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THE DIVISION OF LABOR, INVESTMENT, AND CAPITAL* Xiaokai Yang Harvard Center for International Development
and
This version: December 1998 * The author is grateful to the participants
of International Conference on Dynamic Modeling and of the seminars
at University of London, Monash University and Australian National
University, and the two referees for Metroeconomica for their comments
and criticisms. Special thanks are due to Don Snodgrass, Yew-Kwang
Ng and Jeff Borland for helpful discussion. I am responsible for the
remaining errors.
The purpose of the current paper is to use
a formal dynamic general equilibrium model to criticize saving and
investment fundamentalism which claims an unconditional positive relationship
between current saving and future productivity. This investment fundamentalism
is taken as granted in the growth models of Ramsey (1928), Solow (1956,
1964), Lucas (1988), Romer (1986, 1990), and Grossman and Helpman
(1989, 1990). The specification of production functions in all the
models implies that saving and investment will increase productivity
in the future by increasing capital per person. We may however ask why productivity in the
future can be increased by saving today. This positive relationship
did not exist two thousand years ago. For instance, two thousand years
ago, peasants invested corn seeds each year. But that investment could
only maintain simple reproduction without much increase in productivity.
Also, Chinese peasants invested in houses which were completely self-provided
in the 1970s. Productivity based on such investment in durable houses
was extremely low (Yang, Wang, and Wills, 1992). To the question Lucas and Romer will respond
by pointing to human capital generated by saving and investment. However,
we will again use the Chinese case to argue that investment in human
capital and education does not necessarily lead to an increase in
productivity. Chinese people have a special preference for saving
and for investment in education. However, this had not generated significant
productivity increases until the modern school and university system
was introduced into China at the end of the last century. In traditional
Chinese schools, there was no division of labor between teachers.
Each teacher taught students a broad range of knowledge, from literature
to philosophy. But in a modern university, there is a very high level
of division of labor between different specialist teachers and between
different specialized colleges. Also educated individuals are very
specialized in their professions after their graduation from universities.
It is the high level of division of labor that ensures high productivity
in providing education, so that investment in education can contribute
significantly to productivity progress. To our question above, Grossman and Helpman
might respond by pointing to investment in research and development.
However, Marshall attributed the invention of the steam engine by
Boulton and Watt to a deep division of labor in the inventing activities
(p. 256). Edison's experience is another evidence for the implication
of the division of labor for successful inventions. Not only Edison
did himself specialize in inventing electrical machines for most of
his life, but he also organized the first professional research institution
with more than one hundred employees who specialized in different
inventing activities (Josephson, 1959). The observation implies that investment in
physical capital goods, in education, or in research would not automatically
increase productivity in the future if the investment were not used
to develop the right level and pattern of division of labor. Hence,
the essential question around the notion of capital is not so much
as to how much we invest and save, but rather as to what level and
pattern of division of labor are used to invest in machines, education,
and research. The positive relationship between current
saving and future productivity assumed in the endogenous growth models
generates empirical implications that are called scale effects. Type-I
scale effect exists if there is a positive relationship between growth
rates in per capita GDP and investment rates. The AK model generates
type-I scale effect which is conclusively rejected by empirical evidence
(see Jones, 1995a) . This suggests that "the AK models do not
provide a good description of the driving forces behind growth"
(Jones, 1995a, pp. 508-509). The R&D based model generates a positive
relationship between the growth rates in per capita GDP and the level
of resources devoted to R&D, referred to as type-II scale effect
. Type-II scale effect is also rejected by the empirical observations
(Jones, 1995b). Jones (1995b) and Young (1998) have developed two
models to salvage the R&D-based model, but the modified models
still have type-III scale effect, a positive relationship between
the growth rate in per capita GDP and the growth rate of population,
which is also wildly at odds with empirical evidence surveyed by Dasgupta
(1995). As Jones (1995b) indicates, endogenous growth cannot be preserved
if the scale effect in the R&D-based model is eliminated. Now
endogenous growth economists are busy to find new models that can
avoid scale effects. The current paper will show there is a simple
way to avoid scale effects: formalize classical economic thinking
on investment and growth. The growth mechanisms described by most classical
economists do not have the nconditional positive relationship between
saving and productivity. Instead they emphasized the connection between
the division of labor and investment. Smith (1776) and Allyn Young
(1928) explicitly spelled out the relationship between the division
of labor, investment, and capital. According to them, capital and
investment is a matter of the development of division of labor in
roundabout productive activities. If there is a division of labor
between the production of final consumption goods (say food) and the
production of producer goods (say tractors) and if the production
of tractors takes time to complete due to, for instance, a significant
fixed learning cost, then the specialist producers of tractors cannot
survive in the absence of investment which is used to provide the
specialists with food before they can sell tractors. Hence, capital
is a vehicle for society to increase the level of division of labor
in roundabout productive activities. The high level of division of
labor can speed up the accumulation of knowledge through specialized
learning by doing, thereby generating productivity progress. The current paper will formalize the story
of investment and capital. A dynamic general equilibrium model will
be used to address the following questions. What is the relationship
between capital, which relates to saving and investment, and the division
of labor, which determines the extent of the market, trade dependence,
and productivity? What is the mechanism that simultaneously determines
the investment level and the level of division of labor? and What
are determinants of the equilibrium investment (saving) rate, interest
rate, growth rate, and the equilibrium level of division of labor? Our story of capital runs as follows. There
are many ex ante identical consumer-producers in an economy where
food can be produced out of labor alone or out of labor and tractors.
In producing each good, there are economies of specialized learning
by doing. A fixed cost is incurred in the period when an individual
engages in a job for the first time or when job shifting takes place.
Each individual can choose between specialization and self-sufficiency.
The advantage of specialization is to exploit economies of specialized
learning by doing and to avoid job shifting costs. However, it increases
productivity in the future at the expense of current consumption because
of an increase in transaction cost caused by specialization. Moreover, in producing a tractor, there is
a significant fixed learning cost. The production of a tractor cannot
be completed until the learning cost has reached a threshold level.
Hence, there are tradeoffs among economies of specialized learning
by doing, economies of roundaboutness, transaction costs, and fixed
learning costs. Each consumer-producer maximizes total discounted
utility over the two periods with respect to the level and pattern
of specialization and quantities of goods consumed, produced, and
traded in order to efficiently trade off one against others among
the four conflicting forces. The interactions of these tradeoffs determine
the nature of the dynamic equilibrium for the economy. If the transaction
cost coefficient is sufficiently great, the economy is in autarky
in all periods depending upon the level of fixed learning cost and
the degree of economies of roundaboutness this may involve each individual
self-providing food, or each individual self-providing both food and
tractor, or the evolution in the number of goods. If the transaction
cost coefficient is sufficiently small and economies of specialized
learning by doing and of roundaboutness are significant, in the dynamic
equilibrium the economy is in a market structure in which individuals
specialize in the production of either tractor or food and trade occurs.
For the division of labor there are two patterns of investment and
saving. If the fixed learning cost in producing tractor is not large,
each individual will sacrifice consumption in period 1 to pay transaction
costs in order to increase the level of division of labor, so that
productivity in period 2 can be increased. This is a self-saving mechanism
which does not involve the transfer of a saving fund from an individual
to another. Also, an evolution in the level of specialization and/or
in the number of goods may take place in the dynamic equilibrium if
the transaction cost coefficient and the degree of economies of specialization
and of roundaboutness are neither too large nor too small. If the
fixed learning cost in producing tractor is so large that the production
of a tractor cannot be completed until time for specialized learning
by producing tractor is longer than one period, then an explicit saving
arrangement which involves a loan from a specialist producer of food
to a specialist producer of tractor in period 1 is necessary for specialization
in producing roundabout productive tractors. Under the assumptions of a great fixed learning
cost in producing tractors, a small transaction cost coefficient,
and significant economies of specialized learning by doing and roundaboutness,
dynamic general equilibrium yields the following picture. A specialist producer of food produces food
using his labor only and makes a loan in terms of food to a specialist
producer of tractors in period 1 when the production of tractors is
not complete. In period 2, a specialist producer of tractors sells
tractors to a specialist farmer in excess of the value of his purchase
of food in period 2. The difference is his repayment of the loan received
in period 1. Per capita consumption of food in period 1 is lower than
in an alternative autarkic pattern of organization. But in period
2, tractors are employed to improve productivity of food. The discounted
gains will be more than offset the lower level of per capita consumption
in period 1 if the transaction efficiency coefficient and economies
of specialized learning by doing and roundaboutness are great. Economic
growth takes place not only in the sense of an increase in per capita
real income between periods, but also in the sense that total discounted
real income is higher than in alternative autarkic patterns of organization.
The model generates the following empirical
implications. Returns to investment are higher when division of labor
evolves than when the potential for further evolution of division
of labor has been exhausted. Hence, the returns to capital in a developing
economy experiencing evolution of division of labor are higher than
in a developed economy where the potential for the evolution has been
nearly exhausted. Since transaction efficiency determines if there
is more lucrative opportunity for evolution of division of labor,
returns to investment used to develop division of labor are higher
in a developing economy with higher transaction efficiency than in
a developing economy with low transaction efficiency even if the latter
is short of capital compared to the former. In addition our model
avoid all kinds of scale effects that are the common features of the
AK models and R&D based models and that are rejected by empirical
evidence. The rest of the paper is organized as follows. Section 2 presents the model. Section 3 solves for dynamic equilibrium. In the final section the paper's conclusions are summarized. Inframarginal Economics Society www.inframarginal.com |