A CONCEPTUAL FRAMEWORK FOR THINKING ABOUT ECONOMIC
DEVELOPMENT AND DEVELOPMENT POLICIES. INFORMAL NOTES
Marco Missaglia and Lucia Corno
January 2005
CONTENTS
0. GDP ACCOUNTING
1. THE LEWIS MODEL. AN INFORMAL EXPOSITION
2. SOME REFINEMENTS OF THE LEWIS FRAMEWORK. POLICY ISSUES
3. MIGRATIONS: THE HARRIS-TODARO MODEL
4. LAND REFORM
APPENDIX
0. GDP ACCOUNTING
Measure of Economic Development: GDP per capita (material well-being….)
where :
Agriculture, Industry and Service
where:
Yj
Lj
Lj
sector J
L
N=
Population
L=
Labour Force
A, I, S =
= labour productivity in sector J
= proportion of labour force in
L
= participation Ratio
N
From (1) we can see the potential sources of the gap in per capita income between
different countries.
a. A difference in the participation ratio. An economy with many children and/or
unemployed will have a low ( L N ) .
b. A different occupational distribution; since (YI L I ) >> (Y A L A ) , it is convenient to
have ( LI L) as high as possible.
1
c. (Y A L A ) in the developed countries is roughly 40 times higher than in the
developing countries
d. (YI L I ) in the developed countries is roughly 10 times higher than in the
developing countries.
Thus, there is considerable scope for increasing labour productivity in agriculture in
developing countries. However, statistically speaking, reason b. is by far the most
important in explaining the gap (income gap) between developed and developing countries,
which provides the central justification for an industrialization–led development strategy: the
problem of development may be seen as the problem of moving people from agriculture to
industry, to increase the relative size of the industrial sector.
How can this objective be achieved? We need a broad conceptual framework to think
about this transition, and this conceptual framework lies at the core of development
economics.
1. THE LEWIS MODEL (1954). AN INFORMAL EXPOSITION
If development is structural change (Agriculture→ Industry→ Service), the main roles of
agriculture are:
1.
2.
Supplier of labour to industry (people move)
Supplier of a surplus of food. If international trade is not an option (and it is
not to the extent that countries want to achieve self sufficiency in this is
extremely important field), then a non-agricultural sector can develop only if
agricultural produces more food than its producers need for their own
consumption: this is the agricultural surplus.
There is also a third role played by the agricultural sector:
3.
Source of demand for industrial products, given the relevant size of agriculture
in a developing economy, Lewis is mainly concentrated on roles (1) and (2).
Lewis model has in mind a dual economy
Traditional Sector
Modern Sector
Basically, but
not only
not only rural/agricultural
Basically, but
urban/industrial
2
What is,economically speaking, the main feature of the traditional sector?
It is the existence of surplus labour or disguised unemployment. What does it mean? Be La the
amount of labour employed in agriculture; the production function with surplus labour is:
Y
La
B
A
Figure 1: the production function in agriculture
In the background of this production function: a very limited quantity of capital (we are
basically in a non-capitalistic, pre-modern sector) and a fixed amount of land (from which
diminishing returns to labour).
For any LA ≥ B, the marginal product of labour in agriculture in nil.
Then, if you reduce labour from A to B
total output is unchanged
≡
LABOUR SURPLUS
For a capitalist, the profit maximizing rule is
Real wage = Marginal product of Labour ( MPL )
But what happens in a family farm with labour surplus, where MPL = 0 ?
People are not paid their marginal product, because the objective of the family farm is not
profit maximization, but to guarantee an income to each of its members (an egalitarian, or
pre-capitalistic rule, as opposed to a capitalistic rule). People are paid their average product w (this
happens in the informal sector as well, in the cities. A cub driver might share his driving
with a friend)
3
Y
w
La
B
A
Figure 2: the average product of labour in agriculture
Clearly, in La = A, the average product w > marginal product = 0
If somewhere in the economy there is another sector where MPL > 0 , then moving people
from the traditional sector to this “modern” sector would increase total output of the
economy, there would be an efficiency gain.
But now imagine that,
Y
b
w
La
C
A
Figure 3: disguised unemployment in agriculture
In A MPL = b > 0 , but still w > b . Again, people are paid more than their marginal product.
If somewhere in the economy there is a modern sector where MPL > b , the economy
4
would still enjoy an efficiency gain by moving people from the traditional to the modern
sector, even if the marginal product in the traditional sector is higher than zero. How much
labour would a profit maximizing, capitalist firm employ at a wage rate = w ?
It would hire C units of labour ( MPL = w )
CA is the amount of disguised unemployment. Disguised unemployed are those who
have a job, but are less productive than they would be should they be employed in the
modern sector. In other and hopefully more transparent words: in a fully capitalistic world
these people would be unemployed, without a job.
We are now ready to understand the logic of the Lewis model of economic development
(extended by Fei and Ranis in 1961). The logic of the model is illustrated in Figure 4.
Consider a situation where the entire labour force is employed in agriculture. This is the
starting point of a development process, people are so poorly productive that they must be
all engaged in producing their own subsistence. We are in the labour surplus phase, since
MPL = 0.
Now consider a small reduction in the labour force employed in agriculture, LA: what
happens? If the wage rate in agriculture stays at w (so that workers are now paid a bit less
than their average product1) then, given that total output stays constant, an agricultural
surplus opens up (AS in the lowest diagram). The average agricultural surplus, AAS, is
defined as:
Agricultural Surplus
= AAS
Number of transferred workers
Clearly, AAS = w . And clearly AAS stays constant at w in the labour surplus phase (as
long as the marginal product of labour is nil in agriculture), as depicted in the middle
diagram.
Now, a process of industrialization is possible if and only if the industrial wage paid to the
transferred workers is such that they are able to buy (at least) the same quantity of food
they received when they were employed in agriculture, w ; otherwise they will not move
from agriculture (unless they are forced to). Well, what is the industrial wage (by “industrial
wage” here we mean the wage paid by the industrial sector and expressed in units of
industrial good) wI needed to buy w units of food? It must be true that
 PI 
≥w

 PA 
wI 
1
(2)
The meaning of this assumption will be made clear later on, when we will focus on agricultural taxation
5
wI
Li
x
y
AAS
w
Li
Y
T
AS
w
La
A
B
C
O
Figure 4: the Lewis-Fei-Ranis model of economic development
6
However, industrialists want to make as much money as they can, and therefore (2) will
hold as a strict equality (they do not want to pay more than is strictly needed to attract
people from the rural/informal sector):2
P 
wI = w  A  = w p
 PI 
(3)
From (3) we can see that, for any given level of the terms of trade PA PI (henceforth
simply p for brevity), the industrial wage is constant as far as the agricultural wage w stays
constant as well, i.e. in the labour surplus phase. This is shown in the upper diagram.
Let’s now analyse the disguised unemployment phase (BC), i.e. the phase where in
agriculture MPL > 0 but, assuming that the agricultural wage keeps staying constant (see
footnote 1), w > MPL ? The average agricultural surplus begins to decline (since total output
goes down); this can be seen by inspection of the lowest diagram and is shown in the
middle one. One can therefore guess that, since less agricultural output is marketed (each
worker that moves away from agriculture has to buy food on the market, but on average
less food is available), food (agriculture) prices start to rise.
But look at equation (3): the increase in p will push the industrial wage (w*) up, in order to
make industrial workers able to buy w units of food and hence give them the appropriate
incentive to move to industry. However, at a closer inspection, we can see that even if the
industrial workers are getting more than w*, it is simply impossible for them to buy w
units of food, because there is not enough to go around. To see why, just consider that by
assumption people employed in agriculture are getting w ; if each industrial worker bought
w as well, total agriculture production should be equal to OT, which is not the case. It
follows that, at this stage, industrial workers will have to consume a mix of industrial and
agricultural products. Under these conditions, will the potential “migrants” accept to move
to industry? Clearly, they will if and only if w is not too close to the subsistence level (if it
were, it could not be reduced!). This is a very important result, it says that agriculture must
be sufficiently productive to favour an industrialisation process. In any case, potential
“migrants” will only accept an industrial wage higher than w*: this is the reason why in the
upper diagram the industrial wage becomes an increasing function at the beginning of the
disguised-unemployment phase.
When the transfer of labour reaches point C the disguised unemployment phase comes to
an end. In the CO region MPL > w : agriculture is likely to become a fully capitalistic sector
where wages are set according to the profit-maximisation rule (real wage = marginal
product of labour). It follows that as labour moves from agriculture to industry, agricultural
wage goes up (in other words, the wage bill in agriculture falls more slowly than before as
labour moves from agriculture to industry) and the industrial wage (in the topmost panel)
must increase even faster since it must not only compensate for higher terms of trade (p),
but also for higher incomes in the agricultural sector.
We are now ready to read properly the topmost panel where we have drawn a family of
labour demand curves. For easiness of exposition, let us redraw that diagram:
2
For more realistic cases, a mark-up for higher costs of living in the urban sector or a lager degree of
unionization in the industrial sector as well as some discount factor for the uncertainty of getting a job in the
city are all factors that could be added to this simple model. However, they would not change the main
conclusions in any relevant aspect.
7
wI
Yx
w*
O
πx
πy
x
y
Figure 5: The process of industrialization
LI
Initially, the amount of industrial labour is x. Realised profits are equal to Πx3 and Lewis
assumes they are automatically invested back into the industrial activities (there is not an
investment function in the Lewis – Fei – Ranis model). With more capital, labour demand
(the marginal product of labour) shifts up. The new level of industrial employment is y.
Note that in this labour surplus phase new industrial labour is forthcoming at the fixed real
wage w*. Despite the fact that the marginal productivity of labour in the industrial sector is
going up, the real wage earned by each worker stays constant. In the labour surplus phase
the fruits of industrial expansion are not equally distributed: labour is becoming more and
more productive but this only translates into higher profits (Πy + Πx > Πx) So, one of the
implications of Lewis’ view of economic development is that income distribution (at least
functional income distribution) worsens in the early phases of industrialisation (something
reflected in the well known Kuznets curve). This important issue of the link between
industrialisation and income distribution will be further investigated below with the help of
a formal model developed by Bourgignon (1990). But it is in any case worth stressing that
this unpleasant distributive result is seen by Lewis as an element that helps the economy
grow and industrialise faster: industrialisation comes from capital accumulation and capital
accumulation comes from profits (the propensity to save out of profits is higher than the
propensity to save out of wages). And, do not forget our initial remarks, per capita income
growth is facilitated by industrialisation.
3
By definition of marginal product, total industrial production is equal to the area OXYx; the industrial wage
bill equals the rectangle (OX)w* and what is left, the triangle Πx, goes to profit earners.
8
As is should be clear by our diagrams, once the labour surplus phase is exhausted,
industrial employment can only rise at the price of an increasing wage and, not surprisingly,
the very pace of industrialisation is likely to slow down.
To summarise, the basic ideas of economic development ( = industrialization) behind the
Lewis – Fei – Ranis model are:
a.
b.
c.
the engine of growth is capital accumulation (no problem of demand, saving are
automatically reinvested. Keynes’ preoccupation about the level of effective
demand was considered something relevant for rich economies only).
As development proceeds, there is a process of rural – urban migration and
urbanisation.
As development proceeds, the terms of trade p increase. Food prices rise
because a smaller and smaller number of farmers must support an increasing
number of industrial workers.
Briefly: “development” is driven by capital accumulation but limited by the ability of the
economy to produce a surplus of food (the lower the surplus → the higher p → the higher
the industrial wage → the weaker the incentive to invest in the industrial sector).
The policy implications of such a view are very much controversial and hotly debated.
Consider for instance the role of agriculture. Even if we accept the residual role given to
agriculture in the Lewis framework (agriculture as a source of cheap labour and supplier of
a food surplus), the question is: how these potentialities of agriculture are best exploited?
By taxing agriculture, which would expand industrial labour supply (it is easier to convince
people to move away from agriculture when agriculture is taxed), or by subsidising agriculture
(for instance helping farmers buy relevant inputs like water, fertilisers, etc.), which would
expand agricultural production and the available surplus of food? And what happens when
agriculture does not coincide with food production alone, but it includes the production of
non-food items as well? Again: provided that technical progress in agriculture is good for
growth and industrialisation (since it raises the surplus of food), are we sure that in a poor
economy there are the appropriate incentives to introduce better agricultural techniques of
production? In this respect, what is the role of land reforms and land redistribution? How is
the Lewis picture modified by the introduction of international trade and globalisation? Is
the kind of development process depicted in the model necessarily associated with a
worsening income distribution (growth for whom?) or some more pleasant outcome may
be envisaged? In the following sections we will complicate a bit the Lewis framework in
order to address some (not all) of these policy issues.
2. SOME REFINEMENTS OF THE LEWIS FRAMEWORK. POLICY ISSUES.
Technical progress in agriculture and agricultural taxation
According to the "accumulationist" view of Lewis, the process of industrialization is clearly
helped by maintaining for a sufficiently long period of time a low level of the industrial
wage. The longer the industrial wage stays at w*, the quicker the industrialization process
will be, since more profits will be available for (automatic) re-investment. But look at
equation (3). It is quite clear that the level of the industrial wage is ultimately determined by
the wage prevailing in agriculture and by the agricultural terms of trade, p. It follows that
the policy question is: how can these two variables be kept at a low level so as to ease the
industrialization process? In principle, there are several possibilities, but each of them
entails serious difficulties.
9
•
AGRICULTURAL TAXATION. As people move from the rural to the manufacturing sector
and the economy is in the labor surplus phase, the average product of labor in
agriculture goes up. It follows that if farmers are paid their average product, the
agricultural wage should go up, which is bad for industrialization. One way of escaping
this trap is to tax agriculture: the net payment accruing to the farmer stays at w (see
footnote 1) because the excess of the average product over w goes to the government.
However, by discouraging agricultural production, such a measure could provoke a
(faster) rise in the agricultural terms of trade, which in turn could slow the
industrialization process. It has often been argued that Africa was a typical example of
excessive taxation on agriculture, and this is the reason why several African countries
implemented market-oriented reforms over the last ten years. The case of Africa, for
obvious reasons, deserves a closer scrutiny. We should first try to understand whether
agricultural has suffered from an excess of taxation. Then we should have a look at the
behaviour of the agricultural terms of trade over the last decades and finally try to study
the relation between agricultural production and real producer prices. Of course, these
points are closely related to each other, but let us investigate them separately.
Is it true that Africa agriculture used to be too heavily taxed? To answer this question it
is important to distinguish among three kinds of agricultural products: exportable
(cocoa, cotton, coffee, tobacco, etc.), importable (food crops such as cereals) and nontradable (cassava, plantain, millet, sorghum, white maize and other typically “African”
food staples, which are not consumed outside Africa). As to the exportable, a way of
addressing the question of their taxation is to look at the margin between export prices
(i.e. the world price of the crop expressed in dollars multiplied by the nominal
exchange rate) and prices actually received by farmers. Of course we are discussing the
case when producers and exporters are different entities (and not when producers
export directly, as in the case of plantation and agribusiness based on transnational
corporations). In several African countries, from the days of the independence to the
early 1990s, public marketing boardswere the principal exporting entity. The difference
between the price earned in the international markets by a public marketing board and
the price paid by the marketing board to the farmer is to be considered a “tax” paid by
the latter to the government (in light of the public nature of the marketing board). Sure,
such a difference is a crude approximation of the degree of taxation since no allowance
is made for marketing and transportation costs. As a consequence, we have to take the
margin as an overstatement of the true degree of taxation. Moreover, it must be
stressed that the degree of taxation is linked to the exchange rate. A devaluation (i.e. a
higher nominal exchange rate, you need more pesos to buy a dollar) would raise the
domestic currency price received by the exporters (by the marketing board). If prices
paid to farmers remain unchanged (or are raised by less than the rate of currency
devaluation), the tax rate will rise4. With all this caveats in mind, the evidence presented
by UNCTAD (TDR 1998, pp. 156-159) does not support the widespread view that
African producers have always been more heavily taxed than those in other developing
countries. Of the five export crops studied (coffe, cocoa, tea, cotton, tobacco) with
reference to the period 1970-1994, it is only for cocoa and tobacco that the margin
between border and producer prices was significantly higher in Africa than in the other
major exporters. It must be added that this kind of exportables are not consumed by
the farmers as “food” and therefore, even if they were excessively taxed (which is not
true, as we have just seen), this would not contribute to slow the migration of people
from the agricultural to the manufacturing sector. On the contrary, it could be argued
4
However, when devaluations lead to a widening of the margin but the price paid to the export producers
goes up at least a bit, this tends to raise real producers prices of export crops vis-à-vis nontradables, thus
providing incentives for export.
10
along the same lines followed in the illustration of the Lewis model that this could even
accelerate the industrialisation process. To see why, just go back to equation (3) and
read it from the point of view of a producer of an exportable good like cocoa or coffee.
The terms of trade p must be interpreted as the ratio between the price of food (not
coffee or cocoa) and the price of the manufactured good; w I is the wage paid by the
industrial sector expressed in units of industrial good and, finally, w is the real wage
earned by the coffe or cocoa producer expressed in units of food. w can thus be
thought of as the net nominal earning of the coffee or cocoa producer divided by the
price of food. Well, even admitting (in a counterfactual exercice) that the taxation on
the exportable good is somehow excessive, this should decrease w and therefore
stimulate the transfer of people to the urban areas. Fresh workforce available for the
industrialisation process. Still, the general belief that these exportables were too heavily
taxed lead at the end of the 1980s to a major reform process. In most African countries
the marketing boards were simply abolished and devaluations were applied to several
currencies. The idea was to eliminate the tax paid by the exportable producers by
eliminating the tax collector (the marketing board) and to provide further incentives to
the exporters through a currency devaluation. Well, it may be surprising to see that
from the beginning of the reform process until mid-90s the ratio between producer and
export prices has declined for all the five products considered except coffee. Why is it
that the elimination of the tax collector actually lead to a raise in the tax paid by the
producers? Because the reform process was based on ideology rather than governed by
pragmatism. Indeed, eliminating a marketing board does not imply that a producer
(and, let us repeat, we are not talking about transnational companies and plantations)
suddenly becomes able to sell to the international market. She still needs a trader, and if
a public trader (a marketing board) is not there, a private one will enter into the picture.
No doubt, this private trader will try to maximise his profits and, when faced with a
currency devaluation, what will he do? He will increase the price paid to the producer
by less than the devaluation rate and therefore there should not be any surprise to see
that the reform process was actually accompanied by an increase in the degree of
taxation of the major export crops5.
What about the importable goods? Here we are talking about goods such as rice, wheat
and maize. A local producer can be said to be taxed when the net price she gets is
lower than the price paid (in domestic currency) to import the same good. On the
contrary, a local producer is said to be subsidized when the net price she receives is
higher than the domestic currency import cost6. Well, from 1970 to 1994 the producer
price for this importable good had been systematically higher than the unit import cost,
which indicates a positive rate of subsidization (UNCTAD, TDR 1998, Chart 16). In
principle, this should stimulate the production of these food items, lower the terms of
trade p (look again at equation 3) and thus favour the industrialisation process for any
given level of the real (food) wage earned by farmers.
5
It must be stressed that a further drawback of this reform was the disappearance of the public money
formerly in the pockets of the marketing board. Even when it is heavily corrupted, you can ask a state to build
some roads or develop some utilities. But if the “tax” collector is a private trader, you can’t ask anything.
6
A numerical example may be useful. Imagine that the world price of a unit (a kilo, a ton, a trunk, whatever
you like) of rice is 200 US$. In the country we are considering the exchange rate is 10 pesos per dollar and a
tariff of 15% is applied to the import of rice. Thus the overall price paid by the locals to buy a unit of rice
produced abroad is 200x10x1.15 = 2,300 pesos. If some kind of competition is at work (and usually it is), the
price applied by local producers to sell their own rice will be exactly the same, 2,300 pesos. In this case, local
producers are said to be (implicitly) subsidized since the price they get (2,300) is higher than the import cost
net of tariff (2,000). A tariff is not the only way of protecting a local farmer. Another possibiity is to subsidize
the purchase os some relevant input (water, fertilizers, etc.). In this case the consumers will pay less than the
domestic currency world price to buy rice, but the net price (inclusive of the subsidy) received by the local
producers will be higher than the domestic currency world price.
11
As to the non-tradables, lack of data (to our knowledge) makes it impossible to say
something relevant, but the former analysis should have made clear that it is hard to say
that agriculture in Africa has suffered from an excess of taxation and this has slowed or
even blocked the industrialisation process. All the more so after the reforms and the
dismantling of the marketing boards.
At this point, a question naturally arises: what are the likely reasons of the missing
African agricultural development? There is no doubt that a serious industrialisation
process cannot even start without a significant growth of agricultural productivity, but
the foregoing analysis should have convinced the reader that the main problem does
not lie in perverse (insufficient) price incentives. The main problem for African
agriculture is the weak response to price incentives: even when prices are high or go up,
this is not enough to stimulate more production. There are a host of institutional and
structural factors that may explain this feature. Let us see the most important. In the
short run, aggregate supply response to price incentives can occur through two basic
processes: either idle land is brought into use or more variable inputs (labour,
fertilizers, etc.) are put at work on a given unit of land. In the long run, aggregate
supply response is mainly determined by investment and productivity growth. Well,
even when there are community land resources available (which is not always the case),
poorer farmers simply cannot farm extra land because they cannot mobilize the
necessary complementary inputs. On top of this, high levels of poverty means that
farmers cannot afford to keep either their labour or land idle even at very unattractive
prices. As to the intensification of the agricultural process, i.e. the use of more variable
inputs on a given unit of land, one of the rason why after the reform process the supply
response to higher output prices7 was weak lies in the behaviour of the input prices.
Indeed, together with the abolition of the marketing boards, African farmers had to
face the removal of the subsidies to buy such items like fertilizers. There is something
more: even in the presence of an appropriate incentive for the farmers to put more
variable inputs at work, it must be recognized that buying these extra inputs requires
some credit. Well, “the marketing boards had offered an institutional response to the
problem of missing private credit markets. As they had a legal monopsony over
marketed output, they could provide seasonal inputs on credit against the potential
crop as collateral......With privatization, this system of seasonal credit has broken
down” (UNCTAD, TDR 1998, p.169). Sure, the role once played by the marketing
boards is now played by private traders, but obviously the latter, being moved by the
sacred principle of profit maximization, apply tougher conditions to the farmers8. And,
last but not least, the money earned by a private trader cannot be used (unless you are
able to impose a tax) to finance the provision of public goods.
The issue of pubblic goods (or in any case private goods whose production entails
strong positive externalities) is strictly connected to the long run response of
agricultural output to price incentives. There cannot be any significantly positive
response unless better infrastructure is available, especially transport9. Again: together
with the dismantling of the marketing boards and the removal of the subsidies on
inputs, “reforms” usually asked for a cut of public expenditures...
7
Remember that the basic idea behind the dismantling of the marketing boards was to increase the price
directly received by the producer.
8
See the Appendix for a formal analysis of the relation between a farmer-borrower and a private traderlender.
9
The rural transport bottleneck is so important because it prompts two negative effects. First, it reduces the
real return to a given investment (let us say that the cost of bringing to the market the goods produced thanks
to the investment goes up) and, second, it is a source of product market imperfections (if the transport
network is underdeveloped, a small farmer must sell to a trader and this lowers her market power)
12
•
TECHNICAL PROGRESS IN AGRICULTURE. Technical progress is a way of producing more
output with the same quantity of labor (better: this is labor saving technical progress, but,
as we are going to see, there are also other kinds of technical change). In principle, this
will increase the average agricultural surplus and moderate the upward pressure on the
agricultural terms of trade associated with the process of industrialisation. Note that a
larger agricultural surplus will come out of technical advancement in any case, even if
the fruits of technical progress should be entirely consumed by the farmers. The
following diagram should make the point clearer:
Y’
Y
Lo
La
Figure 6: technical change in agriculture
In the diagram two very standard production functions for the agricultural sectors are
represented. One (Y’) is higher than the other (Y) because of technical change (the same
amount of labour produces more output). Formally, we can write Y = ALα and Y’ = A’Lα,
with α positive but less than one and A’ > A. La is the available labour force in the
economy. The agricultural average product of labor when everyone is employed in
agriculture is Y/L = AL(α-1) with the less productive technology and Y’/L = A’L(α-1) with the
more advanced. Assume, as we did before, that at least in the labour surplus phase farmers
get w ( w ' with the more advanced technique) even when some of them start moving to the
manufacturing sector (and now we know that this may happen because of agricultural
taxation). To be more precise, the wage earned by the farmers is
−1
w = ALα
a
and
−1
w ' = A ' Lα
a
depending on the kind of technology in use. Clearly, w ' > w : the fruits of technical
progress are by assumption enjoyed by the farmers. Well, what is the agricultural surplus
corresponding to a situation where Lo people are employed in agriculture? It’s the
difference between total production and the wage bill. Formally, with the less productive
technique we will have:
13
α −1
α −1 
 α
AS = ALα
o − ALa Lo = A Lo − La L0  ,
and with the more advanced technique
' α −1
' α
α −1 
AS ' = A ' Lα
o − A La Lo = A  Lo − La L0  .
Since A’ > A, we will have AS’ > AS. So, even when the fruits of technical change are fully
enjoyed by the farmers, it still remains a higher agricultural surplus, which is likely to
compensate the upward pressure on the agricultural terms of trade provoked by the
transfer of people in the course of the industrialisation process. As a consequence, there is
no doubt that labour saving technical progress in agriculture is potentially very good for
industrialization and economic development. However, there are two major problems to
be emphasised. First, agricultural technical advancements are not necessarily labour saving.
On the contrary, they could be labour using and, if they are, there will be a weak incentive at
least for the smallhholder producers to introduce them. To see why, one has to think of
Africa and look at Table 1:
Table 1: Non-agricultural to agricultural income ratio. Developing regions
1950-60
1960-70
1970-80
1980-1990
Africa
7.05
8.33
8.74
7.79
Asia
1.87
3.37
3.31
3.57
Latin America
2.42
3.00
2.81
2.51
Other
1.88
2.17
2.15
2.25
Source: UNCTAD, TDR 1998, p.140
It is clear from the table that the ratio of non-agricultural to agricultural value-added per
worker is much higher in Africa than elsewhere in the world. This differential is one of the
key indicators of “urban bias” in Africa (agriculture too heavily taxed? If it is – but go back
to our previous analysis – the farmers will have too low an incentive to invest and increase
productivity and a disruptive process of rural-urban migrations might take off), but it is
ultimately based on lack of investment in African agriculture and agricultural
infrastructures, features that will be examined below. This differential underlies the
attractiveness to farm households of “straddling” between the agricultural and nonagricultural sectors and may explain why labour using technical progress is not adopted:
“..to the extent that off-farm employment opportunities are available, there is a continual
pressure for productive labour to be diverted from agriculture. Under these conditions,
there may be little incentive to adopt high-yielding crop varieties, which can require greater
labour inputs [Italics is ours]. Rather, the types of innovation which are attractive are those
which save households labour time and thus enable the diversion of labour from the farm”
(UNCTAD, Trade and Development Report, 1998)10.
The second problem with agricultural technical progress is due to one of the most
pervasive interlinked contracts in poor countries, that between a farmer (sharecropper)
who is also a borrower and a landlord who is also a lender. The issue was first formally
raised by Amit Bhaduri (1973), who suggested that a landlord-lender may discourage a
technical advancement by the sharecropper-borrower since the former may lose more in
interest income, even though his rental income goes up, as the latter becomes better off
and therefore less dependent on the landlord for consumption credit. In such a case, the
10
Section 3 will present the Harris-Todaro model, one of the most powerful tool to understand the nature of
rural-urban migrations at least in the poor countries.
14
semi-feudal relation between the two subjects is the reason why technical advancements
are not implemented. In other words: technical progress is not a (purely) technical issue; it’s
a socio-political story. However, another Indian economist, T.N. Srinivasan (1979) tried to
moderate Bhaduri’s pessimism and show that under certain conditions technical
advancements may be actually implemented despite the prevailing semi-feudal rural
framework in many poor countries of the world. Here we are not going to present
Srinivasan’s model, but to build a counterexample inspired to that model to show that it is
possible that the introduction of technical progress may increase the interest income earned
by the land-lord borrower. The story goes as follows. There are two periods. In the first,
the slack season, the sharecropper borrows an amount B from the landlord for
consumption purposes (assume she has no other source of income and credit, which is
often quite realistic), and will give this money back to the landlord in the second period
together with an interest rate i. Output is harvested in the second period. The actual output
is θx , where θ is a random variable with expected value equal to unity and which takes the
value θ L with probability p and θ H with probability (1-p), where θ H > θ L and
pθ L + (1 − p )θ H = 1 . The sharecropper gets a fraction α of the harvest, and the landlord gets
(1-α).
If the harvest turns out to be sufficiently high, the sharecropper will pay the rent, repay the
loan and consume the rest. Formally, if θ = θ H the sharecropper in the second period will
pay (1 − α )θ H x + (1 + i) B and consume θ H x − (1 − α )θ H x − (1 + i) B = αθ H x − (1 + i ) B .
On the contrary, if the harvest turns out to be too small to cover the sharecropper’s
minimum subsistence consumption, cs, and repay the loan as well, the sharecropper will
repay the balance at a stipulated price of working γ days of labour per unit of the loan
amount owed to the landlord-borrower. Forrmally, if θ = θ L the sharecropper will consume
cs and will have to work (obligatory work) l = γ [ c s + (1 + i) B − αθ L x] days to repay the loan11.
This obligatory work provokes disutility to the sharecropper, denoted by v(l) with v’ > 0
and v’’ > 0. In each period the overall utility of the sharecropper is u(c) – v(l), with u’ > o,
u’’ < 0 and, by normalisation, u(cs) =0.
The sharecropper chooses her level of borrowing B in the first period in order to maximise
her lifetime expected utility:
EU = u ( B) + β { p[ − v(γ (c s + (1 + i ) B − αθ L x))] + (1 − p)u (αθ H x − (1 + i) B)} ,
where β is the discount factor.
In order to study the behaviour of the sharecropper we have to calculate the derivative of
the expected utility with respect to B and then set it equal to zero:
{
}
u ' ( B) + β − pv ' (γ (c s + (1 + i) B − αθ L x))γ (1 + i) − (1 − p)u ' (αθ H x − (1 + i) B)(1 + i) = 0 .
Now, both the value of u’ and v’ depend on B and x and therefore we can study how B is
affected by a change of x. By totally differentiating the first order condition we get
{u' '+ β [− pv' ' γ
2
}
(1 + i ) 2 + (1 − p )u ' ' (1 + i ) 2 ] dB + β [ pv' ' αθ L γ (1 + i ) − (1 − p )u ' ' αθ H (1 + i )]dx = 0
It follows that
11
It should be clear that the framework we have just described makes sense if and only if
θ L < [c s + (1 + i ) B ] αx . Equivalently, it must be θ H > [c s + (1 + i ) B ] αx
15
dB β [(1 − p )u' 'αθ H (1 + i) − pv' 'αθ L γ (1 + i )] −
=
= >0
dx u ' '+β [ − pv' ' γ 2 (1 + i) 2 + (1 − p )u ' ' (1 + i ) 2 ] −
The logic driving the outcome of this specific example is straightforward: the sharecropper
knows that, thanks to technical progress, in the next period she will get more on average.
Therefore, she borrows (and consumes) a bit more in the first period because, even if the
harvest turns out to be bad in the second period, she will have to work less days for the
glory of the landlord12. But if B increases with x (with technical progress) it is not true, as
claimed by Bhaduri, that the interest income earned by the lender-landlord falls: she has an
incentive to introduce technical advancements because both her interest and rental income
goes up. Of course it is possible to build a different example and show that there are cases
where B decreases with x (see Bardhan and Udry, p. 121). But the point to be stressed is
that, however extremely interesting, the outcome proposed by Bhaduri is just a possibility,
it does not necessarily hold.
Lewis-growth and inequality
Is the process of development and structural change as depicted by Arthur Lewis inevitably
associated with an increase in the degree of inequality? We are going to see, through the
help of a simple model developed by Bourgignon (1990) that it’s difficult to answer this
question without ambiguities. And we will also stress that this issue, however important,
should not be over-emphasised: it’s not that important.
Consider again the Lewis framework, where we can see three types of social groups: 1)
peasants, who are self-employed in the agricultural sector (a) and own their family farm.
Their per capita income is ya; 2) workers, who are employed in the manufacturing sector
(m) and earn a fixed wage, w; 3) capitalists, who employ the workers in the manufacturing
sector and earn a per capita profit equal to π.
Let’s introduce a (very reasonable) hierarchy of incomes: π > w > ya. This assumption
(which could be removed without altering the basic message) implies that there is an excess
supply of labour willing to come to the manufacturing sector, something very close to the
“labour surplus” idea of Arthur Lewis.
There are La peasants, Lm workers and n capitalist. To simplify things, their sum is
normalised to one (so that absolute values coincide with shares) and the number of
capitalists is held constant. The numéraire of the model is the manufactured good (pa/pm =
pa = p as before). The manufactured good is produced with a Leontief technology, so that
output Qm = AK and employment Lm = BK, where A and B are fixed technical
coefficients. Hence, the income of each single capitalist is
π = (Qm − wLm ) n = ( A − Bw) K n
(4)
The per capita income of peasants is, as before, equal to the average product of labour in
agricultural, let’s call it Va. Expressed in units of manufactured good, this income is equal
to ya = pVa. In this framework every peasants would like to move to industry, which means
that the number of peasants is determined as a residual, all those who are not absorbed
elsewhere: La = (1 – n – BK). The mean income of the overall population (equal to one,
remember) is
12
Just to get the basic intuition, imagine that without technical progress the sharecropper borrowed 5 in the
first period, and for simplicity assume a zero interest rate. In the second the harvest was bad, 2 only (2 is the
part going to the sharecropper). Subsustence consumption is 1. Under3γthese circumstances, the sharecropper
must work 4γ days for repaying her debt. Now introduce technical progress. The sharecropper could borrow
6 and, even if the harvest was bad, say 4, he would have to work only
days for the glory of the landlord.
16
y = Qm + pQa = Qm + pLaV a
In such a simplified framework a Lorenz curve is easy to build.
% of income
% of population
1-n-BK
1-n
1
Figure 7: the Lorenz curve
Thanks to the hierarchy of incomes and population normalisation, the cumulated
percentages of population on the horizontal axis of the diagram correspond to,
respectively, the number of peasants (1 – n – BK), the number of peasants plus the number
of workers (1 – n – BK + BK = 1 – n) and 1. Now, before trying to understand whether
inequality increases or decreases with capital accumulation (increase in K), let us calculate
the slope of the three segments of the Lorenz curve, segment A, segment B and segment
C. To this purpose, let us redraw the diagram using a more general notation: Ni stands for
the number of people belonging to the i-th fractile of the distribution (in Bourgignon
model, i = 1, 2, 3, where 1 denotes peasants, 2 denotes workers and 3 denotes capitalists);
yi is the income of each single person belonging to fractile i and N is total population:
17
% of income
C
By
B
Ay
A
% of population
Ax
Bx
1
Figure 8: the different segments of the Lorenz curve
As can be see from the diagram, the calculation of the slopes is straightforward.
Slope of A =
Slope of B =
Ay y1N1 yN y1
=
=
N1 N
y
Ax
By [( y1 N1 + y 2 N 2) yN ] − ( y1 N1 yN ) y 2
=
=
[( N1 + N 2 ) N ] − ( N1 N )
y
Bx
Using the same argument,
y
Slope of C = 3
y
In words: the slope of each “piece” of the Lorenz curve is equal to the ratio of the income
of the corresponding fractile of the distribution to the mean income of the whole
population. In the Bourgignon’s framework we have y1 = ya, y2 = w, y3 = π.
Now, in such a framework, look again at the horizontal coordinates of the Lorenz curve
and try to see what happens with capital accumulation and structural change13. Clearly, La =
1 – n – BK decreases with K, but the second kink is constant at (1 – n). This implies that if
the Lorenz curve were to shift upward (i.e. the distribution were to become unambiguously
more egalitarian), the following necessary and sufficient conditions have to be satisfied
(look at Figure 7 to fully understand the rationale of these conditions):
13
In a Lewis-type model capital accumulation is basically the same thing as structural change. When capitalists
invest in the manufaturing sector people are withdrawn from agriculture.
18
∂( y a y )
≥0
∂K
and
∂(π y)
≤0
∂K
(5)
In words: the slope of the first “piece” of the Lorenz curve must increase (or stay constant)
with capital accumulation, whilst the slope of the last “piece” must decrease (or stay
constant). The economic meaning of this condition is obvious: if income distribution has
to improve, the income of the poorest segment of the population must approach the mean
income from below and the income of the richest segment of the population must
approach the mean income from above.
Well, to check whether those conditions hold we have to write down an explicit formula
for the ratio of the income of both the peasants and the capitalists to the mean income of
the whole population. Let’s call βa the share of agriculture in national income and αm the
profit share in sector m (which is a constant equal to (1 – Bw/A)); by definition we will
have:
βa =
pQ a pL aV a y a (1− n − BK )
=
=
y
y
y
from which we get
ya
βa
=
y 1 − n − BK
(6)
As to the profits of the single capitalist, it can be written as
Total Profits
Q
Qm α m m y
Qm
α (1− β a ) y
y
π=
=
= m
n
n
n
from which we get
π α m (1 − β a )
=
y
n
(7).
From (6) and (7) we can see that conditions (5) are satisfied with certainty if the share of
agriculture in national income increases with K, with capital accumulation and growth. But
historically this has never occurred; well on the contrary, the share of agriculture in national
income declines with economic growth. So, the reduction of βa will make π y increase, as
can be seen from (7). What will happen to y a y ? As one can see by (6), a priori we can’t
say that much, since the changes in the numerator and the denominator push in opposite
directions. But something less vague can be said if we rewrite (6) more explicitly:
y a βa
=
y
La
Now we can say the following: if, during the process of economic growth and structural
change, the decline in the share of agriculture in national income is faster than that of share
19
of agricultural employment in total employment, then y a y will fall. For this condition to
be met, average labour productivity must increase faster than labour productivity in
agriculture, which is almost always the case. So, historically, the likely changes to be
considered are:
∂( y a y )
<0
∂K
∂(π y)
>0
∂K
and
With similar slopes changes we cannot be unambiguous about an increase in inequality
with economic growth and structural change. The two following diagram show one
ambiguous case with intersecting Lorenz curve and a case with unambiguous increase in
inequality, both consistent with the slope changes we have just described.
% of income
% of population
1-n-BK
1-n
1
Figure 9: the ambiguous case
20
% of income
% of population
1-n-BK
1-n
1
Figure 10: the increase of inequality
To sum up: growth and structural change, the transition from an agrarian to a modern,
industrial economy are not inevitably associated with a worsening income distribution as
reflected by a deterioration of the Gini index. That said, two important qualifications must
be added. First: even if inequality increases in the early phase of economic development, is
this a serious problem? Consider carefully the stylised framework described by Bourgignon,
in particular look at the case of unambiguous increase in inequality (the Lorenz curve
moves outward, figure.....). Why is inequality higher than before? Compared to the initial
situation, the new, “more unequal” Lorenz curve depicts a case where: a) there are more
workers than before. Those who were already employed in the manufacturing sector are as
well off as before, since the real wage is constant by assumption. The new employed are
better off than before, since in the agricultural sector they got less; b) there is the same
number of capitalists, and each of them is richer than before (total profits are higher than
before since the share of profits in the manufacturing sector is constant and the share of
manufacturing in total income is higher than before) ; c) there are less peasants than before.
Are they worse or better off? We know that their per capita income is pVa. Well, p, as we
saw in the previous section, is very likely to be higher than before. What about Va, the
average product in agriculture? If we postulate for agriculture a standard production
function with decreasing return to labour, the average product will be higher than before as
well.
In sum, with capital accumulation and structural change everyone gets at least the same
income as before. The overall cake produced by the economy is larger than before (because
labour productivity in the manufacturing sector is higher than in the agricultural sector) and
the only reason why inequality has increased is that the new slices are more unequally
distributed. Still, everyone has a larger slice than before and therefore no one would prefer the preaccumulation, more egalitarian world. All this is to say that inequality is more a political than a
strictly economic problem, since too much inequality could threaten political stability. For
21
instance, “agricultural policy has been used in Africa to promote a pattern of income
distribution which is regarded as legitimate and which therefore does not threaten political
stability. This is an extremely delicate problem in nation-state building in Africa. Some
aspects of agricultural pricing policy, particularly the practice of providing uniform
guaranteed prices countrywide, have been part of an implicit social contract designed to
redress colonial imbalances and ensure that certain ethnic groups with less fertile land and
limited access to markets are not totally excluded” (UNCTAD, Trade and Development
Report 1998).
The second consideration relates to what we observed in the previous section: even in the
labour surplus phase the industrial wage is unlikely to be constant because of the pressure
exerted by a rising p. It follows that the profit share in the manufacturing sector, instead of
being constant as postulated by Bourgignon, is likely to decrease, which in turn produces a
move toward more equality.
3. MIGRATIONS: THE HARRIS-TODARO MODEL (1970)
According to the Lewis model the process of industrialisation entails an “automatic”,
someway harmonious migration of people from the rural areas to the cities. Can we say
more on this migration process? Can we add, on top of the agricultural and the
manufacturing sector, an urban informal sector to the picture? After all, in many poor
countries there is a large urban population engaged in an extremely diverse set of activities
outside the direct scrutiny of the state and not covered by labour unions. And is creating
new employment opportunities in the city always a good idea? Or is there the risk of
providing people the incentive to move too fast to the city, so as to create all the problems
inevitably associated with the concentration of a large mass of people in a relatively small
area? After all, many cities in Africa, Latin America and Asia are growing at 5-7 per cent
per year, which is likely to be above any realistic possibility of giving these people a job.
These questions can be addresses through the help of the model developed in 1970 by
Harris and Todaro (for the subsequent changes to the original framework, see Bardhan and
Udry, 1999). The key institutional assumptions of the model accord pretty well with many
highly visible features of some developing countries:
- the rural labour market is competitive
- the wage paid by modern firms in the city is fixed above the market clearing level,
either because unions’ activities or governmental legislation (for instance minimum
wage regulations) or efficiency wage considerations
- there is an informal sector in which urban residents not otherwise employed can
earn their living out of activities outside the control of the state and performed
using heir labour force alone (petty trade, craft production, urban agriculture).
Let Lr be the rural population, employed in agriculture on a fixed amount of land.
Agricultural output is determined by the standard production function g(Lr) and sold on a
world market at a price normalised to unity. Since the rural labour market is assumed to be
competitive, rural wages will be equal to the marginal productivity of labour:
wr = g ' ( Lr ) .
This relation is represented in Figure 11 by the decreasing right-to-left curve. The urban
population is either employed in manufacturing (Lm) or working in the informal sector (Lu).
Total population is normalised to 1, so that Lr + Lm + Lu = 1. To simplify the calculations
we put the wage paid in the informal urban sector equal to zero (which is nothing but a
way of claiming that people living in the city always prefer to get a job in the formal,
modern sector.
22
wm = f ' ( Lm )
wr = g ' (1 − Lm − Lr )
e
E
w*m
E’
wr*
*
wr
e’
L*m
1
* *
L m + Lu
Figure 11: the Harris-Todaro model
The manufacturing wage, wm, is institutionally fixed. Since manufacturing firms maximise
profits, their demand for labour is implicitly determined by
wm = f ' ( Lm ) ,
where f is the manufacturing production function. The probability for an urban resident of
getting a job in the manufacturing sector is equal to the number of jobs divided by the
number of urban residents, and her expected income in the city will be equal to this
probability multiplied by the institutionally fixed manufacturing wage (remember that the
wage of people employed in the informal urban sector is zero). Of course, migration will
occurs to equalise the expected wage of an urban resident with the wage that the resident
could earn in the rural areas:
Lm (wm )
wr =
w
Lu + L m ( wm ) m
(EC).
The meaning of this equality can be better understood by describing what happens when it
does not hold. Imagine for instance that
Lm (wm )
wr <
w .
Lu + Lm (wm ) m
23
People living in the rural areas will decide to migrate to the city: But since the
manufacturing wage stays constant, Lm will not change and the new urban residents will
increase Lu. At the same time, the reduction of the rural labour force will increase the
agricultural marginal product and therefore the agricultural wage. At the end of the story
the equality will be restored. Let’s call the fixed manufacturing wage wm* . The implicitly
determined level of manufacturing employment will be L*m . The equilibrium condition can
be rewritten as
wr ( Lu + L*m ) = L*m w*m
In words: the rural wage multiplied by the urban labour force must be equal to a constant.
This is the equation of a rectangular hyperbola (like yx = constant): in the diagram, the
curve ee’ represents such an equilibrium locus (of course the hyperbola must pass trough
the point ( w*m , L*m ) ). At points E and E’ there is an informal urban sector of size L*u , a rural
population of 1 − L*m − L*u and thus a rural wage of w*r . Since E’ lies on ee’,
wr ( Lu + L*m ) = L*m w*m and
expected wages are equalised in the urban and rural sectors. For
an even fuller understanding of the model, let us see diagrammatically what would happen
should the rural wage be less than w*r .
wm = f ' ( Lm )
wr = g ' (1 − Lm − Lr )
e
w*m
E
E’
wr*
e’
wr0
*
Lm
L*m + L0u
L*m + L*u
Figure 12: disequilibrium in the Harris-Todaro model
As can be seen from Figure 12, when the rural wage rate is at wr0 , below its equilibrium
value, there are more people employed in agriculture and less people employed in the
24
informal sector ( L*m + L0u < L*m + L*u ). But the point ( wr0 , L*m + L0u ) lies below the equilibrium
rectangular hyperbola, which means that
wr0 ( L*m + L0u ) < w*m L*m ,
i.e. the agricultural wage is lower than the expected urban wage: people will move to the
city and, due to the increase of both the agricultural wage and the pool of informal workers
in the city, the equilibrium condition (EC) will be finally restored (the rural wage line shifts
up).
In this model the informal urban sector with a very low living standard serves to equilibrate
the migration process. If the fixed manufacturing wage is very high (substantially above its
perfect competition level), very few people will be employed in the manufacturing sector.
In the absence of an informal sector (Lu = 0), all the remainder of the population will be
employed in agriculture, where as a consequence the marginal product of labour and hence
the wage will be extremely low. At the same time the probability of employment would be
one (since Lu = 0) and therefore the expected urban wage extremely high. Peasants will
migrate but, faced with the rigidity of the manufacturing wage, will become unemployed
and earn a living only thanks to the informal sector. So, according to the Harris-Todaro
view, the informal sector serves essentially to: 1) provide a subsistence to the urban
unemployed (what would happen with the introduction of a safety net for poor people,
something like a welfare state?) and 2) guarantee the persistence of the gap in living
standards between rural residents and the urban residents employed in the formal sector.
However, one must recognise that the existence of an informal sector has also some
negative, sometimes tremendously negative implication for the urban life (congestion,
slums degradation, lack of any kind of rights’ respect, a high crime rate, etc.). For this
reason, it may happen that a government tries to favour the creation of job in the urban
formal sector, and to this purpose it can implement such measures as tax holidays or better
treatment in the credit market for the urban manufacturing firm. This way, a governement
hopes to reduce the size of the informal sector and increase that of the formal sector. But
what is (could be) the final outcome of such a policy? It might happen that, because of
migrations from the countryside, the pool of informal workers in the city actually increases
despite the governmental policy. This can be investigated by looking at Figure 13. First, a
policy aimed at accelerating the rate of absorption of labour in the formal sector may be
represented by an outward shift of the labour demand curve in the manufacturing sector
(for any given market wage, manufacturing firms are willing to hire more people because of
the incentive they are receiving). It can be seen that in the new equilibrium there will be
more people employed in the urban formal sector (as expected) and less people working in
the agricultural sector (because of migration) earning a higher rural wage than before
(because of the increase n their marginal product). More precisely: in the initial equilibrium,
before the implementation of the governmental policy, the manufacturing wage is m and
manufacturing employment is a; in the rural sector there are 1 – c workers, each getting a
rural wage equal to q; finally, in the urban informal sector there will be 1 – a – (1 – c) = c –
a workers. The governmental policy shifts both the labour demand curve in the
manufacturing sector and the equilibrium locus (the rectangular hyperbola) up, as indicated
by the arrows. If the labour demand (marginal product) curve in the agricultural sector is
LRd , in the new (after-policy) equilibrium there will be b manufacturing workers (with b >
a, as expected); 1 – d agricultural workers, each getting a rural wage equal to r (it can be
seen that 1 – d < 1 – c and r > q, as expected); as to the urban informal sector, the pool of
workers is now equal to d – b.
25
LRd
LRd
'
m
r
s
q
o
a
b
c
d
e
1
Figure 13: a pro-urban/formal sector policy
The question is: is d – b < c – a? Or, to put it differently: does the governmental policy
succeed in shrinking the pool of informal urban workers? A priori, we simply cannot
answer to this question. But we can say something, notably that the answer ultimately
depends on the slope of the labour demand curve in the agricultural sector. Indeed,
'
imagine that the relevant agricultural demand curve is LRd , which is flatter than LRd . In this
case the effect of the governmental policy is to reduce even more the number of
agricultural workers (there will be more migrants to the city), so that in the new equilibrium
there will be e – b informal urban workers, which is clearly greater than d – b. So, in
general, the flatter the agricultural labour demand curve, the more likely is that the absolute
size of the urban informal sector goes up despite the aim of the policy is to reinforce the
urban formal sector. Basically, the free choice of the peasants to move to the city can
render the governmental policy even counterproductive. There are two points that are
worth stressing, the first related to the relative size of the urban informal sector, and the
second to the economic meaning of the slope of the labour demand curve in the
agricultural sector. As to the first point, from the equilibrium condition (EC) we can
immediately infer that after the introduction of the governmental policy the relative size of
the urban informal sector (its size measured as a fraction of the total urban sector) must
have diminished, irrespective of what happens to its absolute size. However, what really
matters in policy and social terms (congestion, crime rates, diffusion of diseases, etc.) is the
absolute size, the relative being quite unimportant. As to the slope of the agricultural
labour demand curve, it is clearly a measure of the elasticity of labour demand to the real
wage: the flatter the curve, the more responsive labour demand. In the limit, with a
horizontal curve, agricultural labour demand is perfectly elastic at a given wage rate and we
are back to the Lewis case of surplus labour. In such a case, any increase in the
26
manufacturing, formal employment will be accompanied by an equivalent (in percentage
terms) increase in the urban informal employment14. The city is larger than before, but the
proportional expansion of the formal and informal sectors has compromised the realisation
of the government’s objectives.
This general principle can be applied to other policies as well, not necessarily linked to
formal labour demand: “ ..policies aimed at directly reducing urban congestion (say, by
building more roads), reducing pollution (say, by building a subway), or increasing the
provision of health (say, by building new public hospitals) might all have the paradoxical
effect of finally worsening these indicators......because fresh migrations in response to the
improved conditions ends up exacerbating the very conditions that the initial policy
attempted to ameliorate” (Ray, pp.381-382).
Exercises:
1) What are the effects of technical progress in agriculture in the framework of the
Harris-Todaro model?
2) What are the effects of introducing full flexibility of the manufacturing wages
(instead of having them fixed)?
3) What are the effects of technical progress in the manufacturing sector?
4. LAND REFORM
•
•
•
Is the enormous inequality in land holdings bad for agriculture productivity?
If it is, can land rental markets and/or land sale markets spontaneously redress the
balance, reduce such inequality and therefore allow for a productivity increase?
If not, what is the role of a land reform?
Let’s start from the first question. Basically, we can contrast two opposite arguments (in
that they produce contrasting conclusions), a technological argument and an economic
argument.
The technological argument rests on the notion of economies of scale and leads to the
conclusion that large land holdings (and then a certain degree of inequality in land holding)
are good for productivity growth in agriculture. Think of those techniques that allow
farmers to achieves a high productivity level:
Draft animals. A minimum size of the plot is needed to use them in an economically
viable way. Imagine you have 2 bullocks, which can be productively employed only on a
plot of at least 1 hectare. But you just have a plot of ½ hectare. There would be no
problem if you could rent one of the bullocks out, but such a rental market is usually very
thin, for two reason:
•
14
If you rent the bullock out, it could be overworked or mistreated (and you would
lose value, for you and your sons).
This point may be better understood by rewriting the equilibrium condition (EC) as
wr =
1
wm .
( Lu Lm ) + 1
Since neither the manufacturing nor the rural wage change under the labour surplus assumption, formal and
informal labour in the city must grow at the same rate from one equilibrium to the other.
27
•
Inside a village (the “natural” dimension of a market, especially when infrastructure
and transport facilities are poorly developed) there is often an almost perfect
correlation in the use of animal power.
Machinery (tractors, pump sets….). Here the minimum size required for efficient
ownership is even higher (despite the scope for a rental market is somehow better).
So, from a strictly technological point of view, no discussion: large plots of land are more
productive than small plots of land. Inequality in land holding is good for productivity growth.
But now consider the “economic argument”, based on people’s incentives to put as much
effort as possible in the production process. We will see that, from this perspective, small
holdings (and then a certain degree of equality in land holding) are good for productivity growth.
2 agents
Landowner
Tenant
risk-neutral
risk–averse
Let us specify the technology in agriculture:
p
G
Y =
B
(1 − p )
with G>B
There are two possible arrangements between the landowner and the tenant:
Fixed Rent Contract:
the tenant pays R to the landowner
Sharecropping Contract : the tenant pays a fraction s (sY) to the landowner.
In terms of efficiency (the effort put in the production by the tenant) a fixed rent contract
is to be preferred to a sharecropping contract (the reason is easy to understand: if you are
the tenant and have to decide whether to put some extra effort in jour job, what do you do
in case of fixed rent contract? And what do you do in case of sharecropping?).
So, why do we observe so many sharecropping contracts all around the world?
Sharecropping
P
Tenant
(1-s)G
Landlord
sG
(1-p)
(1-s)B
sB
28
29
Fixed rent
P
Tenant
G-R
Landlord
R
(1-p)
B-R
R
Let’s fix “s” in such a way that the expected return to the landlord is the same and, given
his risk–neutrality, he is indifferent between the two contracts:
psG + (1-p)sB = R, or
s(pG+(1-p)B) = R, so that
s* =
R
pG + (1 − p)B
Tenant’s return in the good state
Fixed rent
(G-R)
Sharecropping

(1 − s*)G = 1 −


R
GR
G = G −

pG + (1 − p) B 
pG + (1 − p) B
In order to compare these two returns we can calculate the difference between them:






GR
G
 <0
G −
 − ( G − R ) = R 1 −
pG + (1 − p ) B 
pG + (1 − p ) B 
 





<G
It follows that in the good state the tenant gets more with a fixed rent contract.
Tenant’s return in the bad state
Fixed rent
Sharecropping
(B-R)

(1 − s*) B = 1 −


R
BR
B = B −

pG + (1 − p) B 
pG + (1 − p) B
In order to compare these two returns we can calculate the difference between them:






BR
B
>0
B −
 − ( B − R ) = R1 −
pG + (1 − p ) B 
pG + (1 − p ) B 
 





>B
30
It follows that in the bad state the tenant gets more with a sharecropping arrangement.
Overall, the tenant prefers sharecropping because of his risk–aversion. Indeed, if one is
risk-averse she will prefer the option that is better in the bad state. Since, by construction,
the landlord is indifferent, the negotiation between the two will come up to a
sharecropping agreement (with s slightly above s*). So, despite its inefficiency (in terms of
effort provision), sharecropping is the predominant agrarian agreement.
What is the prevailing argument? The argument based on technology (large holdings are
good for agricultural productivity) or the argument based on economic incentives (small
holdings are good for agricultural productivity because in a small plot land can be
cultivated directly by the farmers and his families, no need to reach any agreement –
necessarily: an inefficient sharecropping agreement - with external people. There is
therefore a strong incentive to put the maximum possible effort)?
The evidence suggests that the incentive argument is more relevant and productivity is
higher on small plots of land (see Ray). However, this raises different policy questions:
Pooling Land and Cooperatives
Drawing on what we have just said, it is tempting to claim that small farmers (who do not
need to respect any agreement with external agents) should pool their lands (basically, form
a cooperative) to take advantage of economies of scale.
The validity of this argument depends on whether the source of economies of scale lies at
the cultivation (production) level or outside the cultivation process.
If it lies outside the cultivation process, for instance because the advantage of pooling
comes from marketing (a big, pooled subject is able to get better prices on the market), the
cooperative works: land is cultivated separately in small plots and then the fixed cost of
setting up a marketing group can be pooled and shared
But when the source of economies of scale lies at the production level (say, through the use
of tractors), then the incentive problem returns with full force: additional effort by one
farmer leads to additional output, which is then shared among the team. If the farmers fail
to internalise this positive externality (which requires a complete sense of altruism) effort
will be undersupplied. So, do not expect to see successful wheat or rice cooperatives
(sectors where the economies of scales originate at the marketing level), and do not be
surprised to discover that collectivisation in China lead to a tremendous reduction in
agricultural productivity.
Land Rents and Land Sales
So, a more egalitarian distribution of land would increase agricultural productivity and
therefore help sustain the industrialization/development process.
A quite natural question arises: why doesn’t a large landowner sell his land splitted into
smaller plots to several small farmers? After all, this should be a very good deal for each
part of the dealing. To see why:
31
Figure (14): a large plot subdivided into 4 small plots
Well, we can expect the market value of a plot of land (even more generally: the value of
any asset) to be equal to the discounted value of the stream of future profits generated on
that land (why?). Consider the larger plot in Figure (14) and assume that its market value,
when it is owned by a single landlord who will need to sign a sharecropping arrangement
with one ore more tenants, is 80. In other words: per hectare productivity is such that the
discounted flow of future profits generated on this large plot is 80. Now, what is likely to
be the value of the smaller four plots when they are owned by four distinct smallholders? It
will be, for instance, 25, the relevant point being that 25x4 = 100 > 80. The small plots can
be cultivated by the family farmers without the need of any (inefficient) sharecropping
tenancy arrangement and therefore per hectare productivity will be higher, which in turn
increases the discounted stream of future profits and the market value of the land. So, why
doesn’t the large landowner sell voluntarily his land to four smallholders (getting 25 x 4 =
100) instead of keeping it and getting profits (present value) equal to 80? Why, in other
terms, is the land market so thin?
In a world where the credit market is imperfect (asymmetric information, monopolies,
etc.), the value of the land has two components:
•
•
discounted flow of future incomes (as we saw). Let’s call D this component;
land as collateral (measured by the profitability of the additional loans one can get
in that he/she owns land). Let’s call C this component.
Now, if a buyer must obtain a loan to buy the land (which is typically the case for a small
buyer) and must mortgage that very piece of land for the loan, then he can’t reap the
benefit of the land as a collateral (C) until the loan is paid off. It follows that
For the
Potential Seller:
D+C
D`>D15
Potential Buyer:
D`
If D + C > D` (and it could be), there will be no market for land.
15
In the previous example, D is 20 (80/4) and D’ is 25.
32
So: how to realise a more egalitarian distribution of land and reap the productivity gains
that should follow?
We are left with very few standards:
•
•
“Revolution” (political upheavals in society: Cuba, Japan, Korea, Taiwan).
Government
Public Intervention (Land Reform):
International
Agencies (NGO`s)
The role of public institutions – either the governments or some international agency or
NGO – is, from a strictly financial point of view, to pay for the difference (D + C) – D’.
APPENDIX: THE INTERLINKED CONTRACT BETWEEN A TRADER-LENDER AND A FARMER-BORROWER
Suppose the output produced by the farmer depends only on the working capital she has to
borrow: F(K) is the standard concave production function of the farmer. The farmer
borrows this working capital from “her” trader, i.e. the person who will be in charge of
marketing farmer’s output (the farmer is often too poor, and the rural infrastructure too
poorly developed, to be able to go directly to the market). The opportunity cost of capital
to the trader is the rate r (the rate he has to pay to borrow this money from a formal bank
or the rate he gets from a deposit in the formal bank). Should the samll farmer borrow
from an alternative source (for instance a formal bank), she would pay the rate r0 > r. Let i
the interest rate charged by the trader-lender, with (1 + i) = α (1 + r), and for the moment
α can be less than or equal to or greater than unity (the value of this parameter will emerge
as an optimal and endogenous choice of the trader-lender). The market price of output is
p, but the price offered by the trader to the farmer is q = βp, with the value of β to be
determined endogenously.
α and β are chosen by the trader. It follows that the farmer will take them as given and
maximizes her income
Y = βpF ( K ) − α (1 + r ) K
(A1),
by choosing K. The first order condition is
βpF ' ( K ) = α (1 + r )
(A2)
The minimum income the farmer can get even without entering the contract with the
trader is
Ymin = pF ( K min ) − K min (1 + r 0 )
(A3),
where Kmin satisfies pF ' ( K min ) = (1 + r 0 ) .
The trader will maximize his income
33
π (α , β ) = (1 − β ) pF ( K ) + (α − 1)(1 + r ) K
(A4),
by choosing α and β. The trader will have to take into consideration two constraints,
known in the literature as the incentive-compatibility constraint and the participation constraint.
The former coincides with (A2): it says that the trader will have to chose a value for α and
β by taking into account that his choice will affect farmer’s choice of K and therefore his
own profits. The latter says that the choice of α and β must be such that the farmer does
participate to the transaction, instead of being pushed away (if the trader tries to make too
much money, the farmer will simply go to a formal bank or to some other moneylender).
So, formally the problem of the trader is to choose α and β in order to maximise (A4)
subject to (A2) and Y ≥ Ymin. One way of solving this problem is to observe that (A4) can
be rewritten (and this is obvious) as the difference between what the trader gets from the
market (net of the cost of capital) and what is left to the farmer:
π = [ pF ( K ) − (1 + r ) K ] − Y
But one thing is sure: the trader will choose α and β so as to press down Y to Ymin (there are
no reasons from the point of view of the trader to let the farmer make more money than
what is sctrictly needed to induce her participation to the transaction). Since Ymin does not
depend on α and β, it follows that trader will maximize his income when pF(K) – (1+r)K is
maximized, that is to say when pF’(K) = (1+r). But compare this condition with (A2): it
must be α = β. Let us call γ the common optimal value of these two parameters. From (A1)
the value of farmer’s income can be rewritten as
Y = γ [ pF ( K * ) − (1 + r ) K * ]
(A5),
where K* is the value of K such that pF’(K*) = 1 + r. Using this propety, (A5) can be
rewritten as
Y = γ [ pF ( K * ) − pF ' ( K * ) K * ]
(A6).
But, as we have already stressed, it must be Y = Ymin, and thus
γ=
F ( K min ) − F ' (K min )K min G(K min )
=
F (K * ) − F ' (K * )K *
G(K * )
(A7).
To check whether γ = α = β is greater than or equal to or lower than unity, we have to
understand the behaviour of the function G and keep in mind that Kmin < K* as r0 > r.
Since by definition of G we have G’ = - F’’K > 0, it must be γ = α = β < 1.
The economics is relatively simple: the farmer is given an interest discount (i < r), which is
compensated by the underpayment in the output market (q < p).
Exercises
i.
ii.
What is the effect of a reduction of r0? In the limit, what would happen if r0 = r?
Can you give a policy interpretation to this result?
Imagine that your objective is to prevent underpayment to farmers in the output
market: what is to be preferred in efficiency terms, an intervention directly in the
output market or an intervention in the credit market?
34
iii.
What would happen in this model if the government decided to launch a program
of public works in the city?
Main References
Bhardan, P. and C. Udry, Development Microeconomics, Oxford University Press, 1999;
UNCTAD (United Nations Conference on Trade and Development), Trade and
Development Report 1998, Geneva, 1998;
Ray, D., Development Economics, 1999;
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