Dosi, 1982). Thus, the progress of a technology

is both facilitated and entrapped by the paradigm(s) that guide it. For example, many engines

and methods of transportation (e.g., aircraft) exhibit a tradeoff between speed, weight, and

end energy usage where as noted below; performance rises faster than do costs as the size is

increased. However, there are limits to this IRtS since weight increases as the cube of a

dimension while strength only increases as the square of the dimension1. Although increasing

the strength-to weight ratio of materials can partially solve this problem and enable further

increases in the size of an aircraft, the extent of these increases in scale is limited by the

technology paradigm for the material. Similarly, the technology paradigm for semiconductors

involves a tradeoff between power consumption and speed, as defined by laws of electricity

where shrinking (i.e., smaller scale) the so-called “gate length” of a transistor has enabled

improvements in some combination of power consumption, speed, and other dimensions of

performance (Dosi, 1982; Winter, 2008). On the other hand, shrinking this gate length beyond

a certain point causes quantum mechanical forces to become stronger than electrical ones and

thus requires the creation of a new paradigm (Kurzweil, 2005).

These technology paradigms, including the extent of IRtS in them and the concepts and

1 Some argue that this limits the IRtS of buildings and bridges (Lipsey et al, 2005).

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advances in science that they are based on, can be defined for any level in a so-called “nested

hierarchy of subsystems” (Tushman and Rosenkopf, 1992; Tushman and Murmann, 1998;

Malerba, et al, 1999). Systems are composed of sub-systems, sub-systems are composed of

components, and components may be composed of various inputs including equipment and

raw materials (Simon, 1962; Alexander, 1964; Tushman and Murmann, 1998). For example, a

system for producing ICs is composed of components such as raw materials and more

importantly semiconductor manufacturing equipment. This paper only uses the term

“component” to simplify the description as it addresses the relationship between IRtS in

“components” and IRtS in “systems.”

IRtS can exist at any level in a nested hierarchy of subsystems where there is an

interaction between different levels of such a hierarchy. On one hand, IRtS in a lower level

“component” can drive large improvements in the performance and cost of a higher level

“system” even when there is not IRtS in the system itself. On the other hand, IRtS in a higher

level system depends on the performance and cost of lower-level components.

The first instance can occur when a component performs the key function of a system and

is thus the “core component” (Murmann and Frenken, 2006) in the system. For example,

engines perform the key function in automobiles, trains, and aircraft and integrated circuits

(ICs) perform the key function in electronic systems (including computers). In such cases

long-term improvements in the performance or costs of a system (Kurzweil, 2005; Kressel

and Lento, 2007) may depend more on long-term improvements in the performance and costs

of components that exhibit IRtS than on “novel” combinations of components (Rosenberg,

1963, 1969; Basalla 1988) or technologies (Iansiti, 1995; Fleming, 2001) in a system.

The second instance extends Lipsey et al’s (2005) notion that the “ability to exploit [IRtS]

is dependent on the existing state of technology.” Using the concept of a nested hierarchy of

subsystems allows one to decompose “the existing state of [a] technology” into its relevant

components where improvements in specific components (including advances in science)

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may be necessary before IRtS in a system can be realized. Similarly, insufficient

improvements in a component may cause diminishing returns at the system level to emerge

and a characterization of these diminishing returns to scale might look similar to the way that

Foster (1986) characterizes diminishing returns to technologies in his S-curves. The

difference between diminishing returns to scale and Foster’s diminishing returns to a

technology is that scale is on the x-axis for the former while the amount of R&D expenditures

(or time) is on the x-axis for the latter. Thus the former focuses on the extent of the benefits

from increasing the scale of a technology (either larger or smaller) and the latter focuses on

the extent of the benefits from increasing R&D expenditures. Both approaches help us

understand the relative benefits from continuing to invest in an existing or new technological

discontinuity and its associated technology paradigm.

3. Research Methodology

The author first searched for examples of IRtS in some of the few papers that mention it

(Rosenberg, 1979; Dosi, 1982; Sahal, 1985; Freeman and Louca, 2001; Winter, 2008)2.

Second, whenever a relevant discussion of IRtS was found, the original reference was

searched for using Google and Google Books. Third, the specific technologies that were

found in these examples (such as electricity, energy, aircraft, furnaces, and engines) were also

“Googled” along with terms such as “scale,” “increasing,” and “large.” Fourth, for each

instance of IRtS, the author searched for both the improvements in components and the

advances in science that were needed to realize IRtS, which are summarized in Table 1. The

necessary advances in science were also investigated by reading many histories of technology

of which several were particularly useful (Crump, 2001; Cardwell, 2001; McCellan and Dorn,

2006). Nevertheless, it is likely that this paper’s interpretation of IRtS applies to a much

2 It also skips some of the more well-know examples such as agriculture (Diamond, 1999) that are ordinarily not considered in the

management literature.

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broader number of industries than the ones noted in this paper and there is probably a longer

list of components and advances in science than are listed in Table 1. As discussed at the end

of the paper, more systematic analysis, including empirical analysis, is needed and hopefully

this paper will encourage other scholars to pursue this area of research.

4. IRtS in Production

IRtS in production exists when the output from production equipment increases faster

than does the cost of the equipment, as the size of the equipment is increased. The potential

benefits from IRtS in production were first noted by Adam Smith in his Wealth of Nations

where he described how a finer division of labor directly led to reductions in labor time and

indirectly enabled further reductions in labor time through the replacement of human labor

with machinery. Realizing the benefits from IRtS in this production equipment required the

concept of interchangeable parts, advances in the science of machining (Cardwell, 2001;

Crump, 2001; McCllellan and Dorn, 2006), new forms of management (Chandler, 1977,

1994) and two key components in any modern manufacturing system: special purpose

machine tools and electric motors.

Special purpose machine tools such as lathes and boring machines and ones that could

produce parts with a high degree of tolerances did not become available until the latter half of

the 19th century. This is partly since finer tolerances from these machine tools required that

the machine tools themselves be made from machine tools capable of producing parts with

fine tolerances 3 . Such machine tools became more available for some discrete part

manufacturing operations than others (Rosenberg, 1963, 1969) and thus for certain types of

products such as automobiles and bicycles (Hounshell, 1982) than for other products such as

3 The notion that improvements in manufacturing equipment depend on the use of this equipment to make parts for this equipment is also

evident in computers; improvements in computers are needed in order in for semiconductor manufacturing equipment to produce the ICs for

the computers.

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shoes and apparel. Furthermore, it was easier to increase the size of some types of machine

tools such as lathes and boring machines than for others. Larger machines could cut and bore

metal faster than could smaller machines and they could do this on larger pieces of metal.

New materials for machine tool bits also contributed to increases in the speed of these

machine tools (Cardwell, 2001; Crump, 2001; McCllellan and Dorn, 2006).

Second, the development of electrical generating stations at the end of the 19th century

enabled machine tools to be driven by electric motors. The use of electric motors enabled the

implementation of new forms of factory organization in which the placement of machines in

a factory did not need to be dictated by the system of shafts and belts that drove the machine

tools. It is generally recognized that these new forms of factory organization were important

contributors towards improvements in factory performance (David, 1990) where the percent

of U.S. factories with electric drive had exceeded 90% by 1940 (Freeman and Louca, 2001).

Although electric motors did not exhibit IRtS (Lipsey et al, 2005), the production of them and

more importantly the generation of electricity did exhibit IRtS (see below) where this IRtS

caused the price of electricity to drop by about 90% in inflation-adjust terms in the U.S.

between the late 19th century and 1973 (Hirsh, 1989).

Many scholars argue that limits to scale in discrete parts production had been reached by

the mid-20th century (e.g., in Ford’s River Rouge Plant) for several reasons. First, machines

could only be made so big and so fast, particularly when one considers the limited demand

for standardized products such as Ford’s Model T. Second, big and fast machines required

longer setup times particularly as the demand for variety increased. These and other problems

led to the emergence of a new technology paradigm for manufacturing that focused on just-in

time manufacturing, programmable machine tools, and computer-controlled factories and that

enabled economies of “scope.” Instead of a factory making one kind of product and

benefiting from economies of scale for this single product, factories made a family of

products or a family of parts that could be economically made from the same type of

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equipment and processes (Piore and Sabel, 1984; Freeman and Louca, 2001).

Greater IRtS probably exist in continuous flow than in discrete parts manufacturing.

Organic and inorganic chemicals, plastics, paints, and pharmaceuticals are made in factories

that largely consist of pipes and reaction vessels and the high degree of automation in these

kinds of factories suggest that there are more benefits from IRtS in them than in discrete parts

factories. This caused many scholars to note that the costs of pipes, i.e., surface area of

cylinders, vary as a function of radius whereas the output from a pipe, i.e., volume of flow,

varies as function of radius squared. Empirical analysis found that the costs of these pipes and

reaction vessels only rose about 2/3 for each doubling of output (Haldi and Whitcomb, 1967;

Levin, 1977; Freeman and Louca, 2001; Winter, 2008)4. For example, the cost of catalytic

cracking dropped by more than 50% for materials, 80% for capital and energy, and 98% for

labor between the first installation in 1939 and the year 1960 (Enos, 1962).

Like the IRtS in discrete parts manufacturing, the emergence of IRtS in continuous flow

manufacturing depended on advances in science, improvements in processing equipment, and

on the availability of the equivalent of electric motors for continuous flow manufacturing:

equipment for implementing such techniques as electrometallurgy, electrochemistry, and

electrolysis (Rosenberg, 1979; Morris et al, 1991; Freeman and Louca, 2001). Advances in

our understanding of electricity, the basic chemical elements, and the reactions between them

(Cardwell, 2001; Crump, 2001; McCllellan and Dorn, 2006) were needed before scaling of

these factories could even be considered. Process-related equipment for mixing, separating,

heating, cooling, filtering, settling, extracting, distilling, and drying of gases, liquids and

solids were needed to increase the scale of chemical plants and they became available at the

end of the 19th century partly because machine tools made their production possible.

Advances in electricity also made it possible to use an electric current to drive a variety of

4 Rosenberg (1994, p. 198) estimates the increases in capital costs with each doubling to be 60%.

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chemical reactions involved with the techniques of electrometallurgy, electrochemistry, and

electrolysis (Cardwell, 2001; Crump, 2001; McCllellan and Dorn, 2006). Large-scale

equipment for these techniques also emerged in the late 19th century for some of the same

reasons that other process-related equipment emerged and supported IRtS in continuous flow

manufacturing (Morris et al, 1991; Freeman and Louca, 2001).

In summary, the paper’s characterization of IRtS in production equipment has a different

focus from the conventional wisdom. In the conventional wisdom, innovations in products

give way to innovations in processes as volumes increase, a so-called “dominant design”

emerges (Utterback, 1994), and firms reorganize their factories and introduce flow lines and

special purpose manufacturing equipment (Argote and Epple, 1990; Utterback, 1994;

Freeman and Louca, 2001). Some students of technology change also interpret Christensen’s

(1997) model of disruptive change in this way: the expansion of production that occurs once

a niche is found enables costs to drop and the low-end product to displace the mainstream

products.

However, this paper argues that combining the concept of a nested hierarchy of

subsystems with the notion of IRtS enables us to look much more closely at the sources of

cost reductions (and performance increases) than can be done with the conventional wisdom

about cost reductions. Not only has empirical analyses of Utterback’s model shown that the

number of product (or even process) innovations in specific industries (Klepper and Simon,

1997) do not conform to Utterback’s model, research on IRtS (as noted above) suggests that

the cost reductions from increases in the scale of equipment vary quite differently among

different products and technologies because different types of production equipment benefit

from scaling more than do other equipment5. Third, subsequent sections argue that the

benefits of IRtS often come from the operation (and not just production) of technological

5 It is probably no accident that many of the examples of disruptive technologies (Christensen, 1997) involve components such as ICs that

exhibit IRtS.

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systems and from the existence of IRtS in different levels of these “nested hierarchies of

subsystems.”

5. IRtS in Energy Systems

Many examples of IRtS have been found in energy production and usage including

furnaces, smelters, engines, and electricity production. Furnaces are used in many

manufacturing processes for chemicals, metals, and ceramics and IRtS exists in their

construction and operation. Like the above examples, the cost of constructing a furnace is

largely a function of area while the output is a function of volume. For example, the cost of

welding together a heat furnace is proportional to the length of seams while the capacity is a

function of the container’s volume. Similarly, the heat loss from blast furnaces and other

equipment is proportional to the area of its surface while the amount of metal that can be

smelted or the amount of power a steam engine generates is proportional to the cube of the

surface sides (Lipsey et al, 2005).

Also like the above examples, advances in science in the form of thermodynamics

(Cardwell, 2001; Crump, 2001) and improvements in components enabled this realization of

IRtS in furnaces. For example, the size of a furnace or smelter is limited by the need to

deliver a smooth flow of air to all of the molten metal where hand- and animal-driven bellows

could only deliver a limited flow of air. Water-driven bellows and steam-driven ones allowed

air to be injected with more force so that larger furnaces could be built (Lipsey et al, 2005)

and these larger furnaces caused dramatic reductions in the cost of metals. For example, the

cost of crude of steel dropped 80-90% between the early 1860s and the mid-1890s (Landes,

1969). On the other hand, limits to the size of furnaces have emerged as improvements in air

flow, stronger materials, and other components have not kept pace with what is needed to

further increase their scale (Lipsey et al, 2005).

Steam, jet, and internal combustion engines have experienced IRtS and advances in the

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science of thermodynamics and combustion (Cardwell, 2001; Crump, 2001; McCllellan and

Dorn, 2006) and improvements in components have made these increases in scale possible

(von Tunzelman, 1978). Engines exhibit IRtS for the reasons cited above plus the fact that

larger engines often have higher temperatures and higher temperatures increase the efficiency

of heat engines. Stronger materials and better processing methods enabled the development

of these larger engines, which have been implemented to the greatest extent in the form of

steam turbines and jet engines (Lipsey et al, 2005). The IRtS for steam turbines is one of the

largest reasons for the large drop in the price of electricity cited above. Similar results have

emerged for jet engines as their scale was increased in response to the increases in scale of

aircraft (Sahal, 1985), which is discussed more below. But over time diminishing returns to

scale have emerged for steam turbines (Hirsh and Serchuk, 1996) and may emerge for jet

engines in the near future particularly if improvements in materials slow.

Although IRtS also exist in internal combustion engines, they are much less important for

them than for other types of engines. First, one reason that internal combustion engines

became the dominant form of propulsion in automobiles is that they can be made much

smaller than steam engines due to their use of cylinders and gasoline rather than boilers and

coal (Crump, 2001). Second, although there is demand for large buses and ships, the demand

for big and fast automobiles is not as large as that for small and fuel efficient automobiles.

Unfortunately, there are few IRtS for small automobile engines (unlike small ICs). Instead, it

is advances in science and improvements in components such as lighter materials and better

ICs (for engine control) that have enabled some improvements in the fuel efficiency of

engines.

6. IRtS in Transportation Equipment

IRtS exists in transportation equipment for many of the same reasons that it exists in

engines, furnaces, and continuous flow manufacturing plants. The carrying capacity of trains,

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ships (including tankers) (Lipsey et al, 2005), buses, and aircraft (Miller and Sawyers, 1968;

O’Conner, 2001) rises with the volume (i.e., cube of a dimension) while the cost of them rises

with the surface area (i.e., square of a dimension) (Sahal, 1985; Winter, 2008). Furthermore,

the speed that they can travel also increases as a function of size, partly because the engines

display IRtS. The combination of lower costs and faster speeds is one reason why both global

trade and global travel have grown faster than have overall economic output since the end of

the Second World War.

Like the above examples, advances in thermodynamics, combustion, and fluid flow

(Cardwell, 2001; Crump, 2001; McCllellan and Dorn, 2006) and improvements in materials,

i.e., components, have supported IRtS in transportation. Improvements in steel and steam

engines in the 19th century were needed to make longer trains and larger ships and a change

to electric trains required the large-scale implementation of electricity. Larger buses required

improved steel, better internal combustion engines, and improvements in other materials such

as aluminum and plastics. Larger aircraft has required improvements in aluminum, jet

engines, and more recently composites; the weight of aircraft has dropped significantly over

the last 20 years as the strength to weight ratio of materials has been increased several times

(Freeman and Louca, 2001). On the other hand, limits to this IRtS appeared many years ago

in trains and buses, they are appearing in ships, and they are probably right around the corner

for aircraft.

7. Special Case of Increasing Returns to Smaller Scale for Electronic Components

The IRtS that exist in many electronic components might be considered a special case of

IRtS for several reasons. First, improvements in the performance of ICs, magnetic and optical

storage, semiconductor lasers and sensors, and similar components are sometimes called

“exponential improvements” (Kurzweil, 2005) since the rate of these improvements has been

in multiple “orders of magnitude” (See Table 2) and thus is much higher than anything seen

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in the history of technology. Second, they have had a large impact on the performance of

electronic systems such as computers and the Internet (See Tables 3).

Third, the IRtS of ICs and magnetic and optical storage are primarily from

miniaturization. While the previous examples in this paper are for increasing returns to larger

scale, exponential improvements in the cost and performance of electronic components are

primarily from increasing returns to smaller scale, which was first noted by Nobel Laureate

Richard Feynman (1959) in a speech entitled “There's Plenty of Room at the Bottom: An

Invitation to Enter a New Field of Physics.” He could not have been more insightful about the

future. However, the issues that Feynman addressed, and the increasing returns to smaller

scale that have emerged in many electronic components also has implications for increasing

returns to larger scale in for example liquid crystal displays (LCDs) and solar cells. This

section summarizes the key aspects of miniaturization in electronic components and their

impact on electronic systems before addressing LCDs, solar cells, and also wind turbines.

7.1 Miniaturization and Increasing Returns to Smaller Scale

As noted in the summary of the research literature, the technology paradigm of ICs has

meant that their performance can benefit from placing more of them on a single chip. Smaller

features enable more information to be stored on ICs and also on magnetic disks, drums, and

tape and optical disks. However, it was advances in science and the existence of and

improvements to the relevant equipment that has made miniaturization possible. Advances in

science were needed in the solid state physics of semiconductor transistors, insulators,

conducting materials (Tilton, 1971; Braun and MacDonald, 1982; Riordan and Hoddeson,

1997). Equipment for making and etching patterns and depositing, diffusing, and implanting

materials was borrowed from a diverse set of industries including the printing, aerospace, and

nuclear energy industries in the 1950s before the semiconductor industry began driving

improvements in this equipment (Moore, 1963). Improvements to this equipment reduced

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defect densities (IC Knowledge, 2005) and feature sizes where the reduction in defect

densities has enabled a 30-fold increase in die size over the last 25 years (ICEC) and both

larger die sizes and reduced feature sizes have increased the number of transistors that can be

placed on a single IC chip, which is often called Moore’s Law (Flamm, 2004).

Part of Moore’s Law is driven by the IRtS of semiconductor manufacturing equipment

itself. First, just like the two-thirds scaling law for many chemical processes and furnaces

(discussed above), output probably rises faster than do equipment costs as equipment is made

larger. The reason is that the processing time (inverse of output) falls as the volume of gases,

liquids, and reaction chambers gets larger while the costs rise as a function of the equipment’s

relevant surface area. Second, the ability to process multiple ICs on a single wafer, whose

size has been increased many times over the last 50 years, supports the first reason. Third, the

techniques for miniaturizing patterns on wafers have required firms to also reduce the

thickness of materials that are deposited (and later patterned) on these wafers. This reduces

the cost of materials and the equipment’s processing time. The result is that the costs per

transistor, capital costs per transistor, and even to some extent costs per area of a silicon

wafer (See Table 4) have fallen over the last 50 years even as the cost of fabrication facilities

has increased (ICKnowledge, 2009)6.

On the other hand, the rising cost of fabrication facilities cannot go on forever7 and many

observers (IRTS, 2007) argue that diminishing returns to scale are emerging in ICs and thus

there is a need for a new technology paradigm for them. For example, if one were to plot

increases in the number of transistors per chip versus R&D effort as done by Foster (1986)

and not versus time as is almost always done (IRTS, various years), one would see the

diminishing returns of Foster’s S-curve. Not only has the rate of improvement in the number

of transistors per chip slowed in the last ten years, the R&D effort has certainly increased,

6 It is likely that similar arguments can be made for ultra-filtration equipment that is used in desalination plants (Winter, 2008).

7 The newest fabrication facilities cost more than $3Billion and it is estimated that only six producers can afford these facilities (FT, 2009).

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where the rising cost of equipment is just one example. The need for a new technology

paradigm can be seen in firms searching for new concepts that form the basis for

photolithographic equipment (Henderson, 1995), for interconnect (Lim, forthcoming), and for

“information processing and storage devices” themselves (Kurzweil, 2005).

Similar stories can be told for optical and magnetic storage. In the case of optical storage

(and also fiber optics), semiconductor lasers and sensors are the key components in them and

like ICs, they benefit from increasing returns to smaller scale and rely heavily on

manufacturing equipment from the semiconductor industry. Although magnetic storage is

based on a different concept than are semiconductor ICs, they also benefits from increasing

returns to smaller scale and from equipment that has been borrowed the semiconductor

industry (e.g., sputtering equipment). Furthermore, like ICs, improvements in them have had

a dramatic impact on the performance of systems (See Table 2) and the emergence of

discontinuities in them (See Table 3) and diminishing returns to scale will eventually emerge

in them.

7.2 Impact on Electronic Systems

IRtS in electronic components such as ICs and magnetic and optical storage have had a

dramatic impact on the performance of electronic systems (See Table 2) and probably on the

emergence of discontinuities in them (Kurzweil, 2005; Kressel and Lento, 2007; Malerba et

al, 1999) where these electronic systems benefit from IRtS much less than do electronic

components (Smith, 1988; . In fact, many electronic systems exhibit decreasing returns to

scale with respect to ICs since the number of ICs (even more so transistors) used in electronic

systems (because of their falling prices) has increased much faster than has the performance

of electronic systems. For example, the change from analog to digital-based products required

several order of magnitude increases in the number of transistors in microprocessor and

memory ICs in order to handle the increased data processing requirements of digital products

19

(Kressel and Lento, 2007). Similar things have occurred in the changes from so-called first

generation to second, third, and fourth generation mobile phones (Subramanian, 1999), from

circuit- to packet-based telecommunication systems (MacKie-Mason and Varian, 1994), and

in computers. It was once thought that computers displayed some IRtS. For example, Herb

Grosch concluded in 1965 that the cost of computing power only increased as the square root

of processing power and thus cost per instruction per second declined as computers were

made bigger. However, more recent analyses (Ein-dor, 1985; Smith, 1988; Strassman, 1997)

and the replacement of large (e.g., mainframe) with small (personal) computers suggests that

increasing returns only exist over a very limited range of scale.

The best example of decreasing returns to scale in computers and other electronic systems

can be found in software. The cost of both developing software and implementing this

software in corporate settings increases faster than does increases in the size of the software.

Furthermore, the much touted “economies of scale” in software comes from the ability to

cheaply and quickly replicate software and this ability is the result of the falling cost of

memory and microprocessor ICs, which is due to the IRtS in electronic components, and not

from the software itself. The decreasing returns to scale associated with the high cost of

implementing conventional software is one reason why many expect software-as a service

(SaaS) and utility computing to replace conventional software and computing. SaaS and

utility computing dramatically reduce implementation costs and and improvements in the

speed of the Internet, which are primarily from the IRtS of electronic components, are

reducing the disadvantages of SaaS and utility computing (Carr, 2008).

7.3 Miniaturization and Increasing Returns to Larger Scale

Improvements in semiconductor manufacturing equipment, which enabled increasing

returns to smaller scale for ICs and other semiconductors, have also played in role in the

emergence of increasing returns to larger scale in LCDs and solar cells. Since so-called

20

active-matrix LCDs use transistors to control the output of individual pixels in an LCD, there

are similarities between the technology paradigms for LCDs and semiconductors and many of

the same processing techniques and equipment can be used, albeit some of the materials are

different. The largest difference between their technology paradigms is that reductions in

“feature size” are far less important in LCDs than in semiconductors and increases in “panel

size” are far more important in LCDs than in semiconductors. For LCDs, it is the deposition

of thin-film materials on a scale of multi-meter substrates whereas for semiconductors it is

the forming of sub-micron patterns on a 0.30 meter diameter wafer that is important and that

drives large reductions in cost.

Nevertheless, the reduction in the thickness of materials that has accompanied

miniaturization in the semiconductor industry and the application of this semiconductor

manufacturing equipment to LCDs has led to dramatic reductions in the cost of LCD panels

(Gay, 2008). As shown in Table 4, the recent reductions in cost per area of semiconductors

and of LCDs (as are solar cells) are of a similar magnitude where the greater reductions in

cost per area for LCDs than for semiconductors is expected given that suppliers of LCDs

place more emphasis on cost per area than do suppliers of semiconductors (who emphasize

cost per transistor). One result of the similarities in the processes and the IRtS in them for

semiconductors and LCDs (and for solar cells) is that leading providers of semiconductor and

LCD (and solar) manufacturing equipment are the same firms where Applied Materials is the

leader in all three areas.

8. IRtS for Clean Energy

It is widely recognized that the world needs to replace fossil fuels with cleaner energy

sources such as wind, solar, and perhaps even nuclear power. The technology paradigm for

fossil fuels involves the release of carbon dioxide into the atmosphere and the increasing

concentration of carbon dioxide in the atmosphere is probably the main cause of global

21

warming. Finding new energy sources that involve a new technology paradigm is a major

challenge for the world and given the currently higher prices of many forms of clean energy

such as wind and solar, the technology paradigm for these forms of clean electricity must

involve IRtS in order for their costs to experience large reductions in the near future and thus

eventually fall below those of fossil fuel-based electricity.

Theoretical and empirical analyses suggest that wind energy does exhibit some benefits

from IRtS. The output of a wind turbine is a function of diameter squared and wind speed

cubed, while the cost of making turbine blades probably increases at a rate less than diameter

squared, particularly since materials (various forms of composites) with higher strength to

weight ratios are being borrowed from other industries such as initially pleasure boats (i.e.,

yachts) and now aircraft. A higher strength to weight ratio also enables the use of large wind

turbines in areas with strong wind speeds. Empirical analyses have found that the cost per

kWh of producing electricity from wind turbines has dropped about 50% in the last 25 years

while the blade diameter has been increased by more than 10 times in the last 20 years

(Zervos, 2008). As an aside, there have been no major changes in the design of “the

three-blade, vertical axis, upwind mounted design” during this time frame and thus advances

in wind turbine-science have probably played a much smaller role in these cost reductions

(Nemet, 2009) than have increases in blade diameter. If there are still benefits from further

increases in blade diameter, we can expect further reductions in the cost of wind energy and

wind energy probably deserves further attention. Furthermore, improvements in materials,

either through the modification of materials being used in other industries such as the

airframe one, or the development of new ones from advances in science may contribute more

towards reductions in the cost of wind energy than research on wind turbine design itself.

For solar cells, although the costs of electricity generated from them is currently higher

than from wind turbines, they have experienced a 500 times drop in the cost per peak kilowatt

over the last 50 years, the concept that forms the basis for the cheapest systems is unchanged

22

over that time period (Nemet, 2006), and there have been few recent increases in the

laboratory efficiency of solar cells (Wikipedia, 2009). Instead it has been the existence of

IRtS in their production equipment (and some perhaps in operation8) and the increases in

efficiency that accompany improvements in production equipment that have probably had the

largest impact on falling costs. Like many of the other examples cited in this paper, the cost

of equipment probably does not rise as fast as does output (on a per area basis) and like LCDs

and to some extent semiconductors, the use of thinner materials also leads to lower material

and equipment (through faster processing) costs (Nemet, 2006).

Furthermore, most of the equipment being used to make solar cells has been borrowed

and continues to be borrowed from the LCD and to a lesser extent semiconductor, hard disk,

and printed circuit board industries. In particular, the falling cost per area of LCD panels (Gay,

2008), which can also be seen in the falling price of large screen televisions, suggests that the

cost per area of solar cells will also continue to drop as larger production equipment is

installed. This suggests that solar energy warrants further investments and it also suggests

that research on this equipment and how the equipment from these other industries can be

modified for the production of solar cells may contribute more towards further reductions in

the cost of solar cells than research on the solar cells themselves.

9. Discussion

The purpose of this paper was to explore how IRtS can lead to long-term improvements

and some cases exponential improvements in cost and performance of some technologies.

While the conventional wisdom is that these improvements come from advances in science

(Balconia et al, forthcoming), a change from product to process innovation (Utterback, 1994),

and increases in production volumes (Argote and Epple, 1990), these theories do not explain

8 The operation of electricity production from solar cells may involve some IRtS since some of the operating costs are lower on a per unit

basis for large than small operations (Nemet, 2006).

23

why some technologies experience greater improvements in cost and performance than other

technologies. Although more empirical research is needed (see below), IRtS seems to provide

a more fine-grained explanation for these differences between technologies than does the

conventional wisdom.

IRtS is different from economies of scale. While economy of scale refers to a situation in

which increases in production volume at a single point in time leads to lower cost, IRtS refers

to a situation in which large increases in an input over long periods of time lead to larger

increases in an output than in the input. For example, IRtS in some production equipment has

led to dramatic increases in the scale of this equipment and thus the emergence of large

economies of scale in this equipment. This means that even when the limits of further scaling

to equipment have been reached, economies of scale still exist in the production equipment.

Furthermore, IRtS also applies to the operation of many technologies and it can apply to

both larger and smaller scale. Dramatic increases in the scale of energy-related systems (e.g.,

furnaces, steam engines, internal combustion engines) and transportation equipment (trains,

ships, buses, aircraft) have led to dramatic improvements in their cost and performance where

many of the increases in scale and the resulting improvements can be called exponential.

Similarly, dramatic reductions in the size of features on ICs, in the storage elements on

magnetic platters or tape or on optical disks have also led to dramatic improvements in cost

and performance where many of the decreases in scale and the resulting improvements can be

called exponential.

This paper’s analysis suggests that the emergence of IRtS and the limits to it depend on

the “system” of the technology and the sub-systems and components that are embedded in the

technology’s “nested hierarchy of subsystems.” Such a hierarchy defines the different

sub-systems and the components that are used or could be used in the system where this

paper has just used the terms systems and components to simplify the discussion and where

these components include equipment and raw materials. As shown in Table 1 and discussed in

24

the above sections, every example of IRtS described in this paper was supported by and

depended on advances in science and improvements in components. For example, advances

in the science of high-speed machining, electricity, and chemistry and improvements in

special purpose manufacturing equipment and electric motors supported the realization of

IRtS in discrete parts and continuous flow manufacturing. Improved bellows for increasing

the flow of air to furnaces facilitated the realization of IRtS in furnaces. Advances in

thermodynamics and combustion and the higher tolerance parts and better materials

supported the realization of IRtS in engines. Advances in thermodynamics and fluid flow and

improvements in steel, aluminum, plastics, and composites have supported the realization of

IRtS in most modes of transportation equipment. In all of these examples, the limits to IRtS

have probably been or will soon be reached.

Similar conclusions can be stated for increasing returns to smaller scale. Advances in

solid state physics and improvements in many types of manufacturing supported the

realization of IRtS in ICs, LCDs, and magnetic storage. Furthermore, much of this equipment

has exhibited increasing returns to larger scale for the same reasons that much of the

equipment for continuous flow industries exhibit IRtS. IRtS in optical storage and fiber optic

also depended on advances in solid state physics but the relevant components were

semiconductor lasers, sensors, and amplifiers.

Second, this paper’s analysis suggests that IRtS in a component can lead to dramatic

improvements in the performance and cost of a system. For example, IRtS in ICs have had a

dramatic impact on the performance and cost of many electronic systems including

computers, mobile phones, and the Internet where many of these electronic systems do not

exhibit IRtS. Third, in some cases IRtS existed in both a “component” and a “system” and

they reinforced each other. Examples include IRtS in engines and transportation equipment

and IRtS in equipment and production systems; the most prominent example is IRtS in

semiconductor manufacturing equipment and ICs.

25

This paper also analyzed two types of clean energy: wind and solar. A typical analysis of

wind, solar, and other new energy technologies focuses on existing costs or some generic

aspect of improvement such as learning. A focus on existing costs would suggest that wind

energy is much cheaper than solar energy and thus has a much greater chance of diffusion

than do solar cells. However, a focus on IRtS in the nested hierarchy of subsystems for these

two technologies suggests that solar cells may experience greater reductions in cost than will

wind turbines. Wind turbines directly benefits from the IRtS of the turbine blade while solar

cells benefit from the IRtS of producing solar cells and the IRtS that have already emerged

for the equipment that is being borrowed from the LCD and other industries for them. IRtS

for the equipment can already be found in the dramatic reductions that have occurred in the

production of LCD panels. If solar cells were to experience in the next ten years the kinds of

cost reductions (20 times) that LCD panels experienced between 1995 and 2005, solar cells

would become the cheapest form of energy.

Furthermore, one could also apply the concept of IRtS, or more accurately the recent

lack of them to our environment. Every example of IRtS in this paper has impacted, often

strongly, on the environment and some say that the environment has reached its “limit” in

terms of its ability to handle further economic growth. Can this metaphor improve our overall

understanding of IRtS?

This paper’s review of IRtS suggests many avenues of research. First, and foremost, better

empirical data is needed. Not only is there little historical data available on the performance

and price of most technologies or the systems that comprise these technologies, there is even

less data available on the sizes of the systems and in particular data for the relevant

dimensions of the systems. Without such data, it is difficult to understand the phenomenon of

IRtS and certainly to construct production functions as some economists (Winter, 2008)

suggest are needed. Even in ICs, for which large amounts of data are available, this paper’s

analysis suggests that it would be useful to better understand the degree to which IRtS exists

26

in ICs and the equipment itself. For example, what is the relationship between increases in

equipment size, price, and output for ICs (both area and number of transistors), LCDs (just

area), and solar cells (just area)?

Second, better empirical analysis of the relationship between advances in science,

improvements in components, and IRtS is needed. Is there a way to better examine this

relationship through for example surveys of experts or coding-based analyses of books on the

history of technology books? Combined with better empirical data on cost, performance, and

size, this could probably tell us much more about the benefits from IRtS and the factors that

support IRtS. Such an analysis could also improve policies towards alternative forms of

energy.

Third, models of technological change should include the concept of IRtS. The most

commonly used models in management and economics such as the product life cycle

(Abernathy and Utterback, 1978; Utterback, 1994; Klepper, 1997), cyclical (Anderson and

Tushman, 1990), and disruptive (Christenson and Bower, 1996; Christensen, 1997) models of

technological change do not consider IRtS for technologies nor their impact on the sources of

discontinuities, the displacement of an existing technology by a discontinuity, or the

evolution of competition in the new discontinuity9. For example, some academic analyses of

Christensen’s (1997) theory of disruptive technologies focus on preference overlap (Adner,

2002; Adner and Zemsky, 2005) while this paper’s analysis suggests that the existence of

IRtS can drive large improvements in the performance and/or cost of a system either directly

or indirectly (through a key component). Thus IRtS may have a larger impact on whether a

new technology, independent of whether it is a “disruptive” or “sustaining” one, displaces an

existing one than does the degree of preference overlap. In fact, every disruptive technology

described by Christensen in his 1997 book, which includes computers, hard disk drives,

9 For example, does IRtS in technology impact on Klepper’s (1997) notion of IRtS in R&D?

27

mini-mills (new form of steel plant), and mechanical excavators, exhibits IRtS either in the

system (mini-mill) or in a key component of the system. IRtS exist in ICs for computers,

magnetic platter for hard disk drives, and pumps and actuators (similar to IRtS in engines) for

mechanical excavators.

It is also likely that the concept of IRtS can help us better understand the sources of

technological discontinuities, an issue that is largely ignored by the literature (Kaplan and

Trispas, 2008), and also the reasons for the long time lag between scientific advances and the

commercialization of them (Kline and Rosenberg, 1986; Mansfield, 1991; Klevorick et al.,

1995; Balconia et al. forthcoming). Rapid improvements in components that exhibit IRtS can

impact on the design and performance of systems and thus an understanding of how IRtS

impacts on components and how improvements in components impact on the design of

systems (Funk, 2009) will probably help us better understand the sources and perhaps the

timing of discontinuities. Wind, solar, and other forms of clean energy are just some of the

examples that would benefit from a better understanding of the sources of discontinuities.

10. Conclusions

This paper presents one of the first full-length overviews of IRtS in technologies and it

does so by combining the concept of nested hierarchies of subsystems with IRtS. It shows

how IRtS can emerge at any level in a nested hierarchy of subsystems. IRtS in a higher level

system depends on the performance and cost of components in a lower level of the hierarchy

and IRtS in a lower level “component” can drive large improvements in the performance and

cost of a higher level “system” even when there is not IRtS in the system itself.

28

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Table 1. Summary of Necessary Advances in Science and Components to Realize Increasing

Returns to Scale in Selected Technologies

Technology Sub-

Technology

Increasing

returns to

scale

Necessary

Advances in

Science

Necessary

Components

Reached

limits to

scaling?

Discrete Parts Larger Machining Production

Continuous

Flow

Larger Electricity,

chemical

elements and

reactions

Special purpose and

accurate machine

tools and other

processing equipment

Furnaces Larger Improved bellows

Steam Engine Larger

Probably

Energy

Systems

Internal

combustion

engine

Larger

Higher tolerance

parts and better

materials

Not

demanded

Trains Larger Steel and electricity

Buses Larger

Thermo

dynamics and

combustion

Steel, aluminum and

plastics

Ships Larger Steel

Transpor-

tation

Equipment

Aircraft Larger

Thermo

dynamics,

combustion,

fluid flow

Aluminum and

composites

Probably

ICs

LCDs

Mag. Storage

Smaller

and larger

Manufacturing

equipment

Electronics

Optical Stor.,

Fiber Optics

Smaller Semiconductor lasers,

sensors, amplifiers

May be

close to

limits

Solar Cells Smaller

and larger

Solid state

physics

Manufacturing

equipment

Clean

Energy

Wind

Turbines

Larger Fluid flow Better materials

Probably

not yet

36

Table 2. Components that Exhibit Increasing Returns to Scale and Exponential Rates of

Improvement

Component Measure of Performance Rate of Improvement (OOM:

orders of magnitude)

Integrated circuits Feature size

Defect density

Die size

Number of transistors/chip

>2 OOM in 40 years

>3 OOM in 40 years

>30 times in 25 years

9 OOM in 50 years

Light-emitting

diodes (LEDs)

Luminescence per Watt 3 OOM in 50 years

Minimum feature size in

semiconductors

500 times reductions in 40 years Semiconductor/LCD

Manufacturing

Equipment Cost per area of LCDs 20 times cost reduction between 1995

and 2005

Hard disk platters Areal storage density 5 OOM in 40 years

Magnetic Tape Areal storage density 5 OOM in 45 years

Glass fiber Spectral loss 2 OOM in 10 years

Optical fiber Information capacity

(bits/sec)

Cost per bit

Five OOM in 20 years

Six times reduction in 25 years

Optical discs Capacity

Transfer rates

10 times in 10 years

3 OOM in 10 years

Source: (Kurzweil, 2005) and authors analysis

37

Table 3. Examples of Systems Whose Performance has been Strongly Impacted on by

Exponential Improvements in a Component

Selected Components

from Table 1

Systems whose Performance is Impacted on by

Improvements in the Component

Semiconductors and Integrated

circuits

Many electronic products such as computers (9

OoM improvement in cost per speed in 60 years)

and digital cameras (300 times improvement in

pixels per dollar between 1996 and 2007)

Hard Disk Drives Computers and other electronic products

Hard Disk Drive Platters Hard Disk Drives

Magnetic tape Computers, music and video recorders/ players

Light-emitting diodes (LEDs) Instruments, electronic products and potentially

lighting systems

Liquid crystal displays (LCDs) Many electronic products including computers and

phones

Glass fiber and semiconductor

lasers

Telecommunication systems

Optical discs and lasers Music and video recording and playback

Sources: (Kurzweil, 2005; Kressel and Lento, 2007; Daniel et al, 1999; Turley, 2003)

38

Table 4. Cost Reductions for Semiconductors, LCDs, and Solar Cells

Technology Dimension Time Frame Ratio of New to Old Cost

Price/Transistor 1970-2005 1/15,000,000

Price/Area 1970-2005 1/20

Semiconductors

Price/Area 1995-2005 1/5.7

LCDs Price/Area 1995-2005 1/20

Price/kwH 1957-2003 1/500

Price/kwH 1993-2003 1/5

Solar cells

Price/area 1993-2003 1/4.1

Sources: (Gay, 2008; ICKnowledge, 2009; Kurzweil, 2005; Nemet, 2006) and author’s

analysis