Industry segmentation under environmental pressure: an optimal approach.
Dai, Feng ; Liu, Jingxu ; Liang, Ling 等
JEL Classification: E17, L16, O44.
Introduction
Industry segmentation is a process in which production and
operation are subdivided according to different fields. Industrial
segmentation is based on industrial specialization and market
segmentation, which are used to meet the demands of economic growth.
With the increase in new technologies and innovations, market and
industrial segmentation has become increasingly important and common in
economic development, which poses problems that deeply concern
economists.
Studies on market and industry segmentation include the following.
Pupillo and Zimmermann (1991) contribute to the emerging field of
international trade and industrial organization, and their work
indicates that markets are segmented. Mitchell and McDade (1992)
reconsider the market segmentation theory by focusing on property and
liability insurance companies and find strong evidence of market
segmentation. Allen and Jagtiani (1997) differentiate between depository
institutions, insurance companies, mutual funds, and other financial
firms and find evidence of market segmentation in both market risk
levels and market risk premiums. Shapiro and Shi (2008) investigate the
role of discount travel agencies, such as Priceline and Hotwire, in the
market segmentation of the hotel and airline industries and find support
for an inverse relationship between the quantity and price for market
risk. Liu et al. (2010) discuss the multi-criterion nature of market
segmentation and develops a new mathematical model that addresses this
issue. Menzly and Ozbas (2010) present evidence supporting the
hypothesis that due to investor specialization and market segmentation,
value-relevant information diffuses gradually in financial markets.
Kesting and Rennhak (2011) highlight the general procedures as well as
the challenges arising from the context of developing and implementing
market segmentation concepts and find that segmentation activities may
differ considerably depending on factors such as sector, industry, and
company size. Their field study also identifies some remarkable
trans-sectoral similarities concerning segmentation issues. Ruiz de Ma
et al. (2011) analyse the market for organic products in eight European
countries and identify international segments in the European organic
products market. These works show that the segmentation exists in almost
every economic market and industry. On the other hand, Mu and Lee (2005)
discuss market segmentation and technological catch-up based on the case
of the telecommunications industry in China. Gluschenko (2010) analyses
the role of various market frictions in inducing the segmentation of the
Russian goods market and finds that the spatial disconnectedness of
regions is responsible for approximately 70 percent of the average price
differential. Hoffmann and Soyez (2010) find that, to optimize marketing
campaigns, practitioners need to know the characteristics of this key
segment in the diffusion process and suggest a theoretically founded
cognitive model of domain-specific innovativeness for a product category
with a utilitarian benefit. Zhang and Wu (2012) identify market segments
and estimate the residents' willingness to pay for green
electricity in China. Their findings reveal that the segmentation is
caused by the significant differences in demographic variables, such as
level of education, household income, and location of residence, across
the population segments. These studies have discussed the various causes
and manners of market segmentation.
Industrial segmentation is different from market segmentation,
although the former is caused by the latter. Studies on industrial
segmentation are quite important, especially those incorporating
environmental pressure. In fact, any national government or authority
may have to face the following problem when making economic decisions.
What the current research does not address, however, is (1) how to
determine the optimal number of leading industries for a given economy,
(2) how the optimal number changes and what we can conclude about that
optimal number, and (3) the relationship between the number of
industries and competition.
This paper attempts to address these issues by presenting a
combinatorial growth model under environmental pressure, studying the
problem of industrial segmentation, and positing a method to compute the
optimal number of leading industries in an economy. The computed results
should be regarded as the number standard for leading industries in a
given economy. In addition, this paper will draw the following important
conclusions:
--The optimal number of leading industries in an economy increases
with technological progress and innovative growth;
--Industry segmentation will increase economic output under
environmental pressure;
--The optimal number of leading industries is negatively correlated
with market competition.
1. Foundation
1.1. Categorized production function
Industries can generally be divided into two categories:
traditional and emerging. Traditional industries are those that mostly
involve labor and basic manufacturing, while emerging industries are
those that mostly involve new science and technology. Traditional
industries require large quantities of labor and equipment--resources
that constitute the foundation of traditional industry. In a traditional
industry, capital often takes a material form (e.g. equipment or
buildings), while labor involves the efforts of workers with
standardized skills. Technological progress is measured by the
technologies embodied in capital equipment, final goods and services.
Traditional industries usually employ advanced processing techniques and
complete equipment systems and enjoy stable product markets. Traditional
industries often require a higher cost of capital and better technology.
In addition, technology levels in traditional industries tend to remain
stable for long periods of time. In contrast, powerful technology is
fundamental to emerging industries. In an emerging industry, capital may
take a material or immaterial form; it may include equipment, patents,
software, intangible assets and workers with standardized professional
skills. Technology develops rapidly in emerging industries; thus,
overall technological levels tend to evolve quickly.
For the sake of convenience, capital inputs will be expressed as
the value of capital required in production, labor inputs as the number
of workers required in production and technology inputs as the cost of
research and development. Thus, the production function (Solow 1956,
1957; Barro, Sala-i-Martin 1995) for an economy can be expressed as Y =
A x F(K, L), where Y is real economic output, K is capital, L is labor,
and A is multifactor productivity. For given quantities of capital and
labor, improvements in technology will yield increased output. Thus,
economies with more advanced technology exhibit greater productive
efficiency.
Because capital, labor and technology change over time (K = K(t), L
= L(t), A = A(t)), the technology level A(t), assuming
differentiability, can also be expressed as dA(t)/dt= h(t); thus, A(t) =
[integral] h(t)dt = H(t) where a is a constant. Therefore, output can be
expressed as:
Y = [Y.sub.1] + [Y.sub.2], (1)
where: [Y.sub.1] = a x F[K(t), L(t)] and [Y.sub.2] = H(t) x F[K(t),
L(t)]. In Model (1), the technology level associated with output
[Y.sub.1] = a x F[K(t), L(t)], a, is a constant, signifying a stable
technology level, which is a characteristic of traditional industries.
Therefore, [Y.sub.1], the output of traditional industries, is referred
to as basic output. The technology level associated with output
[Y.sub.2] = H(t)-F[K(t), L(t)], H(t), is a function of time, signifying
that the level of technology is variable, which is a feature of emerging
industries. Therefore, [Y.sub.2], the output of emerging industries, is
referred to as emerging output. Model (1) is referred to as the
categorized production function (CPF) for traditional and emerging
industries, where A(t) = H(t) + a is categorized total factor
productivity. Model (1) indicates that traditional industries have two
inputs, capital and labor, whereas emerging industries have three
inputs, capital, labor and technology. Model (1) can be concisely
expressed as:
Y = [mu] + [sigma],
where: [mu] = a x F[K(t), L(t)] is the production function for
traditional industries; [sigma] = [mu] x q (t) is the production
function for emerging industries; and q(t) = H(t)/a is the ratio of the
technology level of emerging industries to that of traditional
industries, indicating the degree of technological progress and
innovation, or innovation efficiency, of the former. Innovation
efficiency is a dimensionless quantity that expresses the advantage in
productive efficiency of emerging over traditional industries, and
simply as innovation. Here, innovation encompasses all of the benefits
of technological and scientific progress.
In general, traditional and emerging industries have different
capital and labor requirements. Model (1), however, shows that the input
factors of both traditional and emerging industries stem from the
economy's overall quantities of capital and labor. This finding can
be explained as follows. Each unit of capital can be divided into two
parts: one part used in traditional industries and the other used in
emerging industries. Similarly, each unit of labor can be divided into
two skill types: one applicable to traditional industries and the other
applicable to emerging industries. Thus, capital and labor can flow
between traditional and emerging industries. When productive efficiency
increases in emerging industries, capital and labor will flow toward
those industries.
Model (1) illustrates that, for the economy as a whole, part of
total output is produced by traditional industries, and the remainder is
produced by emerging industries. If emerging industries are low in
innovation efficiency, economic output mainly comes from traditional
industries. If emerging industries are relatively high in innovation
efficiency, economic output mainly comes from emerging industries.
During periods of the latter type, the economy will likely be highly
developed, because growth is largely driven by innovation.
1.2. An economic growth model including environmental pressure
Economic growth requires productive inputs and consumes a variety
of economic resources. However, it is important to note that economic
growth can be hindered by various factors, including resource scarcity,
market competition, investment risk, financial risk, environmental
crises, social unrest, natural disasters, disease, and war, all of which
generate environmental pressure (or resistance) to economic growth. It
is also worth noting that, in addition to promoting economic growth,
innovation may itself generate environmental pressure; it may increase
resource consumption, environmental pollution, or investment risk, which
increase the consumption of real output and thus raise innovation costs.
The consumption of social and economic resources due to environmental
pressure generated by economic growth is referred to as exogenous cost.
The exogenous cost of basic output is denoted as [phi] and the
exogenous cost of emerging output as k. Exogenous costs arise from
environmental pressure related to factor inputs. When factor inputs
change, exogenous costs also change. According to Reed (2001) and
Schoenberg et al. (2003), the ratio of the change in exogenous costs to
the change in factor inputs is a power function of current inputs; that
is:
d[phi]/d[mu] = v[[mu].sup.[phi]] and dk/d[sigma] =
w[[sigma].sup.[phi]],
where: [phi] > 0 indicates the existence of environmental
pressure; and v and w are the exogenous cost coefficients for basic and
emerging output, respectively, expressed simply as basic and emerging
cost coefficients. Hence, the basic and emerging exogenous costs are:
[phi] = v/[theta] [[mu].sup.[theta]] and [kappa] = w/[theta]
[[sigma].sup.[theta]],
respectively, where [theta] = [phi] + 1 is called the environmental
pressure index (EPI). Without loss of generality, let the constants of
integration equal zero. Because the capital rental rate and labor wage
rate are inevitably impacted by the economic environment, the costs of
capital and labor can be regarded as parts of the exogenous cost.
Following Sanchez et al. (2007), we assume that the authority can
adjust EPI through economic policy. Specifically, it can reduce EPI
through free and open (free-market and non-protectionist) policy and
increase EPI through a closed and protective policy, but it cannot
eliminate environmental pressure altogether, that is, [theta] > 1.
The formulas for exogenous costs indicate that an increase in productive
inputs will be accompanied by an increase in environmental pressure or
exogenous cost. Generally, the environment for sustained growth is
likely to improve gradually. However, in achieving long-term growth and
development, an economy faces a growing number of challenges of
increasing complexity, challenges (arising from such issues as
institutional policy, financial risk, environmental crisis, social
unrest, natural disaster, disease, and war) that will be increasingly
difficult to address under current approaches. Indeed, traditional and
emerging industries may face different environmental pressures, and
governments may accordingly implement different policies to address
development and growth in the case of each industry type. For
convenience, however, we assume equality between the environmental
pressure indices for traditional and emerging industries (1).
Given that economic growth cannot be neatly separated from
environmental pressure and resulting exogenous costs, the real output
based on Model (1) can be expressed as:
y = [mu] + [sigma] -([phi] + [kappa]) = [mu] x G, (2)
where G = 1 + q - 1/[theta](v +
[wq.sup.[theta]])[[mu].sup.[theta]-1] is the total factor productivity
with environmental pressure and EPI can be expressed as [theta] =
d[kappa]/kappa]/d[sigma]/[sigma]. Model (2), which can be referred to as
a normal growth model with environmental pressure, is also an
advance-retreat course (ARC) model (Dai et al. 2011, 2013). According to
the Cobb-Douglas production function, basic output can be expressed as
[mu] = a x F[K(t), L(t)] = [[mu].sub.0][K.sup.[alpha]][L.sup.[beta]] in
Model (2), where K and L represent capital and labor, respectively;
[[mu].sub.0] = a x [c.sub.0], [c.sub.0] are initial values; and a,
[beta] > 0. The emerging industry output can then be expressed as
[sigma] = [[sigma].sub.0][K.sup.[alpha]][L.sup.[beta]]q. Because the
capital rental rate and labor wage rate will inevitably be affected by
the economic environment, the costs of capital and labor can be regarded
as part of the exogenous costs. Model (2) is simplified to the Solow
growth model (Solow 1957) if v = w = 0, and to the Cobb-Douglas
production function if v = w = 0 and [[sigma].sub.0] = 0. On the other
hand, if [theta] = 1 and v [not equal to] 0 and w [not equal to] 0, the
environmental costs are linear, and thus y = (1 - v)[mu] + (1 -
w)[sigma], which can be discussed according to works on the Solow model.
Model (2) indicates that during normal economic growth,
environmental pressure increases as output increases, which continues
until the economy goes into recession. Only successful policies and
institutional reform can generate a new economic environment, relieve
the existing environmental pressure, and initiate a new cycle of
economic growth. As the economy continues to grow, however, additional
environmental pressure accrues. Hence, the ARC model (2) reflects the
cyclical features of economic growth.
2. Model
2.1. Notation
Suppose an economy includes m economic entities, m > 1. If the
economy is a national economy, the entities correspond to the leading
industries. For the economy and the entity i (i = 1, m), the notations
that will be used are as follows:
r - basic output of the economy, [GAMMA] > 0;
U - emerging output of the economy, U > 0;
F - basic exogenous cost of the economy, F [greater than or equal
to] 0;
K - emerging exogenous cost of the economy, K > 0;
Y - real output of the economy;
[[mu].sub.i] - basic output of the entity i, [[mu].sub.i] > 0;
[[sigma].sub.i] - emerging output of the entity i, [[sigma].sub.i]
> 0;
[[phi].sub.i] - basic exogenous cost of the entity i, [[phi].sub.i]
[greater than or equal to] 0;
[k.sub.i] - emerging exogenous cost of the entity i, [k.sub.i] >
0;
[Y.sub.i] - real output of the entity i.
2.2. Integrated emerging output and exogenous cost
Generally, the emerging output of an economy is the sum of all
emerging outputs of its entities; that is:
U = [[summation].sup.m.sub.i=1] [[sigma].sub.i]. (3)
There may be a clear boundary between the traditional industries
such that the technologies and innovations in an industry are not well
suited to other industries. For example, agricultural technologies are
not usually suitable for industrial production. Thus, each exogenous
cost of traditional industries can be regarded as independent of one
another; thus, the basic exogenous cost of economy is the sum of all
basic exogenous costs of industries. There is usually a high correlation
between emerging outputs; that is, technologies and innovations are
significantly correlated across the emerging outputs. For example,
computer and chip technology have been used in modern industrial
control, weather analysis, aerospace engineering, communication
engineering, and many other fields. Similarly, modern textile
industries, paper industries, steel industries, and mechanical and
electrical industries are inseparable from control technologies and
innovations. Meanwhile, there is intense and extensive competition among
emerging outputs in terms of workers, capital, technologies, products,
and market. Therefore, the influence of environmental pressure on
emerging outputs is correlated, which means that the emerging exogenous
cost of an economy is different from the basic exogenous cost in
structure; in other words, emerging exogenous costs are correlated.
Thus, the growth rate of the emerging exogenous costs of an economy is
comprised of those of its entities in linear way:
dK/K = [[beta].sub.1] d[[kappa].sub.1]/[[kappa].sub.1] + ...+
[[beta].sub.m] [d[[kappa].sub.m]/[[kappa].sub.m] (2),
where: [[beta].sub.i] represents the competitive status of entity i
in the economy, referred to as competitive advantage, [[beta].sub.i]
> 0. The competitive structure of the economy can be described by the
relationship between [[beta].sub.i], ..., [[beta].sub.m]. The larger the
competitive advantage [[beta].sub.i], the higher the pressure caused by
entity on other entities.
According to the expression of emerging exogenous cost, i.e.
[kappa] = w/[theta] [[sigma].sup.[theta]], the EPI of an economy can be
expressed as [theta] dK/K/dU/U and those of entities as [[theta].sub.i]
= d[[kappa].sub.i]/[[kappa].sub.i]/d[[sigma].sub.i]/[[sigma].sub.i].
Therefore, we have dK/K = [theta]dU/U = [[beta].sub.1][[theta].sub.1]
d[[sigma].sub.1]/[[sigma].sub.1] + ... + [[beta].sub.m][[theta].sub.m]
d[[sigma].sub.m]/[[sigma].sub.m] The emerging exogenous cost of an
economy is then as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)
Denoting [[rho].sub.i] = d[[sigma].sub.i]/[[sigma].sub.i]/dU/U, the
EPI of an economy can be expressed as follows:
[theta] = [[summation].sup.m.sub.i=1]
[[beta].sub.i][[rho].sub.i][[theta].sub.i], (5)
where: [[alpha].sub.i] is referred to as the emerging output
elasticity of entity i related to economy, which indicates how the
emerging output growth rate of the entity impacts the EPI of an economy.
2.3. The combinatorial ARC model of an economy
Following Model (2) and Equations (3), (4), and (5), the real
output of an economy including m industries under environmental pressure
is as follows:
Y = [GAMMA] + U -([PHI] + K), (6)
where: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; and U =
[GAMMA] x Q, where Q represents the innovation. Model (6) is referred to
as the combinatorial ARC model.
2.4. Types of competition
Resources (for example, for raw materials, capital, product market,
and people with a particular technical ability) exist in an economy, and
there is competition among the same type of entities in the economy,
which may be complete or incomplete. The competitive relationships among
different entities can be described by the competitive advantage
[[beta].sub.i]. in Equation (5), and these advantages can be placed in
the following four classifications:
--Mutual benefit. When [[summation].sup.m.sub.i=1] [[beta].sub.i]
< 1, there is a mutually beneficial relationship among the entities.
When [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the
environmental pressure on the economy is less than that of any given
entity. Therefore, there exists a mutually beneficial relationship that
allows the entities to develop together;
--Non-competition. When [[summation].sup.m.sub.i=1], there is a
non-competitive relationship among the entities. In this case, the
growth rate of environmental pressure on an economy is equal to the
arithmetic average of the growth rates of environmental pressure on the
entities. Therefore, there is no competition among entities, and there
is no mutually beneficial relationship;
--Incomplete competition. When 1 < [[summation].sup.m.sub.i=1]
[[beta].sub.i] < m, there is an incomplete competitive relationship
among the entities. In this case, the growth rate of environmental
pressure on an economy is larger than the arithmetic average of the
growth rates of environmental pressures on the entities but less than
their simple sum. This implies that there is competition among entities
to some degree, which is incomplete competition. The incompleteness of
the competition is proportional to the change in values of
[[summation].sup.m.sub.i=1] [[beta].sub.i];
--Complete competition. When [[summation].sup.m.sub.i=1]
[[beta].sub.i] [greater than or equal to] m, there is a complete
competitive relationship among the entities. In this case, the growth
rate of environmental pressure on an economy is equal to or greater than
the simple sum of the growth rates of those entities. The competition
among the entities in this case is an intense, life-or-death situation.
In particular, if [[beta].sub.i]. = 1, the competition is called
standard complete competition.
3. Results and discussion
3.1. Results
If there are m (> 1) leading industries in an economy and they
are all equivalent (with "equivalent" meaning that the
importance, output, and market risk of the industries are similar but
their products and raw materials are different, i.e. the industries are
competing with one another, which includes incomplete competition for
capital, labor, and energy, but they are not competing for customers and
market). Then, we suppose that, (1) the emerging output growth rates of
industries are all equal to that of the economy, i.e. [[rho].sub.i] =
d[[sigma].sub.i]/[[sigma].sub.i]/dU/Y = 1;(2) the competitive advantages
of industries are equal to each other, i.e. [[beta].sub.i]. = [beta];
and (3) the EPIs of the industries are equal to each other, i.e.
[[theta].sub.i] = [psi]. According to Equation (5) and Model (6), the
ARC model of each leading industry can be expressed as:
[Y.sub.m] = [GAMMA] - [PHI]/m + U/m - [(w/[theta]
[U.sup.[theta]]).sup.1/m[beta]]. (7)
where: [theta] = m[beta][psi].
According to Appendix A, the optimal number of leading industries
in an economy is as follows:
[m.sup.*] = 1/[beta] ln(w/[theta][U.sup.[theta]]), (8)
where: U [greater than or equal to] ([theta]/w
[e.sup.[beta]])1/[theta]. Then, the real maximum output after industry
segmentation is as below:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)
From Equation (8), the optimal number of leading industries in an
economy depends on competitive advantage, EPI, and emerging output. The
optimal number of leading industries decreases as the competitive
advantage increases and increases as the emerging output increases. We
see, from Appendix A, that the real economic output (9) reaches its
maximum when the number of industries follows Equation (8). That means
that the economic structure is optimal in the number of industries, and
we call the economy has an optimal structure. If economy has always an
optimal structure, the real economic output will maintain its maximum
and economy will keep developing in an optimal approach.
From Appendix A and Equation (8), Conclusion 1 is obtained below.
Conclusion 1. There is an optimal number of leading industries in
an economy. If the current number of leading industries in an economy is
equal to the optimal number, then the real output of the economy
achieves its maximum value. If the emerging output of the economy grows,
that is, the innovation in the economy increases, the optimal number of
leading industries will also increase.
Conclusion 1 states that economy is always pursuing a
high-efficiency state, which leads to an increase in the number of
leading industries with technological progress and innovative growth
because the increase in the number of leading industries promotes
industrial spe cialization, the utilization of various resources, and a
decrease in the environmental pressure in industrial growth. The optimal
number of leading industries in an economy increases, which means that
leading industries are always subdivided in their development.
Therefore, industrial segmentation is an inevitable result of
technological progress and innovative growth. We are able to determine
the optimal number of leading industries at any point of segmentation,
which is a valuable tool for controlling the rhythm of economic
development.
From Appendix B and Equation (B.2), Conclusion 2 is obtained as
follows.
Conclusion 2. There is a critical value for industry segmentation.
If the real number of leading industries is larger than the critical
value, then industry segmentation will increase the real output of the
economy. In this case, the more leading industries there are, the higher
the real output of the economy.
Conclusion 2 states that the government and other authorities need
to reasonably promote industrial segmentation, which can effectively
promote the stable and sustainable economic growth. According to the
critical value, the government and other authorities are able to
reasonably control the number of industries.
From Conclusion 1 and Conclusion 2, Conclusion 3 is derived is as
follows.
Conclusion 3 Technological progress and innovative growth will
increase the optimal number of leading industries and thereby promote
economic growth.
Industry and market segmentation is the most effective method for
reducing the environmental pressure on economic growth and changing
economic structure, as they can:
--Tap the potential for economic growth and market development.
Industry and market segmentation can effectively discover the
"blind zone" of growth and market demand, open up a new field
of industrial growth, meet the needs of increasing consumption, and
promote both employment and economic growth. Here, a "blind
zone" is a market field that has not been previously identified but
does include consumption demand, which will promote industrial growth;
--Avoid increasing economic and financial risk. Because industry
and market segmentation will create a greater number of industries and
markets, it will also decrease resource consumption and competition
between those industries and markets. As a result, these industries can
continue growing even if other industries are in crisis;
--Manage industries in a more standardized and specialized way.
Because industry and market segmentation can produce a more ideal
product and demand configuration in an economy, the economy is more
likely to fully utilize specialized production and management
technology, thus achieving highly efficient classed tax and financial
management.
3.2. Discussion
In addition to the works introduced in the introduction, there are
many other revelant studies:
--Battisti and Pietrobelli (2000) develop a theoretical framework
to analyse intra-industry gaps in technology and explain the existence
of inter-firm technological gaps by factor market segmentation.
Corrocher and Zirulia (2010) argue that in a context of uncertainty,
demand affects firms' innovative strategies by increasing the capa
bility of market segmentation and by providing the incentives to
innovate. Boffa and Panzar (2012) propose a regulatory mechanism for
vertically related industries in which the upstream bottleneck segment
faces significant returns to scale while other (downstream) segments may
be more competitive. Choi (2013) constructs a simple asset market
segmentation model to study the relationship between inflation and theft
when money is the only medium of exchange;
--Degryse and Ongena (2004) believe that increased interbank
activity results in the development of either transactional banking or
bank industry specialization. Clark (2006) finds that industries that
are engaged in vertical specialization-based trade make production
location decisions that cause the specialization of industrial
development. Using measures of diversification based on the diversity in
segment-industry characteristics, He (2009) documents a diversification
premium in the post-1997 period and determines significant positive
effects of cash flow diversity, leverage diversity, and profitability
diversity on excess value. Brandt and Thun (2011) examine how a shift in
the end point of a global value chain alters the prospects for
industrial upgrading in a developing economy through an analysis of the
mobile telecom sector in China and find that domestic Chinese firms have
been able to take advantage of both increasing modularity and their
superior knowledge of low-end market segments to expand sales vis-a-vis
foreign firms;
--Chen and Bell (2012) examine how a firm that faces customer
returns can enhance profit by using different customer returns policies
as a device to segment its market into a dual-channel structure. Ko et
al. (2012) note that researchers have paid relatively little attention
to whether markets can be segmented cross-nationally, and their findings
support the existence of similarities across global fashion markets that
allow the sportswear industry to target market segments based on the
theoretical framework.
Differing from the above studies, Models (6) and (7) integrate
traditional and emerging outputs, technological progress and innovation,
and economic and environmental policy. Equation (8) provides a way to
determine the optimal number of leading industries in an economy and how
technological progress and innovative growth promote industry
segmentation and economic growth. Equation (9) presents the real output
for the optimal number of leading industries in a given economy. We can
measure the competitive relations between industries in a given economy
by the competitive advantages, which differs from the Boone indicator
(Leuvenstei et al. 2011) and many well-known measures of competition.
According to Conclusions 1, 2, and 3 above, as the number of leading
industries increases, the following occurs:
1) Industry segmentation is the inevitable outcome of technological
progress and innovation. Over time, technological progress and
innovation become more specialized and precise. As a demand for economic
growth, economic technological progress and innovation will promote the
subdivision of the industry in more specialized and distinctive ways;
2) Industrial segmentation improves the efficiency of economic
development. Industrial segmentation will also make the subdivided
industries increasingly specialized and distinct from one another, which
will result in improved standards management. This
improvement increases the efficiency and decreases the cost of
industrial development, which pushes industries to develop at a higher
level;
3) Industrial segmentation improves resource integration and
utilization. Industrial segmentation will make the resources in an
industry more similar, which improves integration and efficiency
regarding the utilization of resources, such as raw materials,
throughput, professional labor, capital, and energy, among other things.
Resource integration also encourages the development of specialized
markets and industries and results in the utilization of the particular
resources in a full way;
4) Industrial segmentation promotes product and market
diversification. Because an economy always features multiple levels of
production and various consumption demands, economic diversification is
indispensable. Industrial segmentation can ensure that commodity
diversification and multiple levels of production will occur;
5) An economic boom follows industrial segmentation. After the
industries are fully subdivided in an economy, an increasing number of
new special technologies and products will emerge to meet the diverse
demands of society and consumption, leading to an economic boom.
4. Empirical research
4.1. Using Model (6) to fit the U.S. GDP
To prove the rationality of Model (6) and support all the results
in the paper, Model (6) is used to fit the U.S. GDP below using the
fitting function Fit[ Y(t), D(t), t] in the MAPLE software system. The
real GDP data (3) used in this study were recorded as D(t), t = 1940,
..., 2010.
Without the loss of generality, in Model (6), let [GAMMA] =
[[GAMMA].sub.0]e[[lambda].sup.t], U = [U.sub.0] e[([lambda]+s).sup.t],
Q = [Q.sub.0][e.sup.st], and U = [GAMMA] * Q. where [lambda] is the
basic output growth rate of the economy, s is the growth rate of
innovation; the basic output growth rate [lambda] = 0.110 (4) and
economic innovation growth rate s = 0.097 (5). Model (6) is expressed as
[Y.sub.[theta]](t) = [[GAMMA].sub.0] [e.sup.0.11t] + [U.sub.0]
[e.sup.0.207t] - ([[PHI].sub.0][e.sup.0.11[theta]t] +
[K.sub.0][e.sup.0.207[theta]t]), which can be estimated by the
regression method.
When the error is small and the coefficient of determination is
large, the fitting result based on [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Fig. 1 indicates that Model (6) fits the U.S. GDP data well. The
estimated U.S. GDP ARC curve reaches its Top Time at T = 2009.266529,
which means that the U.S. economy peaked and showed signs of decline
near 2009 and that the tendency to decline continued after 2010. If
there is a recovery in the U.S. economy and no effective reform policy
is implemented, the recovery may be a weak one. In fact, if the current
time is larger than the Top Time and no economic reform is carried out
to the reduce EPI, then the real output (or GDP) will quickly decline
and an economic crash will occur.
absolute error: [[epsilon].sub.1] [square root of
([[summation].sup.2010.sub.t=1940] [[D(t) - [??](t)].sup.2/(2010- 1940)
= 130.44133; coefficient of determination [R.sup.2] = 0.9934295912. And:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where: [??](t) is the [Y.sub.[theta]](t) - based estimated function
of U.S. GDP.
The GDP data and Model (6)-based U.S. GDP fitting curves are
depicted in Fig. 1.
[FIGURE 1 OMITTED]
Fig. 1 indicates that Model (6) fits the U.S. GDP data well. The
estimated U.S. GDP ARC curve reaches its Top Time at T = 2009.266529,
which means that the U.S. economy peaked and showed signs of decline
near 2009 and that the tendency to decline continued after 2010. If
there is a recovery in the U.S. economy and no effective reform policy
is implemented, the recovery may be a weak one. In fact, if the current
time is larger than the Top Time and no economic reform is carried out
to the reduce EPI, then the real output (or GDP) will quickly decline
and an economic crash will occur.
[FIGURE 2 OMITTED]
Fig. 2 compares Model (9) with the Model (6)-based U.S. GDP fitting
curves in Fig. 1. Fig. 2 shows that the optimal ARC curve growth is
sustained after 1990, whereas the original ARC curve declines towards
the end. Therefore, the optimal industry segmentation promotes output
growth under environmental pressure.
4.2. The empirical analysis of industrial segmentation
Based on Equation (8) and the data estimated above, the optimal
numbers of leading industries for U.S. economy can be computed for each
year. The optimal number curves are depicted in Fig. 3 when the
competitive advantages are (3 = 0.01, (3 = 0.02, and (3 = 0.05,
respectively. Some computed data are listed in Table 1.
[FIGURE 3 OMITTED]
Fig. 3 shows that industry segmentation occured in the late 1960s.
As the speed of computers increased dramatically in the late 1960s,
technological progress and innovative growth based on computers required
and caused industry segmentation. Furthermore, industry segmentation is
a fundamental way of changing the economic structure and developing
economy.
Table 1 indicates that, there is incomplete competition among the
industries and that the optimal number of leading industries increases
as the competitive advantage decreases. All the optimal numbers are
larger than the critical value for the given competitive advantage,
which means that industry segmentation based on the optimal number will
promote economic growth.
From Table 1, if [beta] = 0.01, the optimal number of leading
industries is [m.sup.*] (2012) = 1188.59 at time t = 2012. Therefore, in
2012, it will be most favorable to break down the U.S. economy into
approximately 1244 leading industries. This conclusion can be used by
the U.S. government and economic authorities to create better economic
policies. Currently, the U.S. appears to have no clear statistics
regarding their number of leading industries, which means that the U.S.
can perform far better industrial planning than it currently does.
Summary and conclusions
The economy is composed of many industries, and the number of
industries in an economy is always changing. What number is most
favorable for economic growth? What trends do the changes in this number
follow? To address these questions, following investigations are
performed based on the Solow growth model and ARC model:
--Build a combinatorial ARC model. Based on an analysis of the
growth relation between the integrated basic output, innovation, and
environmental pressure, the combinatorial
ARC model is presented. This model can describe large-scale
economic growth under environmental pressure;
--Describe the competition relations between economic entities.
Based on the EPI of an economic group, four competition relationships
between economic entities are generally described: mutual benefit,
non-competition, incomplete competition, and complete competition;
--Compute the optimal number of segmented industries. Under
complete competition or incomplete competition, the approach for
computing the optimal number of industries in an economy is given, and
the real maximum output after optimal industry segmentation is
described.
Based on the works above, the following important conclusions are
reached:
1) There is an optimal number of leading industries in an economy.
Based on the combinatorial ARC model, the optimal number of leading
industries for an economy can be computed. If the number of leading
industries in an economy is equal to the optimal one, then the real
output of the economy reaches its maximum value;
2) Technological progress and innovative growth will promote
industry segmentation. The technological progress and innovative growth
will require and cause industry segmentation. Furthermore, industry
segmentation is a fundamental way of changing the economic structure and
developing economy;
3) Industry segmentation will promote economic output growth. Based
on ARC analysis, a critical value for industry segmentation can be
obtained. If the real number of leading industries is larger than the
critical value, then the industry segmentation will increase the real
output of the economy.
The most important conclusion in this paper is that the main
approach to changing economic structure is through industry and market
segmentation.
The results are valuable to authorities for deciding and controlling
the number of leading industries. If using Model (6) to describe the
output growth of a firm that produces many products, we may analyse
product diversification in the same way as segmentation in this paper.
Conversely, the discussion of market globalization is similar to that of
transnational mergers and acquisitions in that the latter may lead to
the former, and mergers and acquisitions are the inverse problems of
industry segmentation. If using Model (6) to describe the output of an
industry and the industry includes many firms, we may discuss mergers
and acquisitions in a corresponding way, which will be presented in
another paper.
In addition, Models (2) and (6) also apply to developing countries
because economic output in developing countries also grows or declines
and the growth cannot be unlimited; a growth cycle of any developing
countries usually includes four phases: slow growth, rapid growth,
stagnation and decline, and Models (2) and (6) may describe the four
phases.
APPENDIX A
There is an optimal number of industries in an economy, and the
optimal number increases with technological progress and innovative
growth. This proposition can be proved below: Based on Model (7), the
real output of an economy is the sum of real outputs of m industries,
that is: 1
m x [Y.sub.m] = [GAMMA] - [PHI] + U - m [(w/[theta]
[U.sup.[theta]]).sup.1/m[beta]] (A.1)
According to Models (6) and (A.1), the difference between the real
outputs of economy before and after industry segmentation is as follows:
[DELTA] = m x [Y.sub.m] - Y = w/[theta] [U.sup.[theta]] - m x
[(w/[theta] [U.sup.[theta]]).sup.1/m[beta]]
Let d[DELTA]/dm = [(w/[theta] [U.sup.[theta]]).sup.1/m[beta]]
[1/m[beta] ln (w/[theta][U.sup.[theta]]) -1] = 0; we obtain the optimal
number of industries in an economy as follows:
[m.sup.*] = 1/[beta] ln(w/[theta] [U.sup.[theta]]), (A.3)
where: [m.sup.*] > 1, that is, U > [([theta]/w
[e.sup.[beta]]).sup.1/[theta]].
Under Equation (A.3), d[DELTA]/dm = 0 and
[d.sup.2][DELTA]/[dm.sup.2] = 1/[m.sup.2][beta]ln(w/[theta]
[U.sup.[theta]] < 0. In this case, Equation (A.2), i.e. the
difference between the real outputs of economy before and after industry
segmentation, reaches its maximum. None of w, [theta], [beta], or U vary
with m, and 1/[m.sup.*][beta]ln(w/[theta] [U.sup.[theta]]) - 1 = 0, so
-1/m'[beta]ln(w/[theta] [U.sup.[theta]]) - 1 < 0 for any m'
> [m.sup.*] and 1/m'[beta]ln(w/[theta] [U.sup.[theta]]) - 1
> 0 for any m' < [m.sup.*]. Therefore, Equation (A.3) is the
only maximum of Equation (A.2).
Because the emerging output U = G x Q in Model (6), where Q is the
innovation, Equation (A.3) indicates that the innovative growth will
increase the optimal number. Therefore, technological progress and
innovative growth will promote industry and market segmentation.
Substituting Equation (A.3) into Model (A.1), we have the real
maximum output after industry segmentation as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (A.4)
APPENDIX B
There is a critical value for industry segmentation, which is
determined by [[bar.m].sup.*] = 1/[beta](1 + ln [[bar.m].sup.*]). If
the real number of leading industries is larger than the critical value,
then the industry segmentation will increase the real output of an
economy. This proposition is proven below:
Substituting Equation (A.3) in Appendix A into Equation (A.2), the
maximum difference between the real outputs of economy before and after
industry segmentation is as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (B.1)
When [[DELTA].sup.*] = 0, we have:
m = f ([m.sup.*]) = 1/[beta](1 + ln [m.sup.*]). (B.2)
According to Equation (B.2), we have f'(m) = 1/[beta] x m.
Then:
(1) Under incomplete competition, we have 1 < [beta]m < m,
i.e. [absolute value of (f'(m))] = f'(m) = 1/[beta] x m <
1. In this case, there is a fixed point mx for Equation (B.1), and
[m.sup.*.sub.1] = (1 + ln[m.sup.*.sub.1]);
(2) Under complete competition, [[beta].sup.*] [greater than or
equal to] 1 and the number of industries is greater than one, i.e.
[m.sup.*] > 1; therefore, [absolute value of (f'(m))] =
f'(m) = 1/[beta] x m < 1. In this case, there is a fixed point
[m.sup.*.sub.2] for Equation (B.1), and [m.sup.*.sub.2] = 1/[beta](1 +
ln [m.sup.*.sub.2]).
According to the above analysis, there is a fixed point for
Equation (B.2) under incomplete and complete competition, and the fixed
point is related to the competitive advantage. We know from Equation
(B.2) that f'(m) = 1/[beta] x m > 0 and f (m) = 1/[beta](1 + ln
m) is an increasing function. When the real number of leading industries
is larger than the fixed point, the maximum difference between the real
outputs of an economy after and before industry segmentation is greater
than zero, i.e. [[DELTA].sup.*] > 0 ; therefore, the industry
segmentation will increase the real output of the economy. In this case,
the more leading industries exist, the higher the real output of the
economy. Thus, the fixed point is a critical value.
Caption: Fig. 1. U.S. GDP and ARC fitting (1940-2010) Note: The
units are in billions of U.S. dollars. The U.S. GDP data curves for the
period 1940-2010 are illustrated. It can be observed that Model (6) its
the GDP much better.
Caption: Fig. 2. Comparison of the ARC curve with optimal one for
U.S. GDP Note: The optimal U.S. GDP ARC curve is depicted based on Model
(9), and the original U.S. GDP ARC curve is based on Model (6). Both
curves are plotted on a logarithmic scale here. We see that the optimal
ARC curve agrees with the original ARC curve between 1940 and 1990.
After 1990, the optimal ARC curve growth is sustained over time, whereas
the original ARC curve declines towards the end.
Caption: Fig. 3. Optimal number of industries in the U.S. economy
from 1968 to 2020 Note: Figure 3 is depicted based on Equation (8) and
indicates that the optimal number of industries continues to increases
over time. As the competitive advantage increases from 0.01 to 0.05, the
optimal number of industries decreases gradually.
doi: 10.3846/20294913.2014.880081
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Feng DAI is a Professor of Economic Management and Science at
Department of Management Science, Zhengzhou Information Engineering
University (China). His publications include nine books and more than 60
articles in renowned international journals/conferences. He is a
Director of Management Science Society in China and is a Member of IAES.
Jingxu LIU is a Dr and works at the Department of Management
Science, Zhengzhou Information Engineering University (China). Her
publications include two books and more than 10 articles.
Ling LIANG is an Associate Professor at Department of Management
Science, Zhengzhou Information Engineering University (China). Her
publications include two books and more than 30 articles.
Feng DAI, Jingxu LIU, Ling LIANG
Department of Management Science, Zhengzhou Information Engineering
University, Building 75-1-701, No. 5, Jian-Xue Street, Wen-Hua Road,
Zhengzhou, 450002 Henan, China
Received 24 November 2012; accepted 02 November 2013
Corresponding author Feng Dai
E-mail: fengdai@126.com
(1) For convenience, we assume equality between the environmental
pressure indices for traditional and emerging industries. In general,
the environmental pressure index for traditional industry may be
different from that for emerging industry. In the case, the exposition
is similar to current one, but will be more complex.
(2) The linear relationship between the growth rates of the
emerging exogenous costs may clearly and succinctly describe the
integration of environmental pressures, and the all-round competition
between industries in capital, manpower and technique. The later
empirical analysis will indicate that the assumption is appropriate. Of
course, other relationships between environmental pressures on the
industries in an economy can be taken into account if needed.
(3) Data source: the United States White House website,
http://www.whitehouse.gov.
(4) Direct capital average growth rate (1940-2010) is 6.7%, data
source: U. S. White House Web, http://www.whitehouse. gov. Average
growth rate of employment labor force (1940-2010) is 4.3%, data source:
U.S. Bureau of Labor Statistics Web,
http://data.bls.gov/pdq/SurveyOutputServlet.
(5) The growth rate of utility patent applications in U.S
(1969-2010), data source: U.S. Patent and Trademark Office Web,
http://www.uspto.gov/web/offices.
Table 1. The optimal number of industries in the U.S. economy
Optimal number Year
of industries: [m.sup.*]
2012 2013 2014
Competitive advantage [beta] = 0.01 1188.59 1217.82 1247.05
[beta] = 0.02 594.29 608.91 623.52
[beta] = 0.05 237.72 243.56 249.41
Competitive type: [m.sup.*][beta] 11.89 12.18 12.47
Optimal number Year Critical
of industries: value:
[m.sup.*] 2015 2016 [[bar.m].sup.*]
Competitive advantage 1276.28 1305.50 763.84
638.14 652.75 341.70
255.26 261.10 114.88
Competitive type: 13.76 13.06
[m.sup*][beta]
Note: Table 1 shows that the optimal number of industries is smaller
if the competitive advantage is greater and that there is an
incomplete competition among the industries because 1 < [m.sup.*]
[beta] < [m.sup.*]. The critical values are computed according to
Equation (B.2).
