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Department of Economics And Xiaokai Yang Department of Economics, Monash University
and * The authors are grateful to the referee
for Review of Development Economics, Jeff Borland, Bob Rice, and participants
of an AEA session on development economics and of International Symposium
on Dynamic Modeling for helpful comments. Financial support from Australia
Research Council is gratefully acknowledged. We are responsible for
any remaining errors.
Pricing costs and information problems are
introduced into a framework with consumer-producers, economies of
specialization, and transaction costs to predict the endogenous and
concurrent evolution in division of labor and in the information of
organization acquired by society. The concurrent evolution generates
endogenous growth based on the tradeoff between gains from information
about the efficient pattern of division of labor, which can be acquired
via experiments with various patterns of division of labor, and experimentation
costs, which relate to the costs in discovering prices. The concept
of Walras sequential equilibrium is developed to analyze the social
learning process which is featured with uncertainties of the direction
of the evolution as well as a certain trend of the evolution. Introduction The purpose of the paper is two fold. First,
it shall explore the implications of interactions between evolution
in division of labor and evolution in information about the efficient
pattern of division of labor that is acquired by society through the
price system for economic growth. Second, we shall develop the notion
of Walrasian sequential equilibrium to model concurrent evolution
in division of labor and in information of organization acquired by
society. Recent development of endogenous growth model,
represented by Judd [1985], Romer [1990], Grossman and Helpman [1989],
and Yang and Borland [1991] not only explains economic growth by endogenous
accumulation, but also explains growth by evolution in division of
labor which generates increases in the number of goods and in individuals'
levels of specialization as two aspects of economic development. The
spontaneous evolution in division of labor in the models not only
generates growth phenomena (growth in per capita real income, in productivity,
and in per capita consumption) in the absence of exogenous changes
in parameters, but also generates development phenomena, such as increases
in individuals' levels of specialization, in the number of traded
goods, in the degree of market integration, in the degree of diversification
of economic structure, in the number of markets, in income share of
transaction costs, and so on. In contrast, neoclassical growth models,
represented by Ramsey [1928], can only generate evolution in per capita
real income or in per capita consumption, although they may generate
endogenous growth in the absence of exogenous changes in parameters,
as shown by Barro and Sala-i-Martin [1995]. However, evolution in division of labor in
the literature of endogenous growth is generated by a deterministic
mechanism based on individuals' dynamic decisions with infinite horizon.
This evolutionary process involves no uncertainties. As Nelson [1995]
points out, real economic growth process is an evolutionary process
that is featured with uncertainties of the direction of the evolution
and with a certain trend of the evolution. The first purpose of the
present paper is to develop an endogenous growth model that generates
an evolutionary process of division of labor, characterized by the
two features. Since productivity depends on the level and
pattern of division of labor that is chosen by individuals while information
about the efficient level and pattern of division of labor acquired
by society determines which level and pattern of division of labor
will be chosen, the dynamic nature of the information acquisition
is essential for us to understand economic development. As shown by
Yang and Ng [1993], an individual's decision on his level and pattern
of specialization is always a corner solution. As he changes his level
of specialization, he discontinuously jumps from a corner solution
to another corner solution. Hence, a person can only use total benefit-cost
analysis to identify the optimum corner solution after he has conducted
marginal analysis of each corner solution. The discontinuity of decision
variables across corner solutions generates two kinds of complexities.
Suppose it takes a period of time for a person to try a corner solution,
then for a given set of prices, a person can sort out the optimum
corner solution only after a sufficiently large number of periods.
However, market prices that are available are determined by each and
every individuals' decisions to choose a certain corner solutions.
For instance, no market prices will be available if all individuals
choose an autarkic corner solution that involves no trade (that is,
quantities of traded goods are 0). Hence, individuals' decisions to
choose corner solutions determine what information on prices is available,
while the information determines individuals' decisions in choosing
their levels and patterns of specialization (or in choosing corner
solutions). When time dimension is spelt out, the interactions between
information and dynamic decisions will generate concurrent evolution
in information about the efficient pattern of organization acquired
by society and evolution in the level of division of labor that is
chosen by individuals. An example may illustrate the nature of the
information acquisition process. Founding of McDonald restaurant network
can be considered as an experiment with a pattern of high level of
division of labor between specialized production of management and
planning and specialized production of direct services within the
franchise and between specialized production of food and specialized
production of other goods. Since all variables and demand and supply
functions are discontinuous from corner solution to corner solution,
marginal analysis based on interior solutions cannot provide the founder
of this franchise with the information for right decision. The founder
of McDonald restaurant network decided to use the market to experiment
with his new pattern of business organization that involves a higher
level of division of labor within the franchise and between the franchise
and the rest of the economy. Instead of adjusting prices at the margin,
he tried a price of restaurant services that was much lower than the
prevailing price of restaurant services. According to his calculation,
the higher level of division of labor would generate productivity
gains, on the one hand, and more transaction costs, on the other.
His franchise arrangements may reduce transaction costs to the extent
that the benefit of the higher level of division of labor outweigh
its cost, so that the substantially lower price of services can stand
with the test of the social experiment. This idea was substantiated
later, as we have seen in real world. However, the founder may go
to bankruptcy if the business was proved by the social experiment
to be inefficient compared to the prevailing pattern of organization
prior to the experiment. But the social experiment through the price
system is necessary for society to acquire the information about the
efficient pattern of division of labor, even if it generates business
failure because of the interdependency between decisions in choosing
a pattern of organization and available information of prices and
because of discontinuity of decision variables between different patterns
of division of labor. Kreps and Wilson's concept of sequential equilibrium
might be a vehicle for analyzing the interactions between dynamic
strategies and information. However, it is a formidable job to endogenize
evolution in division of labor in addition to endogenization of the
interactions between dynamic decision and information using their
concept. Usually, even without the endogenization of evolution of
division of labor, only extremely simple models of sequential equilibrium
can be solved. Hence, the second purpose of the paper is to develop
the concept of Walrasian sequential equilibrium that makes modeling
of endogenous evolution in division of labor and evolution in information
of organization tractable. The concurrent evolution in division of
labor and in information acquired by society through the price system
are based on adaptive behavior and on limited horizon, so that it
is closer to a real economic development process than what is predicted
by Romer [1990] and Yang and Borland's endogenous growth models [1991]
with spontaneous evolution in division of labor based on perfect information
and infinite decision horizon. Somehow, the present paper bridges
the literature of endogenous growth and the literature of bounded
rationality (see Conlisk [1996] for a recent survey on the latter
literature). In the model to be considered, there are many
ex ante identical consumer-producers with preferences for diverse
consumption and production functions displaying economies of specialization.
Complicated interactions between economies of specialization and transaction
costs in the market generate uncertainties about real income for different
patterns of division of labor. Each person's optimal decision is a
corner solution. Combinations of different corner solutions generate
many possible candidates (corner equilibria) for general equilibrium.
Individuals may experiment with each possible pattern of division
of labor via a Walrasian auction mechanism at a point in time and
thereby eliminate uncertainties and acquire information about the
efficient pattern of division of labor over time. However, the costs
in discovering prices generate a tradeoff between information gains
and experimentation costs in the information acquisition process.
A decentralized market will trade off gains from information acquisition
against experimentation costs to determine the equilibrium pattern
of experiments with patterns of division of labor over time. In the
process, individuals use Bayes' rule and dynamic programming to adjust
their beliefs and behavior according to updated information. Hence,
we refer to the solution to the model as Walras sequential equilibrium.
The determinants of the dynamics of the Walras sequential equilibrium
are transportation cost coefficient for trading one unit of goods,
degree of economies of specialization, discount rate, and pricing
cost coefficient. Suppose the transportation cost coefficient
and the degree of economies of specialization are fixed. If pricing
costs are high, then the market will not experiment with any sophisticated
pattern of division of labor. If pricing costs are sufficiently low,
all possible patterns of division of labor will be experimented with.
In this process, simple patterns of division of labor are experimented
with before the more complicated ones are, so that a gradual evolution
of division of labor may occur. If pricing costs are at an intermediate
level, then only simple patterns of division of labor will be experimented
with, so that society cannot acquire all information about the efficient
economic organization. For a fixed pricing cost coefficient, more
patterns of division of labor will be experimented with as the transportation
cost coefficient decreases and/or as the degree of economies of specialization
increases. Our concept of Walras sequential equilibrium
is an analogue to Kreps and Wilson's concept of sequential equilibrium.
In the game model of Kreps and Wilson [1982], players use dynamic
programming to choose strategies for a given sequence of their beliefs
of their opponents' types and the sequence of beliefs is updated according
to the Bayes rule and the observed strategies. In our model, individuals
use dynamic programming to solve for their experimentation sequence
with different patterns of division of labor for given information
of the ranking of each person's incomes generated by various patterns
of specialization. The information is updated according to the Bayes
rule and observed prices. The difference between our concept of Walras
sequential equilibrium and Kreps and Wilson's concept of sequential
equilibrium will be discussed in section 3. Compared to Again et al [1991], the result
in this paper is more limited to a specific model because the discontinuity
of payoff functions in a general equilibrium model based on corner
solutions makes intractable a model that is as general as Aghion's.
Because of corner solutions and discontinuity of payoff functions
across corner solutions, we assume the absence of information in this
paper, while incomplete information is assumed in Aghion et al. An
experimentation cost in addition to the discount rate is specified
as generated by the process of discovering prices. By contrast, the
experimentation cost in Aghion et al is generated only by the discount
rate. Finally, our model is a general equilibrium model while Aghion's
model is a partial equilibrium model. This makes our model more difficult
to manage, so that we confine attention to a specific model where
all individuals' decisions on learning by experimenting with the patterns
of economic organization are symmetric. The symmetry avoids the problem
of coordination and mismatch in experimentation with various patterns
of the division of labor, thereby keeping the model tractable at the
cost of realism. We leave the analysis of a more realistic model with
the coordination problem caused by information asymmetry, which may
generate interesting implications of the role of entrepreneurship
in experiments with economic organization, to future research. This paper is organized as follows.
Section 1 specifies an equilibrium model that endogenizes the determination
of the efficient pattern of the division of labor in a Walrasian regime.
Section 2 introduces a pricing cost and the information problem into
the model to generate a story about learning by experimenting with
various patterns of the division of labor. Section 3 solves for the
dynamic equilibrium and discusses the implications of the results. Inframarginal
Economics Society
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