| inframarginal economics |
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Centralized Hierarchy within a Firm
and Decentralized Hierarchy in the Market Heling Shi and Xiaokai Yang Introduction The purpose
of the paper is two-fold. First, we develop a general equilibrium
model based on corner solutions to simultaneously endogenize four
aspects of the division of labor: individu-als' level of specialization,
the length of the roundabout production chain, the number of goods
in each link of the chain, and the development of the institution
of the firm. Second, the equilibrium model is used to endogenize the
dividing line between the hierarchical structure of division of labor
within the firm and the hierarchical structure of the network of transac-tions
in the market. According
to Smith [1776], Young [1928], and Houthakker [1956], there are four
as-pects of the division of labor: the level of specialization of
individuals, the degree of diversity of professions, the degree of
roundaboutness, and the institute of the firm. The first aspect may
be related to the degree of specialization at the individual level.
The second aspect (di-versity of professions) may concern the horizontal
division of labor between professional sectors at the same level in
this chain. The third aspect (roundaboutness) may be related to the
vertical division of labor between upstream and downstream professional
sectors in a long production chain. The fourth aspect (firm) relates
the alternative methods in organizing trans-actions required by the
division of labor. Casual observation
indicates a positive correlation between the level of specialization,
the degree of the roundaboutness of production (or the length of a
production chain of round-about productive activities), the variety
of available goods, and the development of the institution of the
firm in an economy. The number of available goods is small, the degree
of production roundaboutness is low, and no firm exists in a less
developed and autarkical econ-omy where the level of division of labor
and specialization is extremely low and all self-provide goods they
need. In contrast, the variety of available goods is great, the degree
of production roundaboutness is high, and structures of the firms
are sophisticated, in a devel-oped economy with extremely high levels
of division of labor. Also, the increase in the roundaboutness is
usually associated with the development of the institution of the
firm. These concurrent phenomena, which contradict a superficial intuition
that entails the counter-action between specialization and product
diversity, may relate to some important mechanism that is essential
for economics and which has not been well understood by economists.
Four recently developed research lines are related to the different
aspects of the mechanism in isolation. The first
line was developed by Dixit and Stiglitz [1977], Ethier [1982], Krugman
[1981], Judd [1985], Romer [1986], and Grossman and Helpman [1989,
1990]. Their models have endogenized the variety of goods by formulating
a tradeoff between the distortions arising from economies of scale
and preferences for diverse consumption or economies of complementarity
between intermediate goods in producing final goods. The endogenization
of the number of consumer goods by employing the CES utility function
in Dixit and Stiglitz [1977] and Judd [1985] captures the second aspect
of the division of labor at the downstream layer of the hierarchy.
Ethier [1982], Romer [1986], and Grossman and Helpman [1990] have
endogenized the second aspect of the division of labor at the upstream
layer of the hierarchy, using the CES production function. However,
their models cannot endogenize the level of specialization for each
individual. To endogenize the level of specialization, the degree
of self-sufficiency of consumers and the range of production of each
individual have to be endogenized. However, the existence of the firm
is exogenously given in the models, therefore, they cannot explain
the emergence and development of the institution of the firm. In an attempt
to endogenize the emergence and the development of the institute of
the firm, Borland and Yang [1994] and Yang and Ng [1995] apply inframarginal
analysis, which implies total benefit-cost analysis across corner
solutions in addition to marginal analysis for each corner solution,
to dynamic and static general equilibrium models involving the institu-tion
of the firm within the new classical framework with consumer-producers,
economies of specialization, and transaction costs. They show that
as division of labor evolves, the institu-tion of the firm will emerge
from the division of labor if transaction efficiency is lower for
intermediate goods than that for labor employed to produce these intermediate
goods. The function of the asymmetric structure of residual rights
is to get the activity with the lowest transaction efficiency involved
in the division of labor while avoiding direct pricing and marketing
of the activity, such that the division of labor and productivity
are promoted. The Yang and Ng [1995] model, which formalizes Coase
and Cheung's theory of the firm (Coase [1937] and Cheung [1983]),
can explain the emergence of the firm from the division of labor and
other endogenously complicated stories in the absence of uncertainties,
exogenous com-parative advantages, incomplete contracts, and other
exogenous complications. However,their models have not endogenized
the number of layers in the hierarchical structure of the division
of labor. As the number
of layers of hierarchical structure of the division of labor and the
emergence and development of the firm are endogenized, the dividing
line between the cen-tralized hierarchy within the firm and the decentralized
hierarchy in the market may also be endogenized. The models of centralized
hierarchy have been developed by Williamson [1967], Calvo and Wellisz
[1979, 1978], Keren and Levhari [1979, 1982, 1989], Rosen [1982],
Radner [1992], and Qian [1994]. In these models a decision maker (a
manager of a company or a central planner) can choose the number of
layers and the number of elements at each layer of the hierarchy.
Yang [1994] has developed a model of decentralized hierarchy of wholesale
and retail network where no single decision maker can choose the two
numbers. In the real world, the centralized hierarchies coexist with
the decentralized hierarchies. Some centralized hierarchies within
the firm may be part of a large decentralized hierarchy in the market
network. The question then is: What mechanism in a general equilibrium
model de-termines the structure of the centralized hierarchy within
the firm cum the decentralized hierarchy in the market and what are
the determinants of the dividing line between centralized and decentralized
hierarchies? This question relates not only to the theory of the firm
and the literature of vertical integration, but also to the literature
of specialization and the division of labor. It is the hierarchical
structure of division of labor that sets up a frame for the structure
of centralized hierarchy cum decentralized hierarchy of economic organization.
Hence, simul-taneous endogenization of the level of division of labor
and the structure of centralized hier-archy cum decentralized hierarchy
has important implications for economics. A natural
conjecture is that a synthesis of the thinking along these four lines
may enable us to decipher the mechanism behind the concurrent increases
in specialization, pro-duction roundaboutness, product diversity,
and productivity and the emergence of the firm. If transaction
efficiency is extremely low, then the gains in introducing more layers
of the hierarchy and further horizontal and vertical division of labor
are outweighed by transac-tion costs. In this case, each individual
will choose autarky, that is, he self-provides all pro-ducer goods
and consumer goods. A tradeoff which still exists in autarky is between
econo-mies of specialization and economies of roundaboutness. If a
large number of producer goods are produced in autarky, a person's
level of specialization in producing each good must be low. Thus,
in autarky the foregone economies of specialization due to the production
of many producer goods at many layers of the hierarchy of goods outweigh
the gains to produc-tion roundaboutness. Therefore, in autarky each
individual will choose a hierarchy of goods with a small number of
layers, so that he can capture more economies of specialization by
concentrating his limited labor in a few activities that directly
relate to his final consumption. This implies that some sophisticated
producer goods based on a large number of layers of the hierarchy
are unlikely to exist in autarky. For example, it is likely that only
food and clothes will be produced using labor alone but no tractors
and weaving machines will be produced in autarky. If transaction
efficiency is extremely high, then people may choose a greater degree
of horizontal as well as vertical division of labor and in the meantime
maintain each individual's level of specialization at a high level
through the division of labor between many differ-ent specialists.
Therefore, a high transaction efficiency may elicit some new layers
in the hierarchy of goods and new producer goods at each layer in
the hierarchy. The emergence of the new layers and new producer goods
implies new technology and new industries which are associated with
industrialization and endogenous technical progress. Hence, a general
equilib-rium model may be used to predict concurrent increases in
the number of producer goods at each layer, in the level of specialization,
and in the number of layers of the hierarchy of goods. The high
level of division of labor generated by great transaction efficiency
can be coordinated either by the goods market or by the labor market.
If the transaction cost coeffi-cient for labor is smaller than that
for intermediate goods, then the institution of the firm which is
associated with the labor market will emerge from a high level of
division of labor in producing final and intermediate goods. If an
intermediate good is an intangible management service instead of a
tangible machine, then a particular structure of ownership of a firm
can be used to incorporate the activity with the lowest transaction
costs involved in the division of labor, while avoiding direct pricing
and marketing of the activity. We will show that the number of producer
goods at each layer and the number of layers of the hierarchy of goods
increase as transaction efficiency is improved. If many intangible
intermediate services are involved in the division of labor and each
of these needs a type of firm to indirectly price its input and output,
then the hierarchical structure of the division of labor will be organized
by several separate simple centralized hierarchies within the firm.
The centralized hierarchies will be connected together by a decentralized
hierarchy of network of transactions in the market. If all roundabout
productive activities emerging from a high level of division of labor
are tangible and have a small transaction cost coefficient in the
market for goods, compared to that of the market for labor, then centralized
hierarchies within the firm are not needed. In section 2, a model with consumer-producers,
increasing returns to specialization, and transaction costs is specified.
Section 3 investigates individuals' decisions and equilib-rium. Section
4 uses two types of comparative static analysis to investigate the
evolution of economic structures and the emergence of the institution
of the firm. The final section con-cludes the paper.
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