The Dual Economy
1. Introduction
2. Classical Approach
2.1 Lewis—Fei—Ranis models
2.1.1 Traditional activities sector
2.1.2 Modern activities sector
2.1.3 Interplay
2.2 Comments and Criticism
3. Neoclassical Approach
3.1 Jorgenson model
3.1.1 Agriculture sector
3.1.2 Manufacturing sector
3.1.3 Development
3.2 Comments and Criticism
4. Neoclassical Approach: An Extension
4.1 Amano model
4.1.1 Agriculture sector
4.1.2 Industrial sector
4.1.3 Development
5. Conclusion.
Appendix A: Agricultural Surplus
1
Introduction
A
distinctive feature of most less developed economies is the predominance of
an agricultural sector characterized by widespread underemployment and high
rates of population growth, side by side with a small but hopefully growing
industrial sector. In such a dualistic (two sector) setting the heart of the development effort may be said to lie in the gradual shifting of the center of gravity
of the economy from the agricultural to the industrial sector. Such a process
can be gauged in terms of the reallocation of the population between the two
sectors in order to promote a gradual expansion of industrial employment and
output.
A complete understanding of the growth process in such a dualistic economy
obviously requires a careful analysis of both sectors and their interdependence.
Fortunately, there is no shortage of dual economy models. In this chapter we will
examine the key models of the dual economy. For each model we will examine
the structural characteristics prevailing in the two sectors taken individually
and then proceed to examine in general outline the nature and extent of the
interdependence between the two sectors in the context of a continuous process
of labor reallocation and growth.
1
This chapter is organized as follows: in this introduction we will first attempt to provide a general definition of a dual economy. Next, we will try to
motivate the reader by asking: “What can we hope to achieve by imagining an
economy composed of dual sectors?” Finally, we will briefly outline some controversial issues arising from the dual economy models, and identify two strands
or approaches of the dual economy.
In section 2 we will examine the first of two approaches to the dual economy:
the classical approach. In section 3, we will examine the other approach: the
neoclassical approach. In the following section, 4, we will extend the neoclassical
approach and conclude this chapter in section 5. We now proceed with an
introduction to this chapter.
Let us begin by describing a dual economy. There are two aspects to the
definition of a dual economy. The first is that when we speak of a dual economy
we are talking about a theoretical model, and not a real dualistic economy. Of
course, we must hope that a theoretical model of a dual economy approximates
a real dual economy. The difference between a theoretical and practical dual
economy is that a theoretical model must, by nature, be more general and abstract than a real dual economy, such as those of most less developed economies.
This means that a theoretical construct may include many features and characteristics not shared by all real dual economies. So we have to be careful— we
are not making statements about reality when looking at an economy through
a dual economy lens. Rather we hope to highlight dualistic aspects of less developed ‘real’ dual economies, which are dominated by an agricultural sector.
Secondly, the possibility of theoretical models of the dual economy precludes a
single definition. This is because that mysterious entity, theory, allows for very
many diverse models of dual economies. To make matters more complex, these
various models can be identified with numerous strands which differ fundamentally. Clearly then, the dual economy, as a theoretical concept is difficult to
define.1
Despite these difficulties, we’ll try to define the dual economy anyway: the
dual economy consists of two sectors which can be characterized in a number of
ways, each having suggestive advantages and each carrying with it the possibilities of error as well. For example, some dual economy models deal with the rural
and urban parts of the economy as if they were conterminous with agriculture
and industry, or with modern and traditional activities. We can clearly supply
examples of rural activities that are modern and industrial, or urban firms that
are traditional in substance and spirit. So given the fact that the two sectors in
a dual economy can be referred to in many ways, we are forced to adopt some
labels for now: let us label the two sectors “agriculture” and “industry”. We
will relax these ‘temporary’ labels and use the correct references when a particular model or approach requires so. With convenient nomenclature in hand, we
are ready to provide a general definition of the dual economy.
The agricultural and industrial sectors (or equivalently, any two sectors in a
1 Of course it is not too difficult to define, identify, or categorize a real dual economy. See
the pioneering work of Kuznets and see Syrquin and Chenery’s paper in the Handbook of
Development Economics, Volume I.
2
dual economy) are asymmetrical, and thus dualistic, in terms of organizational
and production characteristics. The organizational asymmetry stems from
the different initial endowments conditions of the two sectors, their spatial characteristics, as well as their differential potential deployment of technology. The
production asymmetry arises because agriculture disposes over something
approaching “fixed” inputs of land, very little capital, with large pre-existing
inputs of labor. On the other hand, industry requires virtually no land, while
capital can be accumulated and labor absorbed as needed. Together the production and organizational asymmetries imply that the two sectors will develop
in markedly different ways. In other words, there is static and, to a certain
extent, dynamic asymmetry between sectors of a dual economy.
We now question the utility of a dual economy: “Why do we need it and
where does it take us?” In this respect we note that economic development
in a dual economy can be characterized by essentially one way flows of labor
and resources from agriculture to industry, resulting in a shifting of the economy’s center of gravity from agriculture to industry. This shift is known in the
literature as “structural change”. All dual economy models seek to explain or
describe structural changes in an economy— this obviously warrants a further
examination of structural change. This we do below.
The concept of structural change has many uses and abuses2 and requires
clarification. We use ‘structure’ in the sense of the relative importance of the
sectors in an economy, where the relative importance is measured in terms of
production and factor use. Casual observation tells us that the agricultural
sector dominates the total economy of a less developed country. This is true in
terms of production (where agricultural production is often between 50%-70% of
total GDP) and factor use, since typically about three-quarters of the population
of a less developed economy is in agriculture. Now, structural change is
said to occur during a transition from a low income agrarian rural economy to
an industrial urban economy, with substantially higher capita incomes. Note
that structural change includes structural sequences such as: (i) labor flows
from agriculture to industry concomitant to enlargement of the industrial sector
and corresponding to a dimunition of agriculture, (ii) the rationalization of
agricultural production, (iii) capital accumulation in agriculture and industry,
(iv) increase in total factor productivity, and (v) rise in savings rates. This list
of structural sequences is in no way comprehensive, but it serves to highlight
the salient aspects of structural change.
It is important to note that structural change has been historically uniformly
ubiquitous, and it can therefore be said to have been at the center of economic
development. Kuznets, for example says: “Some structural changes, not only in
economic but also in social institutions and beliefs, are required, without which
modern economic growth would be impossible”. Elsewhere, Abramovitz adds:
“Sectoral redistribution of output and employment is both a necessary condition
and a concomitant of productivity growth”.3 Clearly, structural change is and
2 See
Machlup (1963).
see Syrquin (1988), Syrquin & Chenery (1986).
3 Also
3
must be an integral part of any comprehensive model of development. It is in
this respect that the dual economy is important: it is formulated because of a
need to explain, describe and analyze one of the most fundamental aspects of
development— structural change.
In looking at or characterizing a less developed economy as ‘dual’, the many
models of the dual economy attempt to explain and describe structural change.
Thus, when studying the models of a dual economy, we seek to gain an understanding of the various aspects and dynamics of structural change. But lest we
expect a complete explanation, we should note that the dual economy models
treat structural change, and thus structural sequences, as stylized facts.4 Models of dual economies simulate or describe economic development based on these
facts. Thus, like any theoretical model, it cannot and does not tell us what is
actually going on, but how a transition from agriculture to industry might occur
if “things went smoothly”. It is a model of ‘idealized development’.
That the dual economy is a model of idealized development has escaped the
attention and cognizance of many economists, and we hope that the reader does
not commit the same error. Overlooking the fact that models of dual economies
are theoretical treatments has over the course of the last four decades resulted
in massive economic and social costs when policy makers have attempted to
duplicate structural change simply because they think that such ‘interventionist’
policies are called for and implied by models of the dual economy. This is
incorrect and we must be extremely cautious not to make the same error.
To illustrate what we mean, let us focus on one particular aspect of structural change: the enlargement of the industrial sector with a corresponding
decline in agriculture’s size. Many economists believe that because structural
change has been ubiquitous, it must be replicated, no matter what the means or
cost. These economists believe that agriculture does not require resources or a
favorable policy environment because its relative share of the economy declines.
Hence, many less developed countries have wildly pursued industrialization policies without regard to agriculture, or to the fact that there have always been
increases in productivity and rationalization of production in agriculture before any development has taken place— we will see more on this in section 2.2.
Instead, economists in the past have completely overlooked the need for rapid
agricultural growth. As a result, many economies are now cursed with economic
stagnation, and will continue to do so until agricultural sectors see more growth.
All in all, economists forget that the agricultural sector is important because it
provides food— one cannot assume that food production will always be forthcoming. Policies designed to increase food production, rationalize production,
increase agrarian productivity and growth have been in scarce supply— we hope
you take note of the serious catastrophic consequences of taking the lessons of
structural change and the dual economy literally. We hope that the discussion
in this chapter will convince you of agriculture’s importance. One additional
point though. It is easy to say agriculture has been neglected simply because
4 Studies of structural change are in a sense descriptions of real dual economies, while
dual economy models are theoretical treatments of the stylized facts thrown up by structural
changes studies.
4
economists were in a hurry to replicate the process of development experienced
by the now developed world, i.e., structural change in the sense that the center
of gravity shifted from agriculture to industry. Instead, it is important to realize that when government planners intercede, they do so within a framework
of objectives and constraints, which is ultimately conditioned by the prevailing
academic understanding of how economic growth proceeds. And the dominant
paradigm of development for the last four decades has been the dual economy.
It still is one of the most flexible models around, used for understanding and
designing policies for migration, (un)employment, taxation, and food supplies.
Therefore, to begin understanding why economists have been prone to think
that agriculture can and should be squeezed on behalf of industry, we should
start with an examination of the dual economy and its various models. This
will also serve our concern with the agricultural sector, especially its role and
position in the models of the dual economy. Additionally, it serves our preoccupation with agriculture— the dominant theme in this book. We now briefly
identify two major strands of the dual economy models.
The literature on the dual economy has had two strands. The first strand has
been called the classical model or approach. The classical approach includes
the Lewis (1954) and Fei-Ranis (1961) models. The second strand is referred
to as the neoclassical model or approach and includes the work of Jorgenson
(1961) and Amano (1980). A partial synthesis of the two approaches can be
found in Dixit (1970). In this chapter we will be analyzing these two approaches.
But before we begin with the classical approach in section 2, it would serve us
well if we briefly describe what differentiates the classical from the neoclassical
approach.
The classical and neoclassical models differ in their conception of:
(a) Production conditions in the agricultural sector, and
(b) Dynamic of the system.
Examining (a) first, we note that the classical approach postulates a production
function, f (L), of the type depicted in Figure 1.1. In the introduction to the
classical approach we will explain why f (L) has the shape that it does. In contrast, the neoclassical agricultural production function, g(L), shown in Figure
1.2, differs markedly— the reasons for which will be explained in the introduction
to section 3. Let us further differentiate between the two approaches.
From Figure 1 we can see that production conditions in the agricultural
sector differ for each model. Clearly, we cannot talk in terms of an agricultural
sector when it involves different specifications in the two approaches. Therefore,
to make matters easier, we label the ‘agricultural sector’ in the classical approach
the traditional sector, while the neoclassical agricultural sector retains its label.
We have labelled the classical agricultural sector the traditional sector
because it is traditional, as will be explained further in section 2. For now, let
us just say that the initial conditions of the traditional sector imply that there
exist traditional activities in the classical agricultural sector. For example, the
initial condition of abundant labor on fixed land in the presence of no technical progress leads to diminishing returns to labor and high man/land ratios— a
5
Figure 1: Production Conditions in the Classical and Neoclassical Agriculture
Sectors
characteristic typical of traditional activities such as peasant farming and pastorialism. This of course means that the classical approach differentiates between
the dual sectors on the basis of the kind of activity (i.e., traditional or modern),
while the neoclassical approach, as we’ll shortly see, differentiates on the basis
of the kind of product, i.e., agriculture and industry.
That traditional activities are characterized by diminishing returns to labor
is expressed in Figure 1.1. The total product curve in the traditional sector is
completely flat for a proportion of labor. We should emphasize that the classical approach often segues the concepts of labor measured in terms of number
of workers and hours of labor— we will clear up this confusion in chapter 2, but
you must be aware of this aspect of the classical approach to the dual economy. Coming back to the discussion we see that a flat total product curve is
equivalent to a zero marginal product of labor (M P L = 0), implying that there
is redundant, or surplus, labor in the sense that labor may be withdrawn
from the traditional sector without a loss in output. Thus, this surplus labor
can be reallocated to the “modern” sector (this being the classical version of
the industrial sector) where it may be used to expand this sector, all without a
loss in the traditional sector output. In a sense therefore, development in the
classical model is “costless”.5
On the other hand, the neoclassical approach characterizes its dual sectors
5 Costless at least to a certain extent because as is evident from Figure 1.1, when that
much labor has been withdrawn from the traditional sector that we are at the positively
sloped portion of the total product curve, then there will be a decline in traditional output as
labor is reallocated from the traditional to the modern sector.
6
on the basis of product, and in the context of less developed economies the
natural choice is agriculture and industry. The reason why the neoclassical approach does not characterize the dual sectors on the basis of activity is because
it assumes that no matter what the man/land ratio, economic activities will
always be characterized by M P L > 0. Thus, the neoclassical approach does
not assume the existence of excess labor in the sense used above. Hence, when
labor is reallocated from the agriculture to the manufacturing sector, there will
be a loss in agricultural output. Clearly, in contrast to the classical model, there
is no such thing as a ‘costless’ development in the neoclassical model. Instead,
the neoclassical model relies on changes in the parameters of the economy, such
as population, technical progress, capital accumulation to effect development.
Thus, we see that axiomatic differences in the traditional sector and the agriculture sector leads to markedly different growth patterns and dynamics in the
two models— this captures point (b).
Coming back to point (a) above, we note that not only are there differences
in the production conditions of the (classical) traditional and (neoclassical) agriculture sector, but the two models differ in their characterization of organization
in these sectors as well.6 This once again implies that development will proceed very differently in the classical and neoclassical approaches. In the coming
sections, we urge the reader to beware of these differences in production conditions and organizational structures in the traditional and agricultural sectors,
and particularly how these lead to orthogonal development paths in the two
approaches. We now proceed to the classical model.
2
2.1
The Classical Model
Lewis-Fei-Ranis Model
In this section we will study two dual economy models belonging to the classical
approach. These are the Lewis (1954) and Fei-Ranis (1961) models. As its name
suggests, the classical approach borrows many of its assumptions from classical
economics. So, before we plunge into a detailed discussion of the Lewis and
Fei-Ranis models, it will serve us to examine those assumptions borrowed from
classical economics. While we cannot hope to treat this matter comprehensively,
an attempt will be made to lend the reader with some sort of a classical conceptual framework— we hope this enables you to think like a classical economist.
We begin with an examination of the assumptions and concerns present in
the classical approach to the dual economy. The classicals were primarily concerned with the distribution of income and how this affected the growth process
in an economy. For a detailed discussion see book on classical economics.7
6 The sharp reader will note that within the classical (neoclassical) model, the traditional
(agriculture) sector is asymmetrical not only in the inter-model sense— i.e., the (classical)
traditional and (neoclassical) agricultural sector differ— but also in the intra-model sense,
that is, the traditional/modern sectors and the agriculture/industrial sectors, both in the
production and organizational characteristics.
7 See in particular, Lipsey, R., An Introduction To Positive Economics.
7
Having said this, let us examine some of the most fundamental assumptions of
classical economics.
To begin with, classical economics assumed that the agricultural sector any
economy was characterized by: (C1) The absence of technical progress; (C2) A
large and growing population; (C3) Land is “fixed”. A couple of comments are
necessary here. First, why did the classicals assume (C1)-(C3) for any economy? The reason is that at the time classical economics was formulated, many
economists, particularly those belonging to the Malthusian school, thought that
all economies were characterized by the assumptions above. Assumptions (C1)
and (C2) seem to be quite harmless in the sense that it isn’t too difficult to understand where they come from— after all, most classical economists functioned
in the nineteenth century, hardly a time for technical progress in the agricultural sector and times when population growth rates were very high, although
the pessimism of population rates outstripping agricultural production growth
rates contains a strong dosage of Malthusian doctrines. Assumption (C3) may
seem a bit perplexing. To see the logic behind this note, in typical classical
fashion, that (1) land, unlike other factors of production, is not reproducible—
it is not a produced means of production and is therefore fixed in quantity, and
(2) increases through extensive cultivation (that is, increasing cultivable land
through bringing in marginally inferior land, or just simply, cultivating new
land) and intensive cultivation (in which yield per unit land is raised through
technological progress) is not feasible because population pressures has already
pushed cultivable land to its limit. Besides intensive cultivation has been already
ruled out by virtue of assumption (C1).
Now, (C1)-(C3) taken together simply imply that agriculture is, or soon
will be, characterized by the presence of a large population relative to fixed
land— i.e., the existence of very high man/land ratios which in turn implies
that there are diminishing returns to labor. We have depicted this situation
in Figure 2. In Figure 2.1 we have the production contour lines M, M . These
production contours represent the production function in the agricultural sector
with various inputs of land and labor. The two ridge lines Ou∗ and Ov ∗ mark
off the region of factor substitutability. For example, below Ov ∗ the production
contours become perfectly horizontal indicating that, with land held constant,
any further increases in labor render that factor redundant, as output can no
longer be raised. The counter case— where the production contours become
perfectly vertical indicating that with labor held constant, any further increases
in land either through intensive or extensive cultivation will not be possible—
does not interest us because we have made the assumption that population is
large and growing. So, we return to the first case where production contours
are flat because of the fixity of land.
When an economy is endowed with say Ot units of land, we can see that
OG units of labor can be absorbed in agricultural production without becoming
redundant.8 . But in the case of an overpopulated economy, in which agricultural
8 This
is tantamount to the case of a low man-land ratio,
8
L
T
population is say OP ,9 we see that GP units of labor is redundant. We see
therefore how a high TL leads to diminishing returns to labor— so low in fact
that a major proportion of the agrarian population becomes unproductive to
the point of being redundant, a quality which we label as surplus labor.
That this is so is underscored in panels 1 and 3. In Figure 2.2 the total
product of labor curve (T P L) becomes completely flat after OG units of labor.
Whether you choose to measure labor in number or hours does not really matter.
But for simplicity, let’s say labor is measured in terms of number of workers.
This flat portion N M reflects that output can no longer be raised with additional
units of workers. Correspondingly, the M P L curve in Figure 2.3 reflects the
same result: after OG units of labor the M P L curve becomes completely flat
and equal to zero. Clearly, any additional units of labor after OG will not raise
output since M P L = 0.
This property, or rather, economic implication of M P L = 0 was adopted
by Rosentein-Rodan (1943) and Nurkse (1951) in the middle of this century.
More specifically, they realized that the classical assumption of agriculture sectors characterized by high man-land ratios offers a way for development, or
accounts for one way that a structural change may proceed: the presence of
redundant labor in the agricultural sector brought about by high TL means that
surplus labor or this parasitic population— so called because it does not contribute anything to output— can be transferred out of the agricultural sector
with no loss in agricultural output. Surplus labor is therefore a supply of labor which, given the preponderence of the agricultural sector in less developed
economies, is likely to be of major quantitative importance in the development
process of overpopulated less developed economies.
This is the classical tradition which Lewis inherited. His model of the dual
economy contained two analytical advantages over his predecessors. The first
was his logical account of how development would proceed in a dual economy
characterized by classical conditions. This is a point which will anyway be
impressed upon you repeatedly in the discussion to follow, so we will not pay
much attention it here. The second advantage was that the sources of surplus
labor (available for costless development) in the Lewis model were not only in
the agricultural sector but all those sections of the economy where resources
were so scarce relative to an economy with a large population (a situation also
known as a labor surplus economy, which is not to be confused with surplus
labor, which is simply redundant labor) that marginal product of labor was
forced down to zero.
We want to emphasize that it is the abundance of labor relative to a scarce
resource (land) which enabled the agricultural sector to be a source of labor offering the possibility of costless development in the Rosentein-Rodan framework.
Lewis, on the other hand, asked a very obvious question: “Are there other sections of an economy which may be sources of surplus labor?” Put another way,
this question becomes: “Are there other sections with high man/some-resource
ratios which cause labor to be unproductive to the extent of M P L = 0, i.e.,
9 Corresponding
to a high
L
T
9
Figure 2: Classical Production
10 Conditions in Agriculture
surplus labor?”
Before we answer this question, a slight digression is necessary. It might
appear that Ex Ante it makes no difference whether the agriculture sector is
the sole source of surplus labor or whether there are other sources of surplus
labor. We dispute this assertion, but we first note that Ex Post it certainly
pays to know whether surplus labor originates strictly in agriculture. Look: if
agriculture is the single source of surplus labor then the planner should have
focused on policies designed to tap this surplus labor in agriculture. On the
other hand, if there are sources of surplus labor other than agriculture, then
the scope of the model widens. Compared to the earlier case when agriculture
was the single source of labor the pace and extent of the development process
will be markedly different. Had the planner known this Ex Ante she could have
designed policies to take advantage of this situation.
Moreover, if agriculture is not the only source of surplus labor, then Ex Ante
knowledge of a comprehensive supply of surplus labor should not be taken to
mean that policies designed to reallocate labor from these ‘other’ sources of
surplus labor are equally applicable to agriculture. Another way to make the
same point is to note that when there are sources of surplus labor other than
agriculture, we may tend to think of agriculture as ‘just another source of labor’
and neglect its importance as a supplier of food. This is an important point
and we will return to it later in section 2.2.
Returning to our earlier query of whether agriculture is the single source of
surplus labor, we see that if we try to answer in the context of less developed
economies, the answer must be that there are indeed sources of surplus labor
other than the agricultural sector. Why? Casual observation tells us that overpopulated less developed economies have not only a shortage of land compared
to a large and growing population, but a shortage of all other resources, especially capital. Labor surplus economies are therefore characterized not only
by high man/land ratios but also high man/capital ratios. Thus, sections of
L
an economy which are characterized by high K
are also a source of surplus labor, which form a labor supply to the growing sections of the economy. In this
context, Lewis says:
“In those countries where population is so large relatively to capital
and natural resources ... there are large sectors of the economy
where the marginal productivity of labor is negligible, zero, or even
negative”.10
Those sections of the economy which are sources of surplus labor are collectively labelled the traditional sector.11 The traditional sector is so called
because economic activities tend to be what one may typically what one might
10 W. A. Lewis, ‘Economic development with unlimited supplies of labor, in Agarwala &
Singh, The Economics of Underdevelopment, p. 402.
11 Clearly, it is a monumental error— which has been made before and will undoubtedly be
made again— to equate the traditional sector with agriculture. True, agricultural activities in
most less developed economies may be traditional but the reverse does not hold true, as will
be clear from the examples of traditional activities in section 2.1.
11
label traditional— i.e., unproductive, uncommercialized, production units which
are frequently coincident with household units. The principal reason for traditional activities to be traditional is simply because of M P L = 0. It must be
pointed out that once we depart from ascribing M P L = 0 to high man-land
ratios and simply recognize that a more deeper cause is high man-capital ratios,
we get a better idea of why activities in surplus labor sections of an economy
tend to be traditional— these activities are not fructified by capital, which incidentally is another classical assumption invoked heavily in the classical approach
to the dual economy: (C5) Capital fructifies labor’s efforts. We can therefore
approach the issue of traditional activities from the other side. Using (C5) it is
clear that those sections of the economy, where high man-capital ratios persist,
will be characterized by activities “unfructified” by capital and thus resulting
L
in M P L = 0. A high K
in the absence of technical progress gives rise to highly
unproductive activities characterized by primitive technology and uncommercialized small-scale production units with surplus labor (again, in the sense that
additional labor will not affect output), and production units which frequently
coincide with households.
We can now see that the traditional sector as a source of labor supply, when
contrasted with the formulation where the agriculture sector was the single
source of labor, has an obvious analytical advantage: since the (theoretical)
supply of surplus labor in the Lewis dual economy is more comprehensive, development in this model can proceed costlessly to a greater extent.
Having introduced the traditional sector, let us quickly describe the “modern” sector. The modern sector is by a matter of difference what the traditional
sector is not. It is characterized by high capital/man ratios, commercialized
production, productive economic activities characterized by M P L > 0, and
production units which do not coincide with household units. We assume that
the modern sector, at the beginning of the development process in the Lewis
dual economy, is small compared to the traditional sector. But while it is presumed to be small it is assumed to be a growing sector. The Lewis model
does not explain, nor does it care, how or why the modern sector may begin
growing.12 Instead, it assumes that for whatever reason and source, there has
been an investment in the modern sector permitting its creation and viability
for future growth.
Having emphasized the initial conditions— and therefore the assumptions—
of the classical approach, we now discuss each sector, describing its structural
characteristics and then move on to a discussion of the development process in
the classical dual economy. Let us begin with the traditional sector. We choose
to discuss the Lewis and Fei-Ranis model collectively because the difference
between the two is the degree of exposition. They share the same assumptions.
though they label some concepts differently. We will point out these differences
whenever necessary.
12 In
this respect see Hussain, Sayed Mushtaq, (1968)
12
2.1.1
Traditional activities sector
We now examine some examples of traditional activities in less developed countries. The first and most prominent example is of course agriculture. Typically,
agricultural family holdings are so small that if some members of the family
obtained other employment the remaining members could cultivate the holding
just as well. Now, a slight digression: one can imagine this “constant output”
as a consequence of surplus labor in two ways:
(1) that there are so many workers on a piece of land that the departure of some
makes no difference to output, because overcrowding was previously so chronic
that the removal of some workers does not affect output. One can imagine, for
example, 500 people squeezed on 1 acre of land— clearly, if one worker departs
and 499 remain, production is very likely to remain at previous levels— surplus
labor is then said to exist.
(2) One can imagine that all that really matters to keep output constant is
that the total labor hours worked before and after the migration of a (or some)
workers remains the same. Under this scenario, we assume that the remaining
workers put in more labor hours, just sufficient to maintain total labor hours
worked, and hence output, at previous levels— again, surplus labor is said to
exist. The first scenario is compatible with sheer overcrowding— to such an
extent that the withdrawal of a worker makes no difference to output. The
second scenario is compatible with leisure satiation— there is so much leisure
that the remaining workers are glad to work harder. This second aspect is a
distinctly classical concept, for neoclassical economics as you know treats leisure
as a superior good.
The issue of what surplus labor is will be taken up in the next chapter. For
now, it must be reiterated that the Lewis model does not distinguish clearly
between which of the two scenarios of surplus labor is relevant. Lewis mentions
briefly the possibility of the remaining workers working harder but does not
develop the conditions for this, and seems to also suggest the first scenario at
various points. For the discussion of development in the Lewis model, it does
not really matter which scenario is more relevant, but the issue will become
important in chapter 2.
Let’s resume our discussion of the traditional sector: other examples of traditional activities are those in the so-called ‘informal’ sector: casual jobs such
as dock workers, coolies, jobbing gardeners, rickshaw pullers, lottery sellers and
petty retailing. All of these are characterized by high man/capital ratios, redundant13 labor and an organizational structure where family holdings typically are
the production units; thus the family, or part of it, participates in production
and earning— we will return to this point shortly. Clearly, while the traditional
sector consists of markedly different activities, it is the fact that all these activities are characterized by M P L = 0 that allows us to speak in terms of a
13 Lewis notes: “.. These occupations usually have a multiple of the number they need, each
of them earning very small sums from occasional employment; frequently their number could
be halved without reducing output in this sector”
13
traditional sector.
We now discuss M P L = 0. Firstly, we must emphasize that M P L = 0
arises not because of a lack of effective demand but because of a technology and
resource constraint. Secondly, Lewis does not claim that the entire labor force
in the traditional sector is characterized by M P L = 0; only that a substantial
portion of it is producing with M P L = 0. The reason for this is straightforward.
There are some traditional activities which may well be productive. But the
point remains that a major proportion of activities will be unproductive. Most
traditional activities in less developed economies have small holdings, whether
these are land or capital in the form of tools for example.
Furthermore, most agricultural traditional production units, and thus households, are spatially dispersed, creating a market with massive transportation
costs and slow dissipation of information. All this means that most traditional
activities (of which the major portion in less developed economies is the agricultural sector) will be unproductive in the sense of M P L = 0.
Thirdly, note that M P L = 0 is used to convey the spirit of unproductive
activity in the traditional sector. It is not an empirical statement nor is it,
Lewis claims, essential to the classical model. For example, Lewis notes that
if we ignore the question, “Which sections of the economy are characterized by
M P L = 0?”, and simply ask, “Which sections of the economy are a potential
source of surplus labor?”, the answer would include women. In Lewis’ opinion,
the point of M P L = 0 is to simply underscore the existence of a comprehensive,
massive source of labor supply to the modern sector. The economic activities of
women, Lewis emphasizes, are characterized by M P L > 0. As such M P L = 0
is used for convenience- to demonstrate the point that initial conditions of the
traditional sector give rise to unproductive or traditional activities, the agents
of which are a potential source of labor supply for the expansion of the modern
sector.
Fourthly, the existence of M P L = 0 in the traditional sector raises the issue
of compensation. From the point of marginal productivity calculus, it seems
curious that a worker could be working at M P L = 0 and yet earn a positive
wage. That workers must earn a positive wage is obvious. For if not, then
in an overpopulated economy with scarce food supplies forced by high manland ratios, starvation will prevail. Clearly some arrangement must exist in the
traditional sector by which workers earn a positive real wage despite M P L = 0.
This arrangement is best explained through the organizational characteristics
of the traditional sector. Given the large number of spatially dispersed workers
with M P L = 0, the frequent coincidence of households and production units,
the real wage in the traditional sector must be based on some institutional
sharing arrangement rather than on the marginal productivity calculus. Now a
slight digression.
Note that sharing arrangements pose no logical problems in the case of selfemployed workers. Consider for example the case of a family cultivating a plot
of land. Here the members of a family simply share in the work and the income.
Notice that this is only possible because the household is coincident with the
production unit, i.e., the farm. But the work and income sharing explanation
14
is not so simple when we consider cases where labor is employed, i.e., labor
is engaged in traditional activities for wages. Why would an employer pay a
positive wage when his workers are producing with M P L = 0? Lewis explained
that this was because in an overpopulated country:
The code of ethical behaviour so shapes itself that it becomes good
form for each person to offer as much employment as he can.. Social
prestige requires people to have servants.. This is found not only in
domestic service, but in every sector of employment.14
Notice that this notion of an institutional wage does not require that some of
the traditional labor force must be redundant in the sense that it can be removed without affecting output adversely— only that some proportion of the
traditional population receive a food allocation, or earnings, in excess of its
marginal product. It is in this sense that organizational dualism is an important feature of the labor market. Given the abundance of labor and relative
scarcity of cooperating factors, mainly land and capital, this is what is meant
by the phenomenon of underemployment: a situation in which productive
employment opportunities are limited not because of a lack of effective demand
but because of technological and resource constraints.
The initially heavy endowment of labor relative to land and capital means
that a substantial portion of the labor force faces a M P L = 0 condition which
requires, especially in the context of less developed economies, a wage well above
the neoclassical marginal product to be agreed upon by the community, the
family, the commune or whatever organizational structure exists. Such a wage
in excess of the marginal product may be set equal to the average product or—
in order to leave a surplus, say for the head of the family— at some percentage of
the average product. The LFR model assumes that real wage in the traditional
sector equals the average product of labor. Nor do we need to assume that
this institutional or bargain wage is constant over time. Such determination is
likely to persist as long as the supply of traditional labor remains disguisedly
unemployed in the sense that there are too many people relative to scarce
resources to permit a sharing nexus to be replaced by competitive rules.15
The existence of an institutional wage in the traditional sector should thus
not be confused either with assertions about M P L = 0, used for convenience in
formal modeling, or equated in general to the average product, again a matter of
sheer convenience. Instead, the basic assertion is that wages in the traditional
sector contain a strong dosage of output “sharing”, largely a function of the
fact that people cannot be readily be dismissed when household and production
units coincide and/or when decisions are made on a collective basis.
We should also note that by its definition, the traditional institutional wage
cannot be scientifically measured, but in the context of overpopulated less de14 Ibid.,
p. 403.
then is the definition of disguisedly unemployed: that portion of the traditional
sector which earns an institutional wage higher than its marginal product. Note that surplus
labor is not the same as disguised unemployment, though one can expect the two to go
together.
15 This
15
Figure 3: Total and Marginal Product in the Traditional Sector
16
veloped economies, the real wage is likely to be related to the consumption
standard as a floor.16 LFR, in the classical tradition, assume that the institutional wage is so low that it equals the subsistence consumption wage. Hence
the real wage in the traditional sector is a small but positive quantity.
In Figure 3 we have summarized the production and organizational characteristics of the traditional sector. Here we see in panel 1 that if the total
population in the traditional sector is OP then the surplus labor is equal to
GP . We also see that AP L is equal to MP
OP , which is the slope of the line OM .
We assume that the wage w persists in the traditional sector as long as there is
disguised unemployment in this sector. Thus, in Figure 3.2 it is clear that the
surplus labor (GP ) and part of the M P L > 0 portion of the population (OG),
earns a real wage w which is above M P L.17 To reiterate, workers in the tradiQ
tional sector whose wage, w = AP L = MP
OP = L , is above their M P L are called
18
disguisedly unemployed, and w persists in the traditional sector as long as
there is disguised unemployment. Another way to say this is that competitive
wage determination according to marginal product calculus will come in effect
only after the supply of the disguisedly unemployed, SP , is allocated out of the
traditional and into the modern sector. Our repeated statements that sharing
arrangements persist as long as disguised unemployment exists, serves to underscore the essence of the classical model, and how this manifests itself in the
LFR model. Indeed, the classical scenario of family enterprises, characterized
by work and income sharing, as well as subsistence wages is captured through
the concept of disguised unemployment— that portion of the labor force which
consumes in excess of its earnings. If you have been perceptive enough, you will
notice that we have not said anything about a connection between surplus labor
and sharing arrangements. That is because, there is no unambiguous relationship between surplus labor and work and income sharing. Indeed, surplus labor,
as will be demonstrated in chapter 2, can exist even if M P L > 0— a point which
serves to illustrate that surplus labor is not unique to M P L = 0— a condition
one can expect to hold with high probability in a sharing nexus.
Moreover, it is clear that the real wage in the traditional sector obviously
sets the floor to modern sector wages: if the modern sector is to attract labor
from the traditional sector, it must at the very least offer a wage equal or higher
than the real wage in the traditional sector. And here is where the possibility
of rapid and extensive growth exists: because w in overpopulated economy with
16 Institutional explanations of the greater than marginal product real wage in the traditional
sector has not been satisfactory to modern economists. Consequently many attempts have
been made to link up the determination of the institutional real wage to peculiarities of rural
organization, tenure arrangements, linked market failures etc. See Binswanger & Rosenzweig
(1984). The empirical reality of a gently upward-sloping supply curve has been demonstrated
in the case of the agricultural sector by Sen (1966)
17 i.e., The disguisedly unemployed in this sector is the portion SP .
18 We note here that Lewis labels the portion GP as surplus labor while SP is labelled
disguised unemployment. In contrast, Fei-Ranis label surplus labor as redundant labor while
the disguisedly unemployed are also known as surplus labor in their model. Clearly, there
is enormous scope for confusion, and to keep matters tractable, we stick with Lewis’ usage:
i.e., surplus labor is the portion GP (which coincides with Fei-Ranis’ redundant labor force),
while the portion SP is the disguisedly unemployed portion of the labor force.
17
scarce resources will be close to subsistence level, the modern sector need only
pay a slightly higher wage (just how much higher we will see in the next section)
to execute a transfer of labor from the traditional to the modern sector. The
subsistence wage in the traditional sector permits the expansion of old industries
and the creation of new ones without limit at the existing wage; or, to put it
another way, shortage of labor does not constrain the modern sector’s growth.
We now analyze the modern sector before moving on to the interplay between
the two sectors.
2.1.2
Modern activities sector
As mentioned earlier, the LFR model assumes that a less developed, labor surplus economy,19 consists of a traditional sector coexisting with a modern sector.
We now describe the modern sector. The modern sector is by definition what
the traditional sector is not. By difference, modern activities are productive,
i.e., M P L > 0 (recall (C5), uses modern techniques and has specialized production. Accordingly, its’ initial conditions are simply that there exist low
man/land ratios as well as high K
L . Therefore, labor will not be unproductive
and redundant. Instead, M P L > 0, and wages will be determined according to
neoclassical marginal product calculus. This is an important point, for if wages
are determined according to marginal product and not some institutional sharing arrangements, then it means that the organization of production units in
the modern sector approaches that of commercialized organization. Unlike her
traditional counterpart, the modern capitalist is “more commercially minded,
and more conscious of efficiency, cost and profitability”.20
Figure 4 depicts the production and organization conditions in the modern sector. Notice the production and organizational asymmetries between the
modern and traditional sectors.
Panel 1 depicts the various production contours in the modern sector. The
absence of any factor in abundance relative to another factor ensures that the
expansion path OE is continually upward sloping, and that the production
contours do not become vertical or horizontal at the extremes, as was the case
in the traditional sector. Hence, assuming constant returns to scale, the modern
sector production function, g(L), can be depicted in panel 2. Corresponding to
this T P L curve we have the modern sector M P L, which is always positive,
indicating that no factor saturates the production process. Formally, we may
express g(L) as: Q = g(L), g (L) < 0, and limL→∞ g (L) = 0.
We note that the modern sector encompasses the modern sections of an
economy. What we have is not one island of expanding modern employment,
but rather a number of such tiny islands. This is very typical of countries in
their early stages of development.21 We find a few industries highly capitalized,
19 i.e., an economy with a large population compared to scarce resources, such that high
man-resource ratios persist.
20 Lewis, W. A., ‘Economic development with unlimited supplies of labor, in Agarwala &
Singh, The Economics of Underdevelopment, p. 407.
21 This is a Lewisian assumption: that a great number of islands of expanding modern
18
19
Figure 4: Production Conditions in the Modern Sector
such as mining or electric power, side by side with the most primitive techniques;
a few high class shops, surrounded by masses of old style traders; a few highly
capitalized plantations, surrounded by a sea of peasants. Though the modern
sector can be subdivided into islands, it remains a single sector because of
the effect of competition in tending to equalize the earnings on capital. The
competitive principle does not demand that the same amount of capital per
person be employed on each ‘island’, or that average profit per unit of capital
be the same, but only that the marginal profit be the same.
Having described the basic characteristics of the modern sector we turn to
the most important aspect of the model: how does growth, and greater employment, occur in the modern sector? The answer to this is, again, a classical
assumption: the LFR model assumes that the modern sector grows through
capital accumulation. Capital accumulation is the continued investment of capitalists surplus which is simply the profit left after payment of the total costs.
Thus, to calculate the size of the capitalists surplus, we need to first compute
the total costs— let us concentrate on total variable costs of labor first.
To calculate the wage bill we will have to first address the issue of labor
demand and supply in the modern sector. Addressing labor supply first we see
that as long as there is surplus labor in the traditional sector (and we assume
that there is) the labor supply curve ww to the modern sector will be flat,
indicating that any amount of labor can be hired at the prevailing wage w.
We have shown ww in Figure 4.3. On the issue of labor demand we see that
since neoclassical marginal product calculus is in effect, the M P L curve is the
labor demand curve. Thus, the equilibrium in the labor market, where the
quantity of labor demanded is equal to the quantity supplied, will occur where
the labor demand and supply curves intersect. Hence, it might appear that the
total wage bill is simply the quantity of labor hired in equilibrium L2 multiplied
by the prevailing wage, which in this case is w. This is an essentially correct
statement, except for one point. In practice, modern sector wages have to be
higher than w. Lewis estimated that the difference in modern sector real wages,
W , and the traditional sector real wages, w, would have to be about 30% or
more. This difference arises because of several reasons. Firstly, some of this
difference is illusory because of the higher costs of the modern sectors. Again
this has to do with the organizational characteristics of the modern sector since
it tends to be highly concentrated and urbanized. Therefore, congestion and
transport costs are higher. Secondly, the decision for a labor in the traditional
sector to migrate to the modern sector involves a psychological cost. As Lewis
put it:
“[There is a] psychological cost of transferring from the easy going
way of life of the [traditional] sector to the more regimented and
urbanized environment of the [modern] sector”.22
employment exist in the early stages of a developing economy— the key here is employment.
Recent experience suggests that modern activities may be many in number and may even be
expanding, but not necessarily creating employment in the modern sections. See the point
regarding choice of techniques in section 2.2.
22 Ibid., p. 410
20
Finally, the gap in modern and traditional real wages may simply recognize:
“that even the unskilled worker is of more use to the [modern] sector
after he has been there for some time than is the raw recruit from
the [traditional sector]”.23
That modern real wages have to be higher than traditional real wages is
reflected in Figure 4.3 where we depict a now higher labor supply curve W W
reflecting the additional wage which the modern sector must pay the traditional
sector to extract labor out of that sector. The amount of labor demanded, L1
can be read off from the intersection of the labor demand curve, ABC and the
labor supply curve, W W . From this, we can calculate the total wage bill which
is simply equal to L1 W or the rectangle OW B L1 .
Having calculated the total wage bill we can now turn our attention back to
how capital accumulation takes place, which as we have mentioned earlier takes
place through capitalist surplus, which can be calculated with the help of the
total wage bill. Recall that capitalist surplus is defined as the portion of the
total product left over after total costs have been paid. This capitalists surplus
is an investment fund for the modern sector, but surely, agricultural surplus
too can be a source of funds for investment in the modern sector? However,
Lewis assumed that the traditional sector, given the initial conditions, would be
unable to generate an agricultural surplus. This view however is not shared by
Fei-Ranis, who assume that it is through capitalist and agricultural surplus that
capital accumulates. In our present discussion we will stick to capitalist surplus
as investment funds in the modern sector. We take up the issue of agricultural
surplus as an investment fund in Appendix A to this chapter. Coming back to
our discussion, we now calculate the capitalists surplus.
If we examine Figure 5.3 we see that initially the labor demand curve ABC
(corresponding to T P L0 in figure 5.2) and the labor supply curve W W intersect
at B and yield the equilibrium quantity of labor L1 . Here the total wage bill
is represented by the rectangle OW BL1 while the profit to the modern sector,
or the capitalist surplus, is W AB. Now, Lewis, like his classical predecessors,
assumes that this capitalist surplus will be invested. This investment will raise
the capital stock from K1 to K2 , as can be seen in Figure 5.1. This new
capital stock results in a new total product curve T P L1 which in turn means
that the M P L curve will shift out from M P L0 to M P L1 , or from ABC to
A B C resulting in a new equilibrium. At B more labor L2 is demanded and
supplied from the traditional sector. And yet again another capital surplus
W A B is obtained. This capital surplus will again be invested and the process
will continue as long as capitalist surplus exists.
But there is an obvious objection to the preceding analysis. The discussion
assumes that capital surplus will be reinvested and not hoarded. Is this a
reasonable assumption? In this respect Lewis adopts the classical explanation:
Why should the capitalists produce more capital to produce a larger
surplus which could only be used for producing still more capital
23 Ibid.,
p.410-411
21
22
Figure 5: Capital Accumulation in the Modern Sector
and so on ad infinitum? To this Marx supplied one answer: capitalists have a passion for accumulating capital. Ricardo supplied
another: if they don’t want to accumulate, they will consume instead of saving; provided there is no propensity to hoard, there will
be no glut. Malthus ... raised another question; suppose that the
capitalists do save and invest without hoarding, surely the fact that
capital is growing more rapidly than consumption must so lower the
profit on capital that there comes a point when they decide that it is
not worth while to invest? This Ricardo replied, is impossible; since
the supply of labor is unlimited, you can always find employment
for any amount of capital.24
In fact we will see that Lewis and other classical economists were mistaken when
they assumed that capitalist surplus will be invested.25 But now we now proceed
to a discussion of development in a dualistic economy. For this we consider the
interplay between the traditional and modern sectors.
2.1.3
Interplay
The previous two sectors described the structural characteristics of each sector
in the LFR model. We have set the stage for the interplay. Now the action
begins.
We bring the traditional and modern sectors together in Figure 6. Let us
quickly explain a few items about Figure 6. Examining Figure 6.1 we represent
the production conditions in the modern sector. We have shown two M P L
curves df , and d f . We assume initially that the modern sector is very small
relative to the economy. Therefore, we assume that the entire population almost lives and works in the traditional sector. So, to begin our analysis of
development in the classical model we turn to the traditional sector.
Panels 2 and 3 show the production conditions in the traditional sector.
Examining figure 6.3 first we have the traditional sector production function
or total product curve OCF M — only that it has been reflected on the y = −x
line.26 Hence, population in the traditional sector is read from right to left while
output is read from top to bottom. The T P L curve contains a flat region CM
indicating the existence of surplus labor, DP . This fact is also represented in
panel 2 where we have drawn the M P L curve of the traditional sector P DU .
Again, labor is read from right to left but the marginal and average products
24 Lewis, W. A., ‘Economic development with unlimited supplies of labor, in Agarwala &
Singh, The Economics of Underdevelopment, p. 407.
25 Strictly speaking, Lewis was right if he was granted two conditions: (a) that capitalists
did not hoard their capitalists surplus, and (b) that the economy was closed. We can see that
of these two conditions, condition (b) is the more problematic one in these times: because
capital can move across international borders, it becomes difficult to assume that capitalists
surplus will be invested at home, and not in another country where the returns to capital are
higher. Since this book assumes a closed economy, we will not pursue this matter further, but
the point ought to be kept in mind.
26 Or alternatively, it has been reflected on the x-axis and reflected again on the y-axis.
23
Figure 6: Interplay in the Classical Dual Economy
24
are read bottom to top. We see that the M P L curve is flat for the region of
surplus labor DP .
In accordance with the LFR model, the institutional wage in the traditional
sector:
(1) Is equal to the average product of labor. As a first approximation, assuming
that our analysis begins with a full population OP in the traditional sector, the
real wage in the traditional sector, w, is simply w = AP L = MP
OP .
(2) Persists for as long as there is disguised unemployment in this sector. Thus,
by definition of disguised unemployment, in Figure 6.2 we have shown the real
wage w = AP L extending all the way till it meets the M P L curve at U .
From points (1) and (2) above we have a new definition: we define AP workers
as the disguisedly unemployed labor force since all traditional workers until
this point are producing producing less than they consume, i.e., M P L < w =
AP L.27 Of course, when the supply of disguisedly unemployed workers, AP , is
exhausted, the average product of labor becomes less than the marginal product.
This is seen to happen at point U in Figure 6.2. On the left of U an institutional
wage persists. On the right of U competitive wage determination comes into
effect and marginal product calculus is ushered in. At U any worker withdrawn
out of the traditional and into the modern sector will be paid her marginal
product.
We are now ready to discuss the interplay between the two sectors. We will
describe three stages in the development of the LFR model. (1) Stage I is the
range for which M P L = 0 in the traditional sector, i.e., this phase marks off
the surplus labor force DP in the traditional sector. (2) Stage II is the range
for which a positive M P L in the traditional sector is less than the institutional
real wage w. Stages I and II together mark off the end of the disguisedly
unemployed labor force. (3) Stage III is the range for which the M P L in the
traditional sector is greater than the institutional real wage w. We now begin
our analysis of each stage.
STAGE I: Assume that for some reason there is an initial investment in the
modern sector. As mentioned earlier, the Lewis-Fei-Ranis model is silent on the
source of this investment. But what is critical here is that for the modern sector
to grow, this investment must be sufficient to generate a capitalist surplus at the
prevailing real wage in the modern sector which, in turn, implies the notion of a
‘minimum critical effort’. Now, we represent this initial investment in Figure 6.1
by the M P L curve df . This is the demand curve for labor in the modern sector.
The supply of labor in Stage I is represented by the flat curve w = SS . This
curve is partially flat for the portion of the labor force for whom the institutional
wage prevails and is rising when workers are paid according to their marginal
product.
Now at the initial wage of w and labor demand curve df we see that the
labor market will be in equilibrium. In this equilibrium the capitalist surplus
27 Do note that surplus labor is a technological phenomenon brought on by resource and
technological constraints, whereas disguised unemployment is an economic concept- it depends upon the production function, the institutional wage, and the size of the traditional
population.
25
will be equal to W dt which when reinvested will result in a new capital stock
which shifts out the initial M P L curve, df , to another M P L curve, d f . More
labor is demanded and an equal number supplied by the traditional sector. This
process continues until we reach the end of Stage I at point t on the labor supply
curve in Figure 6.1. Let’s make a few comments about Stage I.
Firstly, we can see that as the workers are reallocated from the traditional to
the modern sector in Stage I, output in the traditional sector remains unchanged.
Thus, unproductive surplus, or redundant, workers are being transferred to the
modern sector where they will be more productive, without a loss in traditional
sector output. In a sense then, development process in Stage I is “costless”.
Secondly, the traditional sector, we have noted earlier, includes the agricultural sector. Hence, when workers transfer out of the traditional sector, it is very
likely that some of these will be agricultural workers. In that case, the question
of food transfers enters the picture. Workers cannot move out of the agricultural
sector without the existence of some mechanism which simultaneously transfers
the consumption per head with each transferred worker. If we assume that
transferred workers consume the same amount of food in the modern sector as
they did in the traditional sector, then we can set out some conditions for this
costless development to occur. To do this we must define some concepts, which
is done immediately below.
Assume that the traditional sector is the agricultural sector. (This is only an
assumption and should not be taken to mean that the traditional and agricultural
sectors are actually the same). Now, as workers are transferred out of the
agricultural and into the modern sector we see that a surplus of agricultural
goods begins to appear. That portion of the total agricultural output (read off
the traditional T P L curve, OCM ) in excess of the consumption requirements
of the agricultural labor force at the institutional wage is defined as the Total
Agricultural Surplus (T AS). The amount T AS can be seen to be a function
of the amount of labor reallocated at each stage. For example, if GP agricultural
workers are withdrawn in Stage I and re-allocated, then JG is required to feed
the remaining agricultural workers and a T AS of size JF results. The T AS
at each stage is represented by the distance between the T P L curve in the
traditional sector and the straight line OM .
From the T AS we can define the Average Agricultural Surplus, AAS,
as the total agricultural surplus available per head of allocated modern sector
workers. The AAS curve is represented by the curve wY Z in Figure 6.2. In
Stage I as T AS increases linearly with the allocation of surplus labor from P to
D we can picture each allocated worker as carrying her own subsistence bundle
along with her. The AAS curve for Stage I thus coincides with the institutional
wage curve wY U in Figure 6.2. It is only when the AAS is constant, that
development in the classical model will be costless. The following conditions
must be satisfied for a constant AAS:
(a) The remaining workers in the traditional sector continue to consume the
same amount.
(b) The transferred workers consumes the same amount.
(c) There are no transport costs.
26
(d) If with each transferred worker, AP L units of food are transported.
If the conditions above are met, then development in Stage I of the classical
approach will be costless. For example, if the conditions above are not met,
(say) the remaining workers do consume more than before, then it means that
food supplies per head for the transferred workers will be reduced, putting a stop
to the development process in Stage I. So, some way must be found to prevent
the remaining workers from consuming more than before. Clearly, in some way,
the emergent T AS must be removed from the traditional sector, which raises
the issue of how the T AS will be transferred out of the agricultural sector as
workers are reallocated to the modern sector. One can imagine that it is (i)
siphoned off to the modern sector through the investment activities of landlords
in a process whereby the agricultural surplus is converted into a wage fund, or
(ii) the extra food surplus resulting with every transferred worker will have to
be taxed by the government— a taxation scheme due to Nurkse. Either (i) or
(ii) will be enough to prevent the remaining workers from consuming more than
before. We will return to this point later since the issue of transferring the T AS
becomes more obvious in Stage II.
STAGE II: We left off the development process in Stage I with the M P L curve
in the modern sector congruent with the curve df . As before, the M P L curve
is moving outwards towards d f through the process of investment and further
capital accumulation. But there is a hidden problem.
We can see from Figure 6.2 that the institutional wage w is assumed to
persist throughout Stage II. This stems from our assumption that w persists
as long as there are disguisedly unemployed workers in the traditional sector.
Since the supply of the disguisedly unemployed workers has not been exhausted
in Stage II, the labor supply curve to the modern sector can expected to remain
flat throughout Stage II. But a glance at Figure 6.2 tells us this is not the case;
instead of the supply curve being flat in Stage II it is upward sloping. What is
going on?
The explanation lies in the issue of total and average food surplus we discussed in stage I. Notice that in Stage II, since the the M P L of the now allocated
workers is positive28 , total output begins to fall which means there is insufficient
agricultural surplus output to feed all the new modern sector arrivals at the institutional wage level. This occurs, because while T AS is increasing in Stage
II— because the distance between the curve M CRO and the straight line OM
in Figure 6.3 begins increasing— AAS begins to fall as the number of workers
allocated to the modern sector begins to rise— the falling AAS is illustrated as
Y Z in Figure 6.2.
This scenario, where despite rising T AS, the AAS begins falling occurs due
to a worsening of the modern sector terms of trade.29 The “worsening of the
28 That
is, the portion DU in Figure 6.2 and CRO in Figure 6.3.
note that in order to talk about terms of trade we need to assume that the two sectors
are producing different products. Now we already have an agricultural sector, but there still
remains the modern sector producing ‘modern goods’, which defies easy classification. Hence,
to talk in terms of a terms of trade story let us think of the modern sector as the industrial
sector. We want to emphasize that we are doing this to discuss terms of trade problems and
29 Do
27
terms of trade” for the industrial sector occurs as the result of a relative shortage
of agricultural commodities seeking exchange for industrial goods in the market.
Accordingly, we label the point Y (or equivalently, point D) in Figure 6.2, which
is at the border of Stages I and II, the shortage point. After Y , there is a
tendency for the industrial supply curve to turn up as Stage II is entered because
this is the time when there begins to appear a shortage of agricultural goods
measured in terms of AAS. This in turn causes a deterioration of the terms of
trade of the industrial sector and a rise in the industrial real wage measured in
terms of industrial goods since there is now an excess demand relative to supply
of food. We thus see that the disappearance of surplus labor in the agricultural
sector marks the ‘turning point’ shown as point t in Figure 6.1.
As far as development is concerned, capital accumulation is continually reinvested but at a slower pace and to a lesser extent. We can see that because of
the rising supply curve, brought on by the worsening terms of trade for the
industrial sector, capitalists surplus in the industrial sector declines, which reduces the investment fund meaning that less investment will take place. The
pace of development will also slow down because the costless phase is over. Old
industries and new industries can no longer be created or expanded without
limit— the previous advantage of a constant subsistence level institutional wage
in the agricultural sector no longer holds.
The M P L curve in the industrial sector keeps shifting outwards until we
reach the end of Stage II. The entire disguisedly unemployed labor force has
been transferred out of the agricultural and into the industrial sector. This
brings us to the end of Stage II.
STAGE III: We have now reached Stage III which constitutes a major landmark in the developmental process. With the completion of the transfer of
the disguisedly unemployed, there will occur a switch, forced by circumstance,
in employer behavior. Stage III heralds the advent of a fully commercialized
agricultural sector. The system of institutional wage determination is abandoned and competitive market forces yield the commonly accepted equilibrium
conditions.
The advent of Stage III signals the end of the take off process for the agricultural sector, which has now ceased to be the dominant sector. The center of
gravity has shifted in favor of the industrial sector and the agricultural sector
has now become commercialized, following neoclassical marginal product wage
determination. Indeed, a structural change, in the relative sizes of the sectors,
the production conditions and organizational characteristics has occurred. For
this reason we call the points X, U , and R in Figures 6.1, 6.2 and 6.3 respectively, the Commercialization Point.
We should note that the labor supply curve at the commercialization point
in Figure 6.1 is accentuated. The reason is that since agriculture has become
fully commercialized in Stage III, it must now bid with the industrial sector
for its workers. This leads to an increase in the industrial real wage level if
this should not mean that the modern sector is the industrial sector nor that the traditional
sector is the agricultural sector.
28
the industrial employer is to compete successfully with the landlord for the use
of the, by now, “limited” supply of labor. It can, moreover, be readily seen
that during Stage III, AAS and T AS declines even more rapidly as the now
commercialized wage in agriculture becomes operative. This is seen in Figure
6.2 where the AAS curve dips even further at the edge of Stages II and III,
i.e., at point Z in Figure 6.2. In addition, this declining AAS is also reflected
in Figure 6.3 where the straight line OM has an inward curve QO. With this,
our description of the interplay between the traditional (agriculture) sector and
the modern (industrial) sector is complete. We have seen how the classical
characteristics of the dual economy, in particular the high man-resources ratios
which resulted in M P L = 0, an income sharing setup and subsistence wages,
contributed to the development effort in this model. We now criticize and
comment on this model.
2.2
Comments and Criticisms
Firstly, is it possible to achieve costless development with sources of labor other
than surplus labor? Lewis talks of potential sources of labor supply which,
although not surplus labor, does form an elastic labor supply at a given wage
rate. These potential sources includes women. Hence, it is inevitable that
sooner or later, women will begin to enter the labor force, for employment in
the modern sector— this accounts for another well known structural sequence.
That women provide the possibility of costless or near costless growth, underscores the point, made by Lewis, that M P L = 0 is not fundamental to his
model. But this is not entirely correct. When new workers, such as women, are
employed, what are they going to do with their wages? For one thing, they will
certainly buy food. But whether this food will be forthcoming or not is a valid
question, and is clearly tied up with M P L = 0 phenomenon. Take, for example,
the case of a worker who is openly unemployed in agriculture or industry. How
much does she consume, relative to when she is employed? It can be argued
that there is a huge difference between the food consumption, or even in food
needs, of the chronically unemployed, and the food consumption, or needs, of
the employed. If this is so, the question of where the food is going to come
from is all-important. An economic development which proceeds by absorbing
the openly unemployed generates larger food requirements than that implied by
economic development which soaks up the disguisedly unemployed.
Let’s try to calculate the food demand set up. That is, the extra food that
must be produced if one extra worker is to be employed. If the worker was
openly unemployed, the extra food requirement is given by:
R ≡ Food needs when employed — food needs when unemployed
In the case of the disguisedly unemployed worker, we have to account for two
factors: one, the total food output will fall when this worker finds employment
and is transferred out of the agriculture sector. The fall in total output is
therefore f (L). Two, the departure of this worker raises the income of the
29
remaining workers which will in turn raise their food consumption because of
this higher income. Let the increase in consumption of food be Θ when the per
d(
f (L)
)
L
. Note that f (L)
capita income of the remaining workers goes up by dL
L is the
AP L of the departed worker. Then adding these two factors gives us the extra
food requirements when a disguisedly unemployed worker finds employment:
R̂ ≡ f (L) + Θ|
d( f (L)
L )
|
dL
f (L) − Lf (L)
|
L2
Now, we recall from the previous section that in Stage I, because f (L) is flat, we
have f (L) = 0 and that since we may siphon off the extra surplus by taxation,
we have:
⇒ R̂ ≡ f (L) + Θ|
d( f (L)
L )
|=0
R̂ ≡ f (L) + Θ|
, 1 ,
dL 1
=0
=0
⇒ R̂ = 0
Thus R̂ = 0. However, R can be expected to be significantly positive. The extent
to which additional food production is required will depend on the distribution
of the unemployed between the disguisedly and openly unemployed.
Second, our discussion of labor flows from the traditional (agricultural) sector
to the modern (industrial) sector has not specified what will actually cause labor
to migrate and food to be marketed. This is a controversial issue which will be
taken up throughout this book.
Third, what should be the pattern of labor removal from the traditional
sector? Should incentives be structured so that individuals from each family
farm migrate, or should entire families migrate? Let us begin to consider this
issue by asking what happens to the emergent land once some workers or an
entire family migrate.
If individuals from each family migrate, then we see that the assumptions
of M P L = 0 on the aggregate makes sense and the question of (emergent) land
marketability becomes unimportant, since members of the family remain on the
land. If, however, entire families migrate there is the important question of
where the land goes. Is land sold on departure? If so, to whom? Moreover,
from the perspective of equity, if, as likely in the agricultural sector, rich farmers
buy the emergent land, the distribution of land-ownership is likely to worsen—
what consequences does that have?
In addition, depending on the pattern of labor removal, traditional output
may or may not fall. Thus, the pattern of labor removal is tied with whether
M P L = 0 in the traditional sector or not. We will now show that if a worker
from each family is removed, there will no loss in output, and therefore M P L =
30
0. But if an entire family is removed, then output will fall, and we can no longer
claim that M P L = 0 in the traditional sector.
Consider the following simple hypothetical situation. Let us consider an
agricultural sector characterized by traditional production and organizational
conditions. Let all family sizes and land sizes be identical. Each family has L
laborers and T units of land. Suppose there are N families (N ≥ L). Suppose
that L workers are to be withdrawn from agriculture. This can be done in two
ways:
(i) One worker from L family farms migrates, or
(ii) An entire family migrates.
Let the agricultural production function be given by f (l, t), and suppose that
fl (t, l), evaluated at (T, L) equals zero. We deal with each case, starting with
case (i).
(i) If a worker is removed from each of the L family farms then each farm’s
output falls by fL (T, L). Thus, the total output falls by LfL (T, L). But from
our assumption of fl (t, l)|(T,L) = 0 we have a net loss of zero. Of course, we
have to assume that the removal of each worker does not affect the M P L, and,
more importantly, that each worker puts in an equal amount of work.
(ii) Say the ith family (consisting of L workers) is removed. The output of this
ith farm falls by f (T, L). If we assume that this land is bought by (say) the
j th family, then the j th family’s land holdings double. Thus, the j th family’s
output will increase by f (2T, L) − f (T, L). The net loss in output is therefore:
f (T, L) − [f (2T, L) − f (T, L)]
Assuming f is strictly concave and homogeneous to a degree ≤ 1, the net loss in
this case is: 2f (T, L) − f (2T, L). Clearly, if there is at most constant returns to
T , then there can be no net gain. In all likelihood, there will be some diminishing
returns, and so a net loss in output will occur. We see that:
2f (T, L) − f (2T, L) ≥ f (2T, 2L) − f (2T, L) > Lfl (2T, 2L) = Lfl (T, L)
Thus, the net loss in case (ii), with some diminishing returns, is greater than
in case (i). We note that if the land given up by the ith family could be parceled
out equally to all families, the loss would be reduced, but there are problems
with this since land is not a shiftable input. We now consider an example to
illustrate the discussion above:
example: Suppose the production function in the agricultural sector is:
f (t, l) = min(t, l)
where f is a Leontief production function. Now, let each family have 2 units of
land and 3 workers. Then f (T, L) = min f (2, 3) = 2. Suppose the total number of
farms is N = 3 and that 3 workers are to be reallocated to the modern or industrial
sector.
Now, from case (i) above, if we remove one worker from each family, the net
d2
loss in output will be 0. This is from the fact that 3fL (2, 3) = 3 dL
= 0. In case
31
(ii) if we remove one family we see that the loss in output from this family is 2.
If this land is transferred out to another family then this (j th ) family’s production
function becomes:
f (2T, L) = min(4, 3) = 3
Thus, the net loss is 1 unit of output. But if the land is equally divided then
each remaining family’s output will be:
f (3, 3) + f (3, 3) = min(3, 3) + min(3, 3) = 6
which exactly equals the output before the reallocation. Thus, the net loss in output,
when land is divided equally amongst remaining families is less than when land is
parceled out to just one family. This example is obviously artificial but conveys the
sense of what we are trying to say.
Fourth, we have seen that the essence of the LFR model lies in the existence
of an abundant supply of cheap labor available for use as inputs in the modern
sector. But what sort of workers are these? In the context of overpopulated
less developed economies we see that there is an abundance of unskilled labor,
and so a major portion of the labor supply to the modern sector will consist of
unskilled workers. The flip side of this is obviously that there is a shortage of
skilled labor. How severe is this bottleneck? Obviously, if the modern sector
expands by adopting sophisticated techniques which require skilled workers then
our development story is in trouble. Lewis assumed that the bottleneck of
skilled labor can be overcome by government intervention. In practice though
this is unlikely. The recognition that there is a shortage of skilled labor but
an abundance of unskilled labor in turn introduces the issue of the choice of
techniques: obviously, labor-intensive, or labor-using, techniques are in order
here. We will have more to say about this below.
Fifth, the issue of labor-using techniques raises another question. Because
there is an abundance of labor, especially unskilled labor in most labor surplus
less developed economies, it makes sense for investment in labor-using techniques. But it is possible that the capitalist surplus may be well be invested
in labor-saving, or capital-intensive, techniques. In such a case the employment generated would be less than if the modern sector had invested in labor
intensive techniques of production. Consequently, the shifting of the center of
gravity from traditional (agriculture) sector to modern (industrial) sector would
be delayed. We can illustrate this point below in Figure 7.
Figure 7.1 illustrates the effect on employment when the modern sector invests in labor-using techniques. In Figure 7.2 we have the modern sector investing in capital-intensive techniques. Clearly, the effect on employment is
marginal when compared to Figure 7.1. Finally, Figure 7.3 illustrates the effect
on employment when the modern sector invests in completely labor-displacing
technology. Additional employment is simply nil.
Experience from less developed economies indicates that capitalist surplus
is indeed invested in labor-saving or labor-displacing techniques. Thus, policies
32
Figure 7: Choice of Techniques and Effect on Employment
designed to speed up structural change by heavy investment in industry paradoxically slow the process down. Even worse, some countries are cursed not from
heavy investment in capital intensive techniques but from capital flight, where
capitalists surplus instead of being invested, is spirited off to foreign lands.
Six, we have seen that the rate at which labor is transferred from the traditional to the modern sector is proportional to the pace of capital accumulation
in the modern sector. But the possibility of capital acummulating faster than
population certainly does exist. The effect of this situation is to increase real
wages so high that capitalists’ profits may decline to such an extent that these
may be consumed instead of being saved. Hence, net investment may be nil.
The logic here is simple: if capital is accumulating faster than the population, then the pace at which labor is transferred to the modern sector is faster
than the rate at which it can be replaced through population growth30 This
raises the average product per labor in that sector not because production conditions have changed but simply because fewer workers remain behind to share
the output. The effect of a higher average product is transmitted to the modern sector which must now pay a higher real wage to transfer labor from the
traditional sector. This in turn implies a smaller capitalist surplus which progressively becomes smaller and may result in direct consumption or hoarding of
this surplus. Development may, therefore, come to a stop sooner.
Seventh, In Stage I, if w was originally at minimum subsistence levels then
the development process comes to a stop in Stage II. We can see this by going
back to our explanation of why the labor supply curve begins to turn upwards
30 We are of course talking about net population growth. That is, the excess of births over
deaths.
33
in Stage II, even though the institutional wage w continues to prevail.
The explanation was that since the AAS declines in stage II, the terms
of trade must turn against the modern sector, thus raising the labor supply
curve upwards. This is because as the modern sector expands, its demand for
food increases, and since, simultaneously, the agricultural output begins to fall,
the price of food in terms of modern products rises. The higher food prices
in turn raise the modern wages, turning the terms of trade against it. But
this scenario only makes sense if the original per head consumption was above
basic subsistence. For if not, then no rise in modern wages can compensate for
the decline in the AAS. In effect, the supply curve to the modern sector will
become vertical after stage I. It should be obvious then that a dynamic model,
incorporating population growth, capital accumulation, and technical progress
is necessary if we are to have continued growth in the economy. This is done,
to a limited extent, in the neoclassical model.
Finally, in retrospective, we see the terms of trade issue in Stage II reduces
both the pace and extent of development in the dual economy. Since the institutional wage is assumed to extend into Stage II, we see that, ideally, the economy
can take advantage of this constant wage and expand without limit. But the
worsening of the modern (industrial) terms of trade thwarts this “ideal” possibility. Is there some way that we can bypass the terms of trade problem? There
certainly is, if we are willing to relax the assumption of no technical progress,
which is done in the Fei-Ranis model but not the Lewis model.
If agricultural productivity through technical progress were to increase, then
stage II would be shortened. And if this productivity increase was high enough
(just how high we will see shortly), then Stage II can be eliminated altogether.
We analyze this possibility below. We begin by assuming that technical progress
is exogenous and neutral.
An increase in the agricultural labor productivity can be described by upward shifts of the T P L curves. We can see this in Figure 8.3 below: productivity
increases are depicted by a sequence of T P L curves marked I, II, III, .., among
which the I-curve is the initial T P L curve and II, III represent the T P L curves
after successive increases in agricultural productivity.
Let us make the assumption that as agricultural productivity increases the
institutional wage remains unchanged, i.e., w in Figure 8.2 equals the slope of
OM in figure 8.3 as determined by the initial T P L curve. In Figure 8.2 we may
now plot the sequence of M P L curves marked I, II, III .. Each M P L curve
contains a flat portion representing surplus labor in the traditional labor force.
In figure 8.2, surplus labor is the portion P S1 . In Figure 8.2 we have also drawn
the sequence of AP L curves I, II, III.. corresponding to the T P L curves I, II,
III .. in Figure 8.3. According to the method already indicated, we can now
determine the three stages for each level of productivity, i.e., the sequence of
shortage points, S1 , S2 , S3 .. and the sequence of commercialization points, R1 ,
R2 , R3 .. Reference to these points will facilitate our analysis of the effects of an
increase in agricultural productivity on the supply curve of agricultural labor
and on the AAS curve.
As depicted in Figure 8.2, for every amount of labor employed in the agri34
cultural sector, an increase in agricultural productivity shifts the M P L curves
upward. As a consequence, the agricultural labor supply price curve is transformed from wt1 t1 to wt2 t2 , wt3 t3 .. etc.. with a shortening of its horizontal
portion (i.e., stage II arrives earlier) as the sequence of commercialization points
R1 , R2 , R3 .. gradually shifts from right to left. On the other hand, the sequence of shortage points S1 , S2 , S3 .. etc. gradually moves from left to right.
This is due to the fact that, for each amount of labor allocated to the modern
(industrial) sector, the AAS increases with the increase in T P L; the amount of
food consumed by agricultural labor remains unchanged, leaving more T AS and
hence AAS for the industrial workers. Thus the effect of our increase in agricultural productivity is an upward shift of the AAS curve to positions marked
I, II, III, ...
Sooner or later, the shortage point and the commercialization point coincide,
and the distance S1 R1 , S2 R2 , S3 R3 ... vanishes and stage II is eliminated. In
Figure 8.2 such a point of coincidence is described by R3 = S3 . We shall call this
point the Turning point. There exists one level of agricultural productivity
which, if achieved, will bring about this turning point. In figure 8.3 this level of
agricultural productivity is described by T P L curve III.
Let us now investigate the impact of an increase in agricultural productivity
on the industrial supply curve L1 depicted in Figure 8.1. On the one hand, the
upward shift of the AAS curve will shift the industrial supply curve downward
before the turning point. This is due to the fact that an increase of AAS
will depress the terms of trade for the agricultural sector and, with the same
institutional wage (in terms of agricultural goods) paid to the industrial workers,
the industrial wage (in terms of industrial goods) must decline. On the other
hand, the upward shift of the M P L curve which is accompanied by a higher
real wage in the agricultural sector after the turning point raises the industrial
supply curve after that point. Thus we see, for example, that the L2 curve
crosses the L1 curve from below, indicating that ultimately the “terms-of-trade
effect” (due to an increasing of AAS) has been overcome by the “real-wage
effect” (due to an increase in M P L). For purposes of this chapter, we are,
however, not concerned with stage III which lies beyond the turning point.
Let us now examine more closely the relative positions of the industrial
supply curves before stage III is reached. Let the horizontal portion L1 P1 of
the initial industrial supply curve L1 be extended up to P3 , the turning point,
and let us call this horizontal line segment L1 P3 the balanced-growth path.
We may then claim that all industrial supply curves between L1 and L3 cross
the balanced-growth path at the respective shortage points. This is due to the
fact that at the shortage point for each case (for example f2 in Figure 8.2 for
the case of the industrial supply curve L2 in Figure 8.1) the subsistence wage
rate and the AAS take on the same value as that prevailing in Stage I before
any increase in agricultural productivity has been recorded. Hence the same
real wage, in terms of industrial goods, must prevail at the shortage point as
prevailed previously. In short, before the turning point, the industrial labor
supply curve lies above (below) the balanced growth path when the AAS curve
lies below (above) the horizontal line ww, causing a deterioration (improvement)
35
36
Figure 8: Labor productivity in the agriculture sector
of the industrial sector’s terms of trade.
The economic significance of the equality between our turning point and
the (final) shortage point is that, before the turning point, the economy moves
along its balanced-growth path while exploiting (or making the best of) its
under-employed agricultural labor force by means of an increase in agricultural
productivity. The economic significance of the equality between our turning
point and the commercialization point is that, after the turning point, the industrial supply curve of labor finally rises as we enter a world in which the
agricultural sector is no longer dominated by nonmarket institutional forces but
assumes the characteristics of a commercialized capitalistic system.
With this, our discussion of the classical approach ends. We now move on
to the neoclassical approach.
37
QUESTIONS
1. Consider the Lewis dual economy. Discuss various situations in which the
supply curve of labor to the industrial sector might be upward-sloping, even
in the first stage of development. Relate the upward slope, in particular, to
the ability of the planner to impose confiscatory taxes on agriculture, and to
the extent that the initial average output of foodgrain is close to minimum
subsistence.
2. Finally, briefly discuss which factors could determine (a) the pattern of
migration that may actually occur in a given situation, and (b) the extent of
land redistribution that is likely to take place, if entire families migrate.
READINGS
Lewis, W.A. (1954) ‘Economic development with unlimited supplies of labor’, Manchester
School, 22:139-191. also in Agarwala & Singh (eds.), The economics of underdevelopment.
Fei, J.C.H & Ranis, G. (1961) ‘A theory of economic development’, American Economic Review, 51:533-565. also in Eicher & Witt (eds.), Agriculture in economic
development.
3
3.1
The Neoclassical Model
Jorgenson Model
Once again, as in the case of the classical approach, we feel compelled to provide you with the basis of the neoclassical approach. By now, you are pretty
much steeped in the neoclassical tradition, so there is no need to go into a detailed introduction. Instead, what we will do here is to motivate the dicussion
by highlighting the principal differences between the classical and neoclassical
approaches. We seek to do this first, and then tell you a bit about the logic
and intuition of the foremost example of the neoclassical approach to the dual
economy: the Jorgenson model.
Let us begin by comparing and contrasting the classical and neoclassical
approaches. We have done this to a certain extent in the introduction to this
chapter, but here, having dealt with the classical approach, a compare and
contrast discussion will be more fruitful.
As far as a comparison of the two approaches go, we can only say that
they seek to describe and explain a ubiquitous aspect of economic development:
structural change. The classical model managed to do quite a good job of it. It
developed upon the reasonable assumption that most less developed economies,
or strictly speaking, pre-structural change economies, are likely to be characterized by high man-resources ratios which gives rise to diminishing returns to
labor, to the extent that M P L = 0. The pressures of population on scarce resource forces a situation where work and income sharing arrangements dominate
the traditional sector of an economy. Workers in such a sharing nexus are paid
38
a shared wage which is close to subsistence levels. These low wages, and the
presence of a supposedly unproductive labor force (i.e., surplus labor and the
disguisedly unemployed) permits the modern sector to pay a wage marginally
above subsistence levels and expand without limit (to a certain extent at least).
Included in this scenario are not only differences in production conditions between the two sectors (i.e., traditional, unproductive activities contrasted with
modern, productive activities) but also organizational asymmetries, i.e., uncommercialized family enterprises contrasted with highly commercialized, rationalized production units. This is a very powerful scenario which provides a pretty
accurate picture of most labor surplus economies. Also included in the classical model were structural sequences such as higher savings rate (i.e., capitalists
surplus which is reinvested) and the entry of women into the labor force. So,
the classical approach paints a pretty grand and comprehensive picture. But
it is curiously silent on one point, which was raised in section 2.2. And that
is: what happens when the food production is inadequate to permit development? Suppose, food production is so low, that when workers move out of the
traditional or agricultural sector, that they cannot be fed. Clearly, development
must cease.
It is at this point that the neoclassical approach comes in. Let us understand
the reasons for why the neoclassical approach is so concerned with the viability
conditions for growth, especially with regards to adequate food production. The
neoclassical approach, it was stressed, looks at the dual sectors of an economy in
a very different way when contrasted with the classical approach. The neoclassical approach is not founded on assumptions of large and growing populations,
nor is it interested in pessimistic scenarios of zero marginal products and most
of all, it does not regard leisure as either a free or inferior good.31 Neoclassical
economics treats leisure as a superior good, which implies that no matter what
the circumstances, M P L will always be > 0.
That the two approaches differ in this fundamental aspect requires development in the neoclassical approach to proceed along very different paths. The
neoclassical approach must rely on changes in the parameters of the dual economy, such as population, technical progress and capital accumulation, to spur
growth. It moreover, recognizes that there is no such thing as a given assumption that modern sectors can grow on its own volition or through exogenous
investment, without regard to adequacy of food supplies.
Hence, the first thing a neoclassical approach does is to explore the conditions for the emergence of a food surplus. This is simply done by postulating
that population growth rates increase, but only until a physiological limit. A
population which grows at less than its physiological limit, is a population which
is not meeting its food requirements. Hence, the viability condition is very simply that food production be sufficient to permit the population to grow at its
physiological limit. Once this physiological limit is reached, the neoclassical approach assumes that the population maintains a constant consumption of food
per capita, which is sufficient to maintain the population growth rates at its
31 Recall,
that one interpretation of M P L = 0 was that there was leisure satiation.
39
physiological maximum. Thus, any food production per capita in excess of per
capita consumption of food sufficient to maintain population growth rates at
the physiological maximum, results in a food surplus which permits the release
of labor for work in the manufacturing sector.
Hence, the neoclassical approach in this section will first derive the viability
condition for the emergence of a food surplus which allows the existence of a
dual economy, and permits the release of labor from the agricultural sector for
work in the manufacturing sector. Thereafter, the model, in the neoclassical
tradition, derives the growth rates of population, agricultural labor force, manufacturing labor force, agricultural and manufacturing wages, agricultural and
manufacturing output (total and per capita), and the terms of trade. All this
is done through traditional price theory.
Now, before we plunge into a detailed discussion of the neoclassical approach, we set out the basic assumptions of the model. We assume that technical progress in the neoclassical model is neutral. By this we mean that if output
is held constant, then the marginal rate of technical substitution between factors
of production remains constant before and after technical change. Moreover, we
have not allowed for capital accumulation in the agricultural sector, a weakness
which is corrected by extensions of the neoclassical approach, as will be seen in
section 4. But an obvious question is, “How is technical progress in the agricultural sector possible if there is no capital accumulation?” The answer is that
technical progress occurs in intensive cultivation, such as the timely sowing of
seed, or being extra careful not to trample planted areas etc...
Having sketched out the general framework of the neoclassical dual economy,
let us chart our course through this section. We will begin with an examination of the agriculture sector. Here, we will first explore the case of the single
sector agricultural economy. From this we will explore the viability condition
and show that when this viability condition is met, the single-sector backward
economy transforms into a dual economy with sustained growth. Our analysis
of the agriculture sector will then have to be adapted to fit the dual model.
Having dealt with the agricultural sector we will move onto a discussion of the
manufacturing sector. Here we will investigate, among other things, the behavior of the manufacturing sector population and capital accumulation. Finally,
we will bring the two sectors together and discuss development in a neoclassical
dual economy.
When discussing each sector and development in the dual economy we will
be primarily interested in two measures of the parameters in a neoclassical dual
economy. The first is the level of the parameter: what does it depend upon and
how is its behavior characterized? Secondly, we will be interested in the growth
rates of these parameters. What are the patterns of growth and what do these
depend upon? We want to emphasize that by the rate of growth of a variable
ln x
x we mean xẋ = dx/dt
or simply d dt
, where t is time. Now, enough has been
x
said here. Let us move on to the Jorgenson model.
40
3.1.1
Agriculture Sector
We begin our description of the agricultural sector by assuming that it is the
only sector in the economy. From this we will derive the viability condition
for the emergence of a dual economy. This is the same as saying that if food
productions are not sufficient to enable population to grow at its physiological maximum, the economy will fail to emerge as a dual economy. Hence, the
viability condition for adequate food production (defined according to the requirement that population grows at its physiological maximum) is becomes the
same as the viability condition for the emergence of a dual economy from a
single-sector agricultural economy.
Since we are beginning with the case of a backward, single-sector, economy,
the natural implication is that the entire population P lives and works in the
agricultural sector. Let Y denote the agricultural output. We assume that land
in the agricultural sector L is fixed in supply, in the sense of being fixed with
regard to extensive cultivation. Furthermore, we assume that the agricultural
production function has a Cobb-Douglas form:
Y = eαt Lβ P 1−β
(1)
From the properties of Cobb-Douglas functions, we see that the agricultural
production function exhibits constant returns to scale. In equation [1], eαt
represents technical progress, assumed to take place at a constant rate, α. The
constant β indicates the elasticity of agricultural output with respect to an
increase in the supply of land. In the Cobb-Douglas production function, β also
represents the share of landlords in total output. If we assume that the supply
of land is fixed, then the landlord’s share will take the form of rent which is
defined as: the unimputed residual remaining after the share of labor in the
agricultural product, 1 − β, has been paid to the agricultural labor force.
Now, since land is assumed fixed, we may choose our origin for measuring
time so that the agricultural production function becomes:
Y = eαt P 1−β
(2)
This is the production function that we will be working with in this section.
Now, if we divide both sides of equation [2] by P , the total population (or
equivalently the total agricultural force), we obtain y, the agricultural output
per person:
y = eαt P −β
(3)
We are now interested in obtaining the growth rate of y. As we pointed out
above, the growth rate of y is simply ẏy . Thus, to obtain the rate of growth we
differentiate equation [3] with respect to time and obtain:
ẏ = αeαt P −β − eαt βP −1−β Ṗ
Dividing the expression above by y we obtain:
41
Ṗ
ẏ
=α−β
y
P
(4)
Equation [4] gives the growth rate of agricultural output per capita. But to
complete the expression above we need to say something about the function
which governs the growth of population, Ṗ
P.
We assume that if there is no agricultural production, then reproduction rate
literally falls to zero. Moreover, we assume that the mortality rate is constant
and equal to δ. Thus, when y = 0 then there are no births and the population
declines at a constant rate δ. In the event that there is agricultural production,
we assume that the rate of gross reproduction is an increasing function of the
agricultural output per head, y. It is simplest to assume that the rate of increase
in the gross reproduction rate is constant as per capita income increases. Let
the constant factor be γ. Of course, we cannot assume that the rate of gross
reproduction increases without bound as agricultural output per head increases.
We assume that the rate of gross reproduction is an increasing function of agricultural output per head up to some physiological maximum, say + δ. Thus
Ṗ
the net reproduction rate P
may simply be described by the model in equation
[5]:
Ṗ
= min(γy − δ, )
(5)
P
where γ is the rate of increase in the gross reproduction rate with respect to an
increase in the output of food per person. Here, note that the net reproduction
Ṗ
, is equal to the gross reproduction rate minus the mortality rate, δ.
rate, P
Next, we see from equation [5] that the net reproduction rate is the minimum of
the two rates determined by the physiologically maximum rate of reproduction
and the rate determined by the output of food per head.
Now, we have begun our analysis by assuming that a backward, single-sector,
agricultural economy exists. By our discussion in the previous section, we see
that if the backward economy exists then the population must grow at a rate
less than its physiological maximum. Thus, looking at equation [5] we see that
Ṗ
P = γy − δ. In this case equations [4] and [5] may be combined to give:
ẏ
= α − β(γy − δ) = α + βδ − βγy
y
(6)
Multiplying both sides by y we obtain the fundamental differential equation
for the theory of development of the agricultural sector (or equivalently, the
single-sector, backward economy):
ẏ = (α + βδ)y − βγy 2
(7)
Note that equation [7] fully describes the path of agricultural output. From
this we can derive the viability condition of the economy. This is done as follows:
if the viability condition, which is assumed to exist, is not met, then sustained
42
development will not occur. Development here means that ẏ is increasing. Thus,
if ẏ = 0, the economy is not growing and will remain a backward economy. From
equation [7] we can find out that value of y for which ẏ = 0 and let us call this
value of y the solution to the fundamental differential equation [7]. Now, if we
are interested in deriving the viability condition, then we have to find out if the
solution to [7] is a stationary solution or not: that is, for any initial value y(0)
we are interested in finding out the conditions under which y will continue to
grow without ever settling into an equilibrium. Alternatively, we want to know
the conditions under which ẏ will not grow: that is, are there any values of y
(stationary solutions) which once established will maintain themselves?
We may find all stationary solutions to equation [7] by setting it equal to
zero. We therefore set the rate of change in per capita income equal to zero:
(α + βδ)y − βγy 2 = 0
⇒ y[(α + βδ) − βγy] = 0
We can see that there are two solutions:
y1 = 0, y2 =
(α + βδ)
βγ
The first solution, y1 , doesn’t particularly interest us because by our previous
assumption, if y is zero then the population will fall off at a negative rate given
by the force of mortality, −δ.32 Thus, the population dies off exponentially and
we do not devote any further attention to this case.
The second solution, y2 = (α+βδ)
βγ , is necessarily positive. For this value of
y we have ẏ = 0. One slight point here: note that ẏ = 0 does not imply that
agricultural output or population are not increasing. Instead, both output and
population are increasing, but at the same rate which keeps agricultural output
per capita constant. We can see this from:
Ṗ
(α + βγ)
α
= γ[
]−δ = >0
P
βγ
β
Substituting this in equation [4] we see that:
Ṗ
α
ẏ
=α−β =α−β =0
y
P
β
Thus, population and output are increasing at the rate of
α
β,
forcing ẏ = 0.33
32 Recall, that gross reproduction is zero by assumption; therefore, net reproduction rate is
simply equal to the mortality rate, which is negative and equal to δ.
33 One can show that output is also increasing at the rate α . First, from Ṗ = α , we have
β
P
β
by integrating both sides:
8
1
dP =
P
43
8
α
dt
β
Now, under what conditions is y2 stable? To reiterate, we want to know
the conditions under which y2 will be an equilibrium; conditions, which if met,
will mean that y2 will be approached and maintained no matter what the initial
value of y is.
Let us begin by defining y + the minimum level of income at which pṗ attains
its physiological maximum, . Define y + :
We may find y
+
y + = min(y : γy − δ ≥ )
(8)
from the population model in equation [5]:
ṗ
= γy + − δ =
p
Hence:
y+ =
+δ
βγ
This is the value of y at which the population attains is maximum growth rate.
We can now derive our viability conditions by considering two conditions:
CONDITION 1 y2 < y +
CONDITION 2 y2 > y +
We will consider these two conditions and argue that if condition (1) is true
then the economy will reach a stationary point and remain there in equilibrium.
On the other hand, if condition (2) is true then the economy will grow without
bound— i.e., there will be no stationary solution. Before going on we wish to
point out that condition (1) is equivalent to:
y2 < y +
⇒
+δ
α + βδ
>
γ
βγ
where the expression above is obtained simply by substituting for the values for
y2 and y + in condition (1). Since γ > 0, the expression above becomes:
α−β <0
(9)
α−β >0
(10)
Thus, y2 < y + is equivalent to α − β < 0. On the other hand, by the same
method above, it is evident that condition (2) is equivalent to:
From which we have: ln P =
α
t.
β
Substituting this in equation [1] yields:
αt
Y = eαt P 1−β = eαt [e β ]1−β
from which it follows that Ẏ =
α
.
β
44
Now, assuming that the solution y2 exists we will show that the condition for
y2 to be an equilibrium is equivalent to α − β < 0, or y2 < y + (CONDITION
1). Alternatively, we will show that if α − β > 0 (CONDITION 2), then a
long-run sustained growth in per capita output will be achieved from any initial
output.
First, let us solve the fundamental differential equation. We have:
ẏ = (α + βδ)y − βγy 2
Let us have a change in variables. We define a new variable u:
y = y2 −
1
u
u̇
u2
We substitute this in the fundamental differential equation and obtain:
⇒ ẏ =
1
1 2
u̇
=
(α
+
βδ)(y
−
−
)
−
βγ(y
)
2
2
u2
u
u
Multiplying and dividing the first term on the right hand side by βγ, we obtain:
u̇
(α + βδ)
1
1 2
=
βγ
−
−
(y
)
−
βγ(y
)
2
2
u2
βγ
u
u
Notice that the term (α+βδ)
on the right hand side is equal to y2 by definition
βγ
so the expression above reduces to:
u̇
1
1 2
=
βγy
(y
−
−
)
−
βγ(y
)
2 2
2
u2
u
u
⇒
u̇
1
1
1 1
= βγ(y2 − )[y2 − (y2 − )] = βγ(y2 − )( )
2
u
u
u
u u
We eliminate y2 by setting y2 =
(α+βδ)
βγ
obtaining:
βγ α + βδ
u̇
1
=
[
− ]
u2
u
βδ
u
⇒
βγ u(α + βδ) − βγ
u̇
(α + βδ) βδ
=
[
]=
− 2
u2
u
uβδ
u
u
Multiplying throughout by u2 we obtain the fundamental differential equation
completely expressed in terms of u:
u̇ = (α + βδ)u − βδ
We can now solve this differential equation:
du
= −βδ + (α + βδ)u
dt
45
(11)
by setting βδ = A and (α + βδ) = B. Then equation [11] becomes:
du
= −A + Bu
dt
Multiplying both sides by dt and dividing both sides by (−A + Bu) we obtain:
du
= dt
(12)
−A + Bu
Before we integrate both sides though we need to specify an initial condition.
Notice that since this is a first order differential equation, we need specify only
one initial condition. Let this initial condition by y(0) at t = 0. Now we express
the initial condition in terms of u. We have y = y2 − u1 and substituting y(0)
into y we have:
y(0) = y2 −
Therefore, u(0) =
1
y2 −y(0) .
1
u(0)
The differential equation is therefore:
8
8
du
= dt
1
−A + Bu
0
y −y(0)
2
Integrating this, we have:
1
= |t|t0
| ln(−A + Bu)|u 1
y2 −y(0)
B
Which further expanded is simply:
Or:
1
B
1
ln (−A + Bu) − ln (−A +
)=t−0
B
B
y2 − y(0)
1
−A + Bu
)=t
ln(
B
−A + B
C
where C = y2 − y(0). Taking anti-logs of both sides we have:
−A + Bu
= eβt
−A + B
C
Which solved for u gives:
eBt
B
A
[−A + ] +
B
C
B
Substituting the expressions for A, B, and C, we have the final solution for u(t):
u(t) =
u(t) = e(α+βδ)t [
1
βγ
βγ
−
]+
y2 − y(0) α + βδ
α + βδ
But remembering that y(t) = y2 −
1
u(t) ,
we have the final solution for y(t):
46
y(t) = y2 +
βγ
e(α+βδ)t [ α+βδ
1
1
+ y(0)−y
]−
2
(13)
βγ
α+βδ
where equation [13] is valid for y(0) = y2 . We will now show:
(1) That y2 is a stationary equilibrium when y2 < y + . Recall from above that
this is equivalent to α − β < 0, or CONDITION 1.
(2) That y2 will not be a stationary equilibrium when y2 > y + , which is equivalent to α − β > 0, or CONDITION 2. In other words, when this condition
holds, there will be sustained growth in the economy. Let us now deal with one
condition at a time.
CONDITION 1: In essence, we want to show that no matter what the initial
output per head, the economy in the long run (i.e., for a time T , where T >> t)
will settle down to a level y2 . This per capita agricultural output will maintain
itself once established. Now, there are three possibilities for y(0):
Case (a) 0 < y2 < y + ≤ y(0)
Case (b) 0 < y2 < y(0) < y +
Case (c) 0 < y(0) < y2 < y +
Let us first deal with cases (a) and (b) together. In both these cases, it is
sufficient to show that (i) the difference y(t)−y2 is always ≥ 0, and (ii) that this
difference is declining to zero from above as t → ∞. Let us begin by showing
that (i) and (ii) holds for cases (a) and (b).
Examining the expression below we see that if y(0) > y2 , i.e., cases (a)
1
and (b), then the fraction y(0)−y
must be positive and therefore the entire
2
denominator of the expression below is positive. This shows that y(t) − y2 ≥ 0,
which completes (i) for cases (a) and (b). We now show that (ii) holds for these
two cases: that is, we show that this difference approaches 0 from above as t →
∞. To see this, examine the term e(α+βδ)t in the denominator of the following
expression. Clearly, as t → ∞, e(α+βδ)t approaches a very large number which
means that the right hand side of the expression below, and hence y(t) − y2 ,
must approach zero from above:
y(t) − y2 =
1
βγ
1
e(α+βδ)t [ α+βδ
+ y(0)−y
]−
2
βγ
α+βδ
We can summarize these cases in figures 9.1 and 9.2.
For case (c), let us show that (i) the difference y(t) − y2 is always ≤ 0, and
(ii) that this differences approaches zero from below, as t → ∞. Handling (i)
1
first, we see that the fraction y(0)−y
is negative. Moreover, it can be easily
2
shown that by virtue of this, the denominator on the RHS of the expression
above is negative.34 Therefore, the right hand side of the expression above is
negative when 0 < y(0) < y2 < y + . This proves (i). Now, we show that
(ii) is true. Notice that as t → ∞, the denominator decreases, thereby raising
34 All you have to do is to expand the denominator and substitute y =
2
algebra, the result follows.
47
α+βδ
.
βγ
With a little
Figure 9: y2 as a stationary solution in CONDITION 1, Cases (a) and (b)
Figure 10: y2 as a Stationary Solution in CONDITION 1, case (c)
the (negative) fraction as a whole. Therefore, the difference y(t) − y2 becomes
smaller as t → ∞, and approaches 0 from below. This is shown in figure 10.
Together, cases (a)-(c) prove that CONDITION 1 corresponds to a stable
stationary solution to the fundamental differential equation. Now it remains
to prove that CONDITION 2 corresponds to a continuous growth situation—
i.e., y2 will not be approached in the limit. Equivalently, this condition will be
seen to be the viability condition for the single-sector agricultural economy to
emerge as a dual economy.
CONDITION 2: This condition corresponds to y2 > y + , which, as we have
shown above, is equivalent to α − β > 0. There are three cases which are
possible in CONDITION 2:
Case (a) 0 < y + < y2 < y(0)
Case (b) 0 < y + < y(0) < y2
Case (c) 0 < y(0) < y + < y2
With regards to cases (a) and (b) it is clear that y2 by definition is that stationary level assuming that the population growth has not reached its maximum.
But if y(0) is already greater than y + , then population cannot grow any faster
than the physiological maximum. Thus, the stationary level, y2 , will not be
reached and instead the economy will be characterized by continuous growth.
This is shown below in figure 11.
In case (c), when 0 < y(0) < y + < y2 , the general solution has the form:
y(t) − y2 =
1
1
e(α+βδ)t [ y12 + y(0)−y
]−
2
48
1
y2
Figure 11: Sustained Growth in CONDITION 2, Cases (a) and (b)
1
1
We see that the fraction y(0)−y
is negative. Since, y12 < (y2 −y(0))
< 0, the
2
right hand side remains negative and approached zero from below. But y(T ) =
y + < y2 for T >> t, since y(t) approaches y + from below and cannot surpass
it for, once again, it would require population growth at a rate greater than the
physiological maximum. Hence the growth path is stable.
It is clear from the discussion above that depending upon the conditions of
production and the net reproduction rate, the system is characterized either by
a low-level equilibrium, in which output per head is constant, or by a steady
growth equilibrium, in which output per head is rising and population is growing
at its physiologically maximum rate. This has some important implications for
policy making, which we discuss below.
First of all note that any change in social policy affects some parameter
of the system. Now, if an economy is in a low-equilibrium trap, i.e., y2 is a
stationary solution and thus ẏ = 0, and if β is assumed constant, then the
planner can only affect two parameters: α, the rate of technical progress, and
, the maximum net rate of reproduction. We can conceive of a situation where
α can be increased (without changing β) such that the sign of α − β changes
from negative to positive, or equivalently, the economy experiences sustained
growth (CONDITION 2) instead of a low-level equilibrium (CONDITION
1). In the case of sustained growth there will be a steady increase in the output
of food per capita. Alternatively, an improvement in medical technique will
increase , which will also decrease δ, thereby worsening the test criterion. On
the other hand, if is decreased this may result in a lowering of y + to a level
that it falls below y2 , at which point, sustained growth becomes possible. Thus,
in this model, to escape the low-level equilibrium trap, changes in the rate of
introduction of new techniques or measures of birth control are required— the
resulting situation will mean sustained growth in the economy which in turn
means there will be steady increases in the output of food per capita.
This model further assumes that when sustained growth commences, the
population continues to consume an amount of food equal to y + per capita,
since this is sufficient to enable the population to grow at its maximum rate
of reproduction, . In this case, since output per head y is increasing but
consumption per head y + is constant, a steadily increasing agricultural surplus,
49
s, will emerge, where agricultural surplus s is defined as:
y − y+ = s
(14)
We see that s is defined as the amount of food in excess of what the population requires to maintain its maximum net reproduction rate. Thus, when
the agricultural output per head, y, exceeds y + — the level of output necessary
to bring about the maximum rate of increase in the population— an agricultural
surplus, s, is generated which implies that part of the labor force may be released from agricultural production. The released labor will produce industrial
goods, and because y − y + > 0, the rate of growth of the total labor force will
not be affected.
Since our model has a food surplus which has permitted labor to be released
for use in the manufacturing sector, we may now begin to talk in terms of
a dual economy. We assume that our viability condition has been met, and
therefore there is sustained growth in output and a growing manufacturing
sector. We will now formulate a model of a dual economy with an agricultural
and a manufacturing sector.
First, let us denote manufacturing population by M , and the agricultural
population by A. Thus, the total population becomes:
P =A+M
Now, how does the theory of population change for a dual economy with
an agricultural and manufacturing sector? The net reproduction rate is the
minimum of the physiologically maximum rate and the gross reproduction rate
corresponding to the output of food per capita for the total population, less δ
the mortality rate. For the latter we note that the total agricultural output—
recalling that y is the agricultural output per head— is equal to Ay. Thus, the
A
output of food per capita for the total population will be y P
. Our population
model is therefore:
Ṗ
A
= min( , γy − δ)
P
P
Clearly, when A = P the population model above reduces to that where the
entire labor force is engaged in agricultural activities.
Now, as we have mentioned earlier, if an agricultural surplus exists in the
dual economy, then labor from the agricultural sector may be released to the
manufacturing sector. We assume that the rate at which labor may be freed from
the land is such that it is just sufficient to absorb the agricultural surplus. If, as
it may well happen, the growth of the manufacturing sector is not sufficiently
rapid, then some of the excess labor force will remain on the land and part or all
of the surplus may be consumed in the form of increased leisure for agricultural
workers. Such an event will lead to the destruction of manufacturing activity or
the importation of food by increased manufactured goods. To simplify matters,
we assume that there is a balance between the expansion of the manufacturing
labor force and the production of food. We say that the proportion of the
50
total labor force engaged in agriculture, A, is the ratio of the subsistence level
of agricultural production to the actual agricultural output per man in the
agricultural population:
y+
A
=
y
P
What this says is simply this: if there is no agricultural surplus, then y = y +
and the entire population will be engaged in agriculture. But if y > y + then
an agricultural surplus exists and some of the agricultural labor force may be
released for manufacturing activities. Assuming that s exists, the rate at which
A
agricultural labor force can be released for manufacturing is simply P
, because
the total food production is Ay while the total food consumption is P y + — for
there to be a balance we thus require that the expression above hold true. Note
that the relationship above holds only when y > y + ; hence, we restate the
relationship of the distribution of labor between agriculture and industry as:
A
y+
= min(1,
)
P
y
(15)
From equation [15] we can see that at the very least, the entire population
is engaged in agricultural activities (corresponding to the case: y = y + ), or,
A/P = 1). Otherwise, in the event y > y + , some of the agricultural labor
force is released into manufacturing activities, in which case the proportion of
+
population engaged in agriculture is simply = yy .
We have so far described the agricultural sector and the distribution of the
labor force between manufacturing and agriculture. We now move onto a fuller
discussion of the manufacturing sector.
3.1.2
Manufacturing Sector
We denote the manufacturing labor force by M and the capital stock by K.
We assume that the level of manufactured output, X, is a function of M and
K. Since we can expect technical progress to be quite rapid in the manufacturing sector we have a third argument in the manufacturing sector production
function: technical progress. This is represented by the time t at which manufacturing takes place:
X = F (K, M, t)
(16)
We assume that F exhibits constant returns to scale which is equivalent to
the assumption that the manufacturing output is exhausted by factor payments
to labor and the owners of capital. Let us now suppose that the relative share of
labor in the manufacturing output is constant and equal to 1−σ. Further assume
that technical change is neutral and represented by some function of time, A(t).
Then the production function, F , can be represented in a Cobb-Douglas form
as:
51
X = A(t)M 1−σ K σ
(17)
Let us suppose that the rate of growth, A, is constant, say:
Ȧ
=λ
A
Then cross multiplying by A and setting Ȧ = dA/A we have the following
differential equation:
dA
= λdt
A
Let us impose the initial condition that at t = 0 we have A = A(0). Thus, our
differential equation becomes:
8
8
dA
= λdt
A(0) A
0
Which is simply:
| ln A|A(0) = |λt|0
⇒ ln A − ln A(0) = λt
⇒ ln
A
= λt
A(0)
Taking anti-logs of both sides and multiplying throughout by A(0) gives us:
A = A(0)eλt
(18)
Inserting this into equation [17] gives us another form of the production function:
X = eλt A(0)M 1−σ K σ
(19)
Now, just as in the case of the agricultural production function, we can obtain
the output per man in the manufacturing sector by dividing the equation above
by M . Letting x be the output per man and k, the capital per man, we have:
X
M 1−σ σ
= A(0)eλt
K
M
M
⇒ x = eλt A(0)(
K σ
)
M
⇒ x = eλt A(0)k σ
Let us further choose our units of X such that A(0) = 1. We therefore have the
final version of the production function:
x = eλt kσ
52
(20)
If we differentiate the equation above with respect to time and then divide by
x, we obtain the growth rate of manufacturing output per capita:
eλt kσ−1 k̇
eλt kσ
ẋ
= λ λt σ + σ λt σ
x
e k
e k
This gives us an expression describing the net growth of manufacturing output
per capita:
ẋ
k̇
=λ+σ
(21)
x
k
Our model is almost complete: we have described the growth rates of agricultural and manufacturing output per capita. However, a glance at the previous
equation tells us that we still need an expression for the rate of capital accumulation, kk̇ . We will now solve this problem.
One way to solve for kk̇ is to use the Ex Post identity that consumption plus
investment in the manufacturing sector must equal output in the same sector.
If we assume that industrial workers do not save (that is, they consume their
entire income) and that property owners do not consume (that is, they save,
or equivalently, invest all their income), then the consumption of manufactured
goods, in the manufacturing and agricultural sectors, is simply equal to the
share of labor in the product of the manufacturing sector. Now, in the manufacturing sector, the industrial wage-rate, w, must, by neoclassical marginal
product calculus, be equal to the marginal productivity of labor, or:35
∂X
= (1 − σ)x = w
∂M
The first equality above, which states that the marginal product of labor in
the manufacturing sector, or the industrial wage-rate, is equal to the share of
labor in the manufacturing product can be simply derived by taking the partial
derivative of equation [19] with respect to the manufacturing labor force, M .
Letting A(0) = 1 as before, we differentiate equation [19] to obtain:
σ
∂X
Kσ
= (1 − σ) eλt σ
∂M
M1
,
K
σ
But M
σ = k , and thus the underbracketed terms in the righthand side are
equal to x by virtue of equation [20]. We therefore obtain:
∂X
= (1 − σ)x
∂M
where, as before, x is the output per person in the manufacturing sector and
1 − σ is the share of manufacturing labor in the product of the same sector.
The condition that the industrial wage-rate is equal to the marginal product is
35 Note that the following expression is written incorrectly in Jorgenson (1961). Instead of
∂X
writing ∂M
he has written ∂M
. Please note this error. See p. 322 of Jorgenson (1961).
∂X
53
a necessary condition for profit maximization. That manufacturing firms seek
to maximize profits is quite a reasonable assumption; however, the case is quite
different for the agricultural sector. Here, we can assume that there is a difference in the wage rates between the manufacturing and the agricultural sector.
This is a reasonable assumption because we can assume that whereas the wage
in the manufacturing sector is determined according to marginal product calculus, no such neoclassical determination takes place in the agricultural sector.
In fact, assuming, as we have, that agricultural production is carried out on
traditional lines, we can expect wage determination in the agricultural sector to
defy marginal product calculus.
However, despite the fact that we assume a difference in manufacturing and
agricultural marginal products (which is transmitted to a difference in wage rates
between the two sectors) neoclassical analysis does not postulate the existence
nor the possibility of zero marginal product. A difference in manufacturing and
agricultural marginal products exists because of different techniques of production and organization; but, agricultural marginal product is never zero— always
positive. This is, as we have emphasized repeatedly, the fundamental difference
between the classical and neoclassical approaches. For this reason, the analytics
of the development process are markedly different in the two models.
We have postulated that there exists a wage differential between the manufacturing and agricultural sectors of the dual economy. Now, what is the
direction of this wage differential? Quite clearly, in a dualistic setting, where
(a) manufacturing activity is more productive than agricultural activities, and
where (b) the economy is assumed to grow through labor movements from the
agricultural to the manufacturing sector, we can see that agricultural workers
will respond to wage differential between manufacturing and agriculture only
if the industrial wage-rate is greater than agricultural income (which includes
agricultural wage and rent).
Let us then assume that the wage-differential is proportional to the industrial
wage rate. Let µ, where 0 < µ < 1, denote the ratio between agricultural income
y
per capita, y, and the industrial wage-rate, w. Thus, µ = w
. Then the total
wage-bill for the entire economy is simply equal to:
wM + µwA = (1 − σ)X + qY
(22)
where wM is the industrial wage bill and µwA is the total agricultural income,
expressed in terms of manufactured goods. On the right hand side of equation
[22] we have (1−σ)X which is the consumption of manufactured goods by workers in both sectors and qY is the value of agricultural output measured in terms
of manufactured goods. Thus, q is the terms of trade between agricultural and
industry. Note that equation [22] assumes that the entire agricultural output is
consumed. This is a natural consequence of an agricultural sector where production is not fully rationalized— were it not so, then equation [23] would have
to be modified to reflect the fact that marginal products in the two sectors will
be equal in the long-run. However, as mentioned earlier, we assume that agricultural organization is traditional, ensuring that marginal products will differ
54
between the two sectors.
The assumption that agricultural production is traditional in nature and
spirit— the consequence of which, again, is that land-owners will consume their
income— has an immediate implication: investment in the manufacturing sector
is completely and totally financed out of the incomes of the property holders in
that sector.36 Therefore, it is clear that once the share of labor in the manufacturing product is distributed to workers in the form of food and consumption
goods, and agricultural workers have received the proportion of manufacturing
output which must be traded for food, the remainder of manufacturing output
is available for capital accumulation, i.e., investment.
Here, capital accumulation is defined as investment less depreciation, where
depreciation is a constant fraction of the capital stock. Thus, the net capital
accumulation, K̇, is the total investment I minus the capital depreciation, ηK:
K̇ = I − ηK
(23)
where η is the constant proportion of capital depreciation. Then by definition
that total industrial output equals total consumption plus total investment, we
have:
X = (1 − σ)X + I
which implies the following relation between output and capital stock:
X = (1 − σ)X + K̇ + ηK
(24)
Equation [24] closes the system. We have fully described the growth of
output in the agricultural and manufacturing sectors. We now study some
important results of development in a neoclassical dual economy.
3.1.3
Development
In the previous two sections we have developed some very important results. The
first, and major, result is to note that a dual economy may grow only if there
exists an agricultural surplus. The existence of an agricultural sector permits
the emergence and, subsequently, the growth of the manufacturing sector by
releasing labor from the agriculture to the manufacturing sector.
That an agricultural surplus is necessary for the dual economy to grow is
equivalent to α − β > 0. We shall assume in the forthcoming analysis that
this condition holds. For if not, that is, α − β < 0, then the economy remains
in an undeveloped state for the simple reason that no agricultural surplus exists, which means no agricultural labor can be released for the emergence and
growth of a manufacturing sector. Thus the undeveloped, stagnant economy
in which output of food per capita remains constant and population grows at
36 Do recall that we do not have the income of manufacturing labor force as a source of investment in that sector because we have assumed that the entire wage bill in the manufacturing
sector is consumed by the workers.
55
less than its physiological maximum, will produce only food and other products
of the traditional sector. For this reason, we are, obviously, not concerned or
particularly excited with the case when α − β < 0; for in such a situation, the
theory of a dual economy reduces to that of a backward, single sector economy.
Clearly, the more interesting case is when an agricultural surplus does exist,
or α − β > 0. Here, we will add to the analysis of the preceding sections by
detailing the dynamics (i.e., level and growth) of the agricultural and manufacturing labor force, population, capital, terms of trade and manufacturing and
agricultural wages.
Let us the begin our analysis at that stage when an agricultural surplus
comes into being, which occurs when y = y + . When this happens, two events
follow immediately; one, an industrial labor force comes into being and, second,
agricultural output has attained that minimum level at which population may
grow at its maximum rate of net reproduction . Thus, at time t = 0 when
y = y + , the path of population level, P (t), may be expressed through the
equation:
P (t) = e t P (0)
(25)
where P (0) is the population at time t = 0. Now, note that population is
growing at a constant rate and if we assume that consumption per capita is also
constant, then food output and population must grow at the same rate:
Y
(26)
= y+
P
Here the left hand side is the per capita food consumption, which by our assumption must equal y + once y equals y + . Thus the growth rate of Y can be
calculated by:
Y = P y + = P (0)e t y +
(27)
Given the equation above we can calculate the required rate of growth in
the agricultural labor force necessary to maintain the growth of the agricultural
surplus. First, from equation [2] note that Y = eαt P 1−β . But in a dual economy
setting, where the agricultural sector ceases to be the sole sector, we must denote
the agricultural labor in equation [2] by the variable A, and not by the variable
P which previously stood for the agricultural labor force, but now denotes the
total population in the economy. Hence, setting equations [2] = [27] equal to
each other, we have:
Y = eαt A1−β = P (0)e t y +
Dividing both sides by eαt we have:
A1−β = P (0)y + e[
Taking the
1 th
1−β
−α]t
root of the expression above, we have:
56
−α
1
A = [P (0)y + ] 1−β e[ 1−β ]t
(28)
Now, let us recall from equation [3] that y = eαt P −β . But now see that we
have chosen our present origin of time when y = y + . Then, substituting t = 0,
y = y + and P = P (0) in equation [3] we have:
y + = eα0 P (0)−β
⇒ y + = P (0)−β
We substitute this in equation [28] and obtain:
−α
1
A = [P (0)P (0)−β ] 1−β e[ 1−β ]t
−α
1
⇒ A = [P (0)1−β ] 1−β e[ 1−β ]t
−α
⇒ A = P (0)e[ 1−β ]t
But note that at t = 0, P (0) = A(0). Therefore, our final expression for
agricultural labor force is:
−α
A = A(0)e[ 1−β ]t
(29)
It is clear from equation [29] that A may either grow, decline or remain
constant depending only on the relative magnitude of the two parameters α
and .37 Also, from equation [29] we can immediately deduce an expression for
the manufacturing labor force. First, we have the total population P as the
aggregate of the manufacturing and agricultural labor force, or P = A + M .
Thus, subtracting equation [29] from P we have:
M (t) = P (t) − A(t)
−α
⇒ M = e t P (0) − P (0)e[ 1−β ]t
Which gives us the final expression for the manufacturing labor force:
−α
M = P (0)(e t − e[ 1−β ]t )
(30)
Do note that when t = 0, M = 0.38 This is in accordance of our earlier statement
that until the economy generates a positive food surplus, a dual economy cannot
emerge.
Ṁ
Examining equation [30] we are led to ask, if M
will grow faster, slower or
the same rate as the population, which grows at . To answer this we must check
37 Recall
38 This
0.
that we have β fixed.
is clearly obvious from simple substitution: M = P (0)(e 0 −e
57
−α
[ 1−β
]0
) = P (0)[1−1] =
−α
the relative magnitude of and [ 1−β
]. From the fact that we require α − β > 0,
we can add to each side and obtain:
< +α−β
⇒ − α < (1 − β)
which yields:
>[
−α
]
1−β
(31)
From equation [31] it is immediately obvious that the manufacturing labor force
will grow at a rate much more rapid than the population growth rate.39 Finally,
in the long-run the growth rate of the manufacturing labor force will approach,
in the limit, the rate of growth of population, . We can show this result in yet
another way. Consider the expression for M :
−α
M = P (0)[e t − e[ 1−β ]t ]
−α
To make matters simpler let us denote [ 1−β
] as v. Differentiating the expression
above we have:
Ṁ = P (0)( e t − vevt )
We can now obtain
Ṁ
M
by simple division of the two expressions above:
Ṁ
( e t − vevt )
=
M
(e t − evt )
We can easily see that over the interval (0, ∞), Ṁ
M declines from ∞ to .
Having examined the dynamics of the growth of the manufacturing labor
force we now turn our attention to capital accumulation. To study the dynamics
of capital accumulation we require three important relations. First we have the
expression for the size of the manufacturing labor force; reproducing equation
[30] we have:
−α
M = P (0)[e t − e[ 1−β ]t ]
(32)
In addition, from equation [19] we have the production function for the manufacturing sector:40
39 Yet another way to see this result is to note that the result in equation [32] indicates by
virtue of equation [30], that the agricultural labor force will grow less rapidly compared to the
population growth rates. This is in turn implies that the manufacturing labor force will have
to grow more rapidly than the population growth rates, since the rate of growth of population
is simply the weighted average of the rates of growth of each of its two components.
40 Notice that compared to equation [19] the following equation has chosen the units of X
such that A(0) = 1.
58
X = eλt K σ M 1−σ
(33)
And finally, we reproduce from equation [24] the identity of industrial output
equal to consumption and investment:
X = (1 − σ)X + K̇ + ηK
(34)
Equation [34] can also be expressed as:
σX = K̇ + ηK
,1
, 1
(35)
K̇ + ηK = σeλt K σ M 1−σ
(36)
A
B
where A is savings and B is investment. Now, we can substitute equation [33]
into equation [35] and obtain:
All that remains for us is to substitute the expression for M (from equation
[32]) into the expression above, thereby obtaining:
−α
K̇ + ηK = σeλt K σ [P (0)(e t − e( 1−β )t )]1−σ
(37)
The expression above simplifies to the fundamental differential equation for the
development of a dual economy:
−α
K̇ = σeλt K σ P (0)1−σ [e t − e( 1−β )t ]1−σ − ηK
(38)
The solution to the differential equation above is much too long for us to consider
here. Instead, we will discuss some major aspects of the solution to equation
[39].41
Firstly, we note that no stationary situation is possible for an economy in
which capital accumulation is possible. This is equivalent to the statement that
there is no stationary situation in an economy with an agricultural surplus, i.e.,
α − β > 0. Indeed, once the economy has begun to grow (which occurs when
y = y + ) it must continue to grow. But what will be the pattern of the growth
of the dual economy? That depends on two initial conditions:
(1) The size of the population when growth begins, i.e., P (0), and
(2) The initial capital stock, K(0).42
Of these two, only (1) has an effect on the long-run growth of the economy.
The influence of (2), the initial capital stock, dies out very quickly; indeed,
the greater the rate of depreciation η and the larger the share of labor in the
manufacturing product, (1 − σ), the more rapidly will the effects of the initial
capital stock disappear.
Secondly, there is no “critical” level of an initial capital stock. In contrast
to the classical model, where there is a critical level of initial capital stock required for sustained growth in that dual economy, the neoclassical dual economy
41 The
interested reader can see Jorgenson, D., (1961) p. 331 for solution to equation [38].
again, we have chosen t = 0 as that stage when growth begins, or when y = y + .
42 Once
59
experiences sustained growth given any level of initial capital stock. The combination of a positive and growing agricultural surplus s combined with a small
positive capital endowment will give rise to a rapid rate of growth, akin to the
“take-off” stage discussed in Rostow’s model.
Thirdly, if sustained growth occurs, then in the long-run capital and output
must grow at the same rate, even if there is no technical change. Let us show
this result starting with the case of no technical change. If there is no technical
change, then capital, output and population will grow at the same rate . If,
on the other hand, there is technical change, then population will grow at its
maximum rate of while capital and output will grow at a more rapid rate of
λ
1−σ + , where, λ is the rate of technical progress and 1 − σ is the share of labor
in the manufacturing product.
Fourthly, growth in the manufacturing output is more rapid the greater the
rate of growth of the labor force or the more rapid the rate of technical progress,
λ; the rate of growth of manufacturing will be less rapid the greater the share of
labor in output or the smaller the savings ratio. We can show the results above
by decomposing the rate of growth of manufacturing into the rate of technical
progress, the rate of growth of the industrial labor force and the rate of capital
accumulation. First, we have the production function in the manufacturing
sector:
X = eλt A(0)M 1−σ K σ
Differentiating this, we have:
Ẋ = λeλt A(0)M 1−σ K σ + eλt A(0)(1 − σ)M −σ Ṁ + eλt A(0)M 1−σ σK σ−1 K̇
Dividing the expression above by X we have the rate of growth of manufacturing
output:
K̇
Ẋ
Ṁ
+σ
= λ + (1 − σ)
X
M
K
,1
,1
A
(39)
B
So that the rate of growth of output in the industrial sector is equal to the rate
of technological progress plus a weighted average of the rates of growth of the
manufacturing labor force (A) and the rate of growth of the capital stock (B).
Now, since the capital stock always grows at some positive rate and the growth
of the manufacturing labor force begins at an extremely high rate and declines to
the rate of population growth, the initial rate of growth of manufacturing output
must be extremely high, declining gradually and approaching its equilibrium
value. This result has an interesting policy implication: if one considers the
experience of the now developed countries, we observe a “big-push”. Many
economists have attributed this big-push to high levels of capital stock, arguing,
therefore, that the same big-push can be replicated in the now less developed
countries by massive infusion of capital. It is clear from the discussion above
60
that such an infusion is unnecessary for development leading to sustainable
growth.
We have so far described the dynamics of the population, manufacturing
labor force, capital accumulation and manufacturing output. We now discuss
some final aspects of the neoclassical dual economy— we will discuss the development of wages and the terms of trade between the advanced manufacturing
sector and the backward agricultural sector. First, recall that wages per person,
w, must be equal to the share of labor, (1 − σ), multiplied by the output per
person, x:
w = (1 − σ)x
To inspect the development of wages we differentiate the expression with respect
to t obtaining:
ẇ = (1 − σ)ẋ
Dividing throughout by w to obtain the rate of growth of wages we obtain:
ẇ
(1 − σ)ẋ
=
w
w
But w = (1 − σ)x and therefore:
ẇ
(1 − σ)ẋ
ẋ
=
=
w
(1 − σ)x
x
But
ẋ
x
=
Ẋ
X
−
Ṁ
M
by definition. Hence, the expression above becomes:
ẋ
Ẋ
Ṁ
λ
ẇ
= =
−
=[
+ ]−
w
x
X
M
1−σ
λ
+
by virtue of the fact that the rate of growth of output in the long-run is 1−σ
ẇ
while that of the manufacturing labor force is simply . Thus, w can be
expressed as:
ẇ
λ
=
(40)
w
1−σ
Clearly, if there is no technological progress in the manufacturing sector, real
wages will reach some constant level. If, on the other hand, there is technical
progress, real wages rise more rapidly, the more rapid the rate of technical change
and the higher the savings ratio. Another way to state this is, the higher the
share of labor in the manufacturing output, the less rapid the rise of real wages.
Having dealt with the dynamics of real wages, let us now turn to the dynamics of the terms of trade between the manufacturing and agricultural sectors.
Let us first reproduce the fundamental relation of the terms of trade q. From
equation [22] we have:
61
a
c
b
d
1, 1 , 1 , 1,
wM + µwA = (1 − σ)X + qY
,
1 ,
1
W
C
Let’s examine the expression above, which is really equation [22] once again. a
is the manufacturing sector wage bill while b is the total agricultural income.
Thus, a + b is the total wage bill of the economy W , which, with the assumption
that workers do not save, must equal total consumption in the economy C,
consisting of the consumption of manufactured goods c and agricultural goods
d. Since a ≡ c, we can cancel these out and obtain:
µwA = qY
All that remains now is to insert the appropriate expressions for A and Y . Recall
−α
from equation [29] that A = P (0)e( 1−β )t and Y = P (0)e t y + . Substituting these
into the expression above we have:43
−α
µwP (0)e( 1−β )t = qP (0)e t y +
Canceling out P (0) from both sides and taking q on one side we have:
−α
µwe( 1−β −
q=
y+
)t
(41)
Now, to obtain the rate of growth of q, qq̇ , we require q̇. Accordingly, we
differentiate the equation above with respect to t and obtain:
q̇ = [
−α
−α
µ
− ]w + e[ 1−β −
1−β
y
]t
+
−α
u [ 1−β
− ]t
e
ẇ
+
y
We can now obtain an expression for the rate of growth of q by dividing the
expression above by q:
−α
−α
[ 1−β
− ]w yµ+ e( 1−β −
q̇
=
−α
− )t
(
q
µwe 1−β
)t
+
−α
u ( 1−β − )t
ẇ
y+ e
(
µwe
y+
−α
− )t
1−β
y+
And we therefore obtain the final expression for the rate of growth of q:
ẇ
−α
q̇
=[
− ]+
q
1−β
w
, 1 ,1
A
(42)
B
Two items of interest are immediately apparent from the equation above.
One, notice that the underbracketed terms A are negative, by virtue of equation
[31]. On the other hand, from equation [40] we can see that ẇ
w is positive
43 Note that Jorgenson has made an error in the following expression. He has P (0) only
on the left hand side, not on both sides, which is the case actually. See p. 330 of Jorgenson
(1961).
62
λ
and equal to 1−σ
. We now see that if technical progress in the manufacturing
sector declines to zero then the terms of trade for agriculture must decline.
Alternatively, the more rapid the technical progress in the manufacturing sector,
the less rapidly the terms of trade for agriculture deteriorate; if terms of trade
is sufficiently rapid, the terms of trade for agriculture may even improve. The
reverse holds true for technical progress in the agriculture sector— the more
rapid technical progress in that sector, the more rapidly must the terms of
trade deteriorate. Secondly, note that the more rapid the growth of population
the less rapidly will the terms of trade decline.
With this, our dicussion of the Jorgenson model is complete and we now
criticize and comment on the model.
3.2
Comments and Criticism
In this section we will first criticise Jorgenson’s neoclassical model and then
compare the classical and neoclassical models of the dual economy. We begin
with a criticism of the Jorgenson model.
Firstly, the model suffers from the fact that it relies on a Cobb-Douglas
production function. The model, as proposed by Jorgenson, does not apply to
all forms of the production function. This drawback has been corrected by later
neoclassical models of the dual economy, in particular Amano (1980), whose
model is the subject of the next section.
Secondly, recall that even though the neoclassical approach allows for technical progress in the agricultural sector, it does not account for the possibility of
capital accumulation in this sector. This is a serious drawback, that is tackled,
once again, in Amano’s model.
Thirdly, it seems somewhat curious that, once population grows at the physiologically maximum growth rates, everyone in the economy continues to consume at y + . The model does not allow for the food consumption per capita to
rise above y + as output of food per capita, y, increases. Another way to say this
is that the agricultural surplus is not dented by the increased consumption of
the remaining workers. This is, admittedly, somewhat of a copout— after all, one
of the strongest criticisms of the classical model was precisely that one could not
expect the remaining workers in the traditional sector to maintain consumption
at previous levels. Thus, to thwart the possibility of increased consumption by
the remaining workers in that model, a taxation scheme, such that it siphoned
off the extra surplus was devised. Such a scheme is also admittedly very hard
to formulate and implement. So it seems that this problem has been tackled in
Jorgenson’s model by assuming that everyone continues to consume the same
amount, for y ≥ y + . This defect is also addressed and overcome by Amano
(1980).
Finally, It will be interesting to compare the results of the two approaches.
Such a comparison was undertaken by Dixit (1970), whose results we now discuss.
Dixit’s discussion begins with a discussion of a 1967 paper by Jorgenson.
In that paper, Jorgenson claimed the following points when he contrasted the
63
classical and neoclassical approaches:
(1) The classical model implies a fall in the industrial capital/output ratio as
the economy develops. The ratio is asymptotically constant under Jorgenson’s
neoclassical model.
(2) The rate of growth of capital increases over time in the classical model, but
is asymptotically constant in the neoclassical model.
(3) In the classical model, output and employment in manufacturing grow at
the same rate so that productivity is constant, while it rises in the neoclassical
model.
(4) There must be an absolute decline in the agricultural labor force before
the surplus labor phase ends in the classical model; this is not a necessary
consequence of the neoclassical approach.
We are going to see that the differences between the classical and neoclassical
approaches are less striking than made out in the four points above. We begin
by restating some fundamental aspects of Jorgenson’ model. We assume that
we are at time t = 0 when the viability condition has just been satisfied. That
is, y = y + and the manufacturing sector has come into being. In this case, from
equation [30] we see that the manufacturing sector labor force is given by:
v
1 ,
−α
[
]t
t
1
M = P (0)(e − e − β )
−α
We simplify the expression above by employing v to denote [ 1−β
] Now, we will
attempt to find an expression for the rate of growth of M , i.e.,
by differentiating the expression above:
Ṁ
M.
We begin
Ṁ = P (0)( e t − vevt )
Therefore:
Ṁ
( e t − vevt )
=
M
(e t − evt )
(43)
Ṁ
declines from ∞ to . Having done this,
Clearly, over the interval (0, ∞), M
let us find the rate of growth of manufacturing output and then the rate of
growth of capital accumulation. The rate of growth of X is given by equation
[39] and is reproduced below:
Ẋ
K̇
Ṁ
= λ + σ + (1 − σ)
(44)
X
K
M
Now if we neglect depreciation, since it makes no difference to the results
below, we can then see from equation [35], substituting η = 0, that:
K̇ = σX
64
(45)
From this we can calculate the rate of growth of capital
sides of the equation above by K:
X
K̇
=r=σ
K
K
Now, we take the logs of both sides and differentiate:
K̇
K
by dividing both
(46)
ln r = ln σ + ln X − ln K
ṙ
Ẋ
K̇
=
− ln
r
X
K
Substituting equation [44] above we have:
⇒
λ+σ
K̇
K̇
+ (1 − σ)
K
K
Which yields:
ṙ
Ṁ
K̇
= λ + (1 − σ)[
− ]
r
M
K
Noting from equation [46] that r =
obtain:
K̇
K
(47)
we substitute in the equation above and
K̇
ṙ
= λ + (1 − σ)[ − r]
r
K
⇒ ṙ = λr + (1 − σ)r
⇒ ṙ = (1 − σ)r[
Ṁ
− (1 − σ)r2
M
λ
Ṁ
−r+
]
(1 − σ)
M
λ
, where µ is the rate of industrial technical progress in laborWriting µ = (1−σ)
augmenting form, and substituting this in the expression above we obtain:44
Ṁ
+ µ − r)
(48)
M
We are now ready to discuss points 1 through 4 above. First of all, we have
Ṁ
will decline from ∞ to over the interval
noted from equation [43] that M
Ṁ
(0, ∞). Therefore, it is obvious that M
+ µ will decline from ∞ to + µ over
the same interval (0, ∞).
Now, from equation [46] we can see that with M = 0 at t = 0, we have r = 0
at that instant. But if we take all the proper limits of equation [48] we see that
ṙ = (1 − σ)r(
65
Figure 12: Growth Rates of
Ṁ
M
+ µ, r
ṙ is infinite.45 This means that both r and ṙ become positive and the path of r
can be proved to be of the form shown in figure 12.
We can see that r rises monotonically to + µ, passes this value, equals
Ṁ
+
µ at some time t∗ , and then declines thereon to its asymptotic level + µ.
M
Clearly, during the first phase of development, r is rising. Correspondingly,
X
from equation [46] we see that K
is rising or that K
X is falling. This conclusion
is exactly the same that Jorgenson found for the classical model. Thus, we see
that point 1 above is not as striking as it first seemed.
We can also see from the analysis so far that point 2 arises from the simple
fact that Jorgenson is contrasting the asymptotic results of his model with those
of the surplus-labor phase in the classical model. Indeed, if we limit ourselves
to a finite time period, we see that the classical and the neoclassical yield the
exact same result: initially, the rate of growth of capital increases. It is only
asymptotically that the neoclassical rate of growth of capital approaches a limit
and settles there.
With regard to point 3 above, see that constant real wage in the classical
model implies a constant marginal product of labor. Clearly, if the production
function is of the Cobb-Douglas form, the average product is a constant multiple
of this, and hence, it too remains constant. This is the justification which
Jorgenson offers for his claim that productivity remains constant in the classical
model. But obviously, we see that the classical result need not be the case
44 Be
45 See
careful: the µ here is different from that used in Jorgenson’s model.
Dixit (1970), p. 234-235 for proof.
66
when we consider other forms of production functions.46 Moreover, productivity
change can also be explained by allowing for changes in the industrial real wage,
either because of technical progress in the agriculture sector or because of a shift
in the terms of trade.
For the neoclassical model we have already calculated the rate of change of
industrial productivity. By definition, change in industrial productivity, ẋx (= ẇ
w)
is simply:
Ẋ
Ṁ
−
X
M
From equation [44], we have:
Ẋ
Ṁ
K̇
Ṁ
Ṁ
K̇
−
=λ+σ −σ
= λ − σ[
− ]
X
M
K
M
M
K
λ
= µ. Thus, λ = µ(1 − σ). Also,
But note that by definition (1−σ)
Substituting above, we have:
K̇
K
= r.
Ẋ
Ṁ
Ṁ
Ṁ
−
= µ(1 − σ) − σ[
− r] = µ − µσ − σ
+ rσ
X
M
M
M
Which gives the final expression for the rate of change of industrial productivity:
Ṁ
Ṁ
Ẋ
−
= µ − σ(
+ µ − r)
(49)
X
M
M
What is the sign of the equation above? Clearly, the answer is ambiguous. Initially, the gap [ Ṁ
M +µ]−r is quite large and hence the rate of change of industrial
productivity is negative. But as time increases, this rate turns from negative to
positive at time t , which is indicated in the diagram above. We can therefore
see that point 3 above was overstated. In fact, the possibility of productivity
changing does exist in the classical model and contrary to Jorgenson’s claims,
neoclassical productivity is actually negative in the beginning of the growth
process.
With regards to the final point above, we can see that the absolute decline
in the agricultural labor force depends on the assumption in Fei-Ranis’ classical model and Jorgenson’s neoclassical model, that technical progress in the
agriculture sector is exogenous and neutral, and that there is no capital accumulation in that sector. This implies that the level of employment, L∗ at which
M P L = 0, is constant over time. But clearly, if there is surplus labor, then
one effect of technical progress in the agricultural sector is to render that labor
productive, which directly implies that the level L∗ changes. The same thing
will happen with capital accumulation in agriculture. Thus, it is possible that
through technical change the surplus labor phase may be overtaken by letting
46 See Marglin, S. A., Comment on Jorgenson, in Adelman and Thornbecke (eds.), The
Theory and Design of Economic Development, pp. 60-66.
67
L∗ overtake the agricultural labor force. This discussion indicates that the exogeneity and neutrality of technical progress are rather poor assumptions in the
context of a labor surplus model. This completes our discussion of point 4.
READINGS
Jorgenson, D. (1961) ‘The Development of a Dual Economy’, Economic Journal,
June 1961, pp. 309-334.
Dixit, A. (1970) ‘Growth Patterns in a Dual Economy’, Oxford Economic Papers,
1970.
<< We are not yet done with Amano’s discussion. >>
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