Economic Development Theory
Lecture One
Dr. Patrick J Nolen
EC 902
January 26, 2017
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EC 902: Economic Development Theory
Module Supervisor: Patrick Nolen, 5B.327
Office Hours: Thursdays, 13:30-15:30
Office Hours are subject to revision so please check the webpage for
the most up to date information.
Email: [email protected]
Moduel Meetings:
One Lecture per week, Thursdays 16:00-18:00, Room NTC 1.02
Class website: http://orb.essex.ac.uk/EC/EC902/
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Reading
We will not rely solely on one book for this class. Instead we will
take parts from three different books and a lot of papers.
The book by Kaushik Basu entitled
Analytical Development Economics is one of the best for economic
development theory at the graduate level.
Development Economics by Debraj Ray is an advanced
undergraduate textbook and covers almost every topic we will examine
in this course. It is a good book and is a must have for anyone who is
going to continue doing research into development economics.
Development Microeconomics by Pranab and Udry will cover some
of the topics we are looking at in detail.
The module outline has a list of all the papers at which will be
looking. We will not be covering every paper that is on the outline in
lecture so I will let you know which ones to focus on as we go through
the semester.
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Assessment
Coursework: Term paper that will be a maximum of 4,000 words.
Exam: 2 hour exam that will take place during the summer term.
Final Mark:
EITHER
50% of your coursework mark plus 50% of your exam mark
OR
100% of your exam mark.
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Reading and Outline
Poverty Trap Reading
KB Chapters 2.
Kremer, “The O-Ring Theory of Economic Development”
Hoff and Stiglitz, “Modern Economic Theory and Development”
Young, “Increasing Returns and Economic Progress”
Outline
Poverty Trap Models.
MSV Model
O-Ring Model
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Poverty Trap
Poverty has a tendency to persist and understanding why that is the
case may give us some idea of how to better deal with it.
A poverty-trap can also be referred to as a “low-level equilibrium
trap.”
When talking about economics in the usual Walrasian framework
every outcome is pareto optimal but our idea of a poverty trap
suggests we may want to consider a different framework.
Can a “Big Push” from one equilibrium to another make everyone
better?
Are there sub-optimal equilibria?
When looking at poverty traps we are going to see some models that
allow for these possibilities and, of course, we are going to see lots of
multiple equilibria.
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Murphy, Shleifer, and Vishny (MSV) Model
A less developed economy with:
k sectors and k goods.
1 consumer who has L units of labour to supply.
k
Say the consumer’s utility is u = x1 ∗ x2 ∗ ... ∗ xk = ∏ xi and let the
i =1
consumer have income Y .
k
The demand for each good by this consumer is then max u = ∏ xi
i =1
such that p1 x1 + p2 x2 + ... + pk xk = Y
k
∏ xi
k
∏ xi
By the FOC we get xi = λpi ⇒ λ = xi pi . Thus
x1 p1 = x2 p2 = ... = xk pk which means the product of each must be
Y
Y
k and we get xi = kpi
i =1
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MSV Model
Let π be the aggregate profit in the economy and wage equal one,
that is w = 1.
Then we have that Y = π + L
Now let us discuss the “features” of this economy.
Say that there are two technologies, one modern and one traditional,
such that:
Traditional technology has 1 labour input ⇒ 1 output
Modern technology has 1 labour input ⇒ α > 1 output with a fixed
cost of F units of labour.
We assume that a modern firm would be a monopolist if it enters
that sector.
The traditional firm is competitive because everyone has access to
that technology.
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MSV Model
Since we assume that the firm with modern technology is a monopoly
then its demand function looks like below.
Since the competitive firms all have cost=1 then price=1 if the
traditional technology is used (line AB).
The curve from B to C is the rest of the demand curve and comes
from the demand equation above (xi ).
The curve ABQM is the marginal revenue (MR) curve (which is
zero!) and 1α is the MC.
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MSV Model
Since a monopolist will produce where price equal MR then, as can be
seen by the preceding graph, q ∗ = ky .
This means that the profit a monopolist earns will be
( α −1)
1 − 1α ky − F = α ky − F .
Now define a =
π M = ay
k − F.
( α −1)
α
< 1 but greater than 0 and we get that
Note that in the non-modernized sectors, profits
will
be zero. That
means that aggregate profit, π (y , n ) = n ay
−
F
where n is the
k
number of firms that have modernized.
Since there is only one person and from before
we had
h
i that
ay (n)
Y = π + L, then we know that y (n ) = n k − F + L and we
can now solve for y (n ) .
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MSV Model
k ∗ y (n ) = n ∗ a ∗ y (n ) − n ∗ k ∗ F + k ∗ L
⇒ y (n ) [k − n ∗ a ] = k ∗ L − n ∗ k ∗ F
nF )
⇒ y (n) = k (kL−−na
We can then substitute this into our profit function to see that, if n
industries have modernized, then the profit from another sector
−kF
becoming modernized is π (n ) = aL
k −na
If π (n ) < 0 a monopolist will not enter and if π (n ) > 0 a
monopolist will enter.
Depending on aL − kF then < or > 0 we have a unique equilibrium;
either no one modernizes or everyone does.
Note that this model does not have multiple equilibria! It says that
the economy will be in one condition or another and that it will not
move between those two conditions.
We now want to get multiple equilibria out of this model.
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MSV Model
To get multiple equilibria we have to have spillover between markets,
i.e. from the type of market one is in to the wage.
Let the work in the modern sector be harder than in the traditional
sector. Therefore the wage in the modern sector will be 1 + v where
v > 0.
Thenthis new wage makes profit in the modern sector
α−(1+v ) y
π=
− (1 + v ) F = by
α
k − (1 + v ) F where
k
α−(1+v )
b=
.
α
This one person is dividing her time between working in the n modern
sectors and the (k − n ) traditional
sectors.i Therefore her total wage
h
is (k − n )
y (n )
k
+ (1 + v ) L − (k − n) y (kn) .
This
i y (n ) =
h
i
h means that we have
b ∗y (n )
y (n )
y (n )
n
−
1
+
v
F
+
k
−
n
+
1
+
v
L
−
k
−
n
(
)
(
) k
(
)
(
) k
k
and can now solve for what y (n ) is.
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MSV Model
(1+v )(L−nF )k
We can reduce the above equation to y (n ) = (1+v )k −n(v +b ) and can
substitute this into the profit equation of the monopolist to get the
following profit function:
π=
(1 + v ) [b (L − nF ) − F (1 + v ) k + Fn (v + b )]
v (k − n ) + k − bn
Note that the denominator is always positive...
Also (1 + v ) is always positive...
We then have to examine
Ψ (n ) = b (L − nF ) − F (1 + v ) k + Fn (v + b ).
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MSV Model
If n = 1 then
Ψ (1) = bL − bF − Fk − Fvk + Fv + Fb = bL − Fk − Fv (k − 1) < 0.
Which means no firm is going to want to modernize if no one else has
modernized.
If n = k then
Ψ (k ) = bL − bkF − Fk − vkF + vkF + bkF = bL − Fk > 0. Which
means if every other firm is modernized then you want to modernize
as well.
Therefore we have two equilibria that could exist: everyone
modernizes AND no one modernizes.
This model gives us the idea of the “Big Push.” Once a critical
amount of sectors have modernized then all the remaining sectors
want to modernize.
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The O-Ring Theory
This model was motivated, in part, by the idea that a worker doing a
job in the USA might get paid 20 times that of a worker in Mexico
doing the same job.
Another example is that an engineer in India could move to the UK
and, even adjusting for PPP, that engineer will make more to do the
same job in the UK as she did in India.
The name of this model comes from the space shuttle Challenger
explosion when one small component, the O-rings, malfunctioned.
The biggest difference we are going to see with this model in is the
production function.
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The O-Ring Theory
n
Let y = q1 ∗ q2 ∗ ... ∗ qn ∗ nB = ∏ qi nB where qi ∈ [0, 1]
i =1
Think of qi as the quality or probability of success of a certain task
required in output.
Let B be per capita output.
Thus y can be thought of as “expected” output.
Also note that q is visible and that there are lots of firms with this
type of production function.
Let the number of workers N be distributed uniformly on the unit
interval, that is p (i < q ) = qN, the probability of having a worker of
quality i less than q is qN.
In this model we are going to have skill clustering, that is, at each
firm q1 = q2 = ... = qn . Which means we have sorting based on
skills.
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The O-Ring Theory
Lets prove that skill clustering is true in this model – that is, if
(q1 , q2 , ..., qn ) maximizes a firm’s profit, then q1 = q2 = ... = qn .
Assume that there is no skill clustering. Then there exists a qH and
qL such that qH > qL .
Since (q1 , q2 , ..., qn ) is the profit maximizing amount then it must be
the case that any other “team” of workers must bring the firm the
same, or a lower, profit.
n
Let πHL = qH qL Ω − w (qH ) − w (qL ) − θ where Ω =
n
∏ qi nB
i =1
qH qL
and
θ = ∑ w (qi ) − w (qH ) − w (qL ) then πHL ≥ πHH and πHL ≥ πLL
i =1
where:
2 Ω − 2w (q ) − θ and
πHH = qH
H
2
πLL = qL Ω − 2w (qL ) − θ.
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The O-Ring Theory
Consider πHL ≥ πHH
⇒ qH qL Ω − w (qH ) − w (qL ) − θ ≥ qH2 Ω − 2w (qH ) − θ
⇒ w (qH ) − w (qL ) ≥ (qH − qL ) qH Ω
Since we know that qH > qL then we have that
w (qH ) − w (qL )> (qH − qL ) qL Ω or
qL2 Ω − 2w (qL ) − θ > qH qL Ω − w (qH ) − w (qL ) − θ
πHL < πLL
Thus it cannot be the case that two of the inputs are of a different
level QED.
∂y
Note: ∂q
= ∏ qj nB. This means that the marginal product (MP) of
i
j 6 =i
a worker goes up if all the skills of other workers are higher. Thus an
engineer who moves from India to the UK gets paid more because of
her colleagues.
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The O-Ring Theory
Now lets look at the competitive equilibrium of a firm of this type in
the market.
The firm faces the following problem:
n
n
Max ∏ qj nB − ∑ w (qi )
{ qi } i = 1
i =1
The FOC of which is w 0 (qi ) = ∏ qj nB which, by the skill clustering
j 6 =i
theorem is w 0 (q ) = q n−1 nB.
Since the firm is in a competitive industry it is making zero profit so
q n nB − nw (q ) = 0 or w (q ) = q n B.
Note that this means we are done and have an equilibrium!
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The O-Ring Theory
Thus we have a model that
Shows clustering of skills,
The same wages for all people at the same level, and
Why someone’s wage will go up simply because they move from one
country to another.
This model can also explain why the same job pays more at one firm
that another.
A firm that has highly-skilled people will be willing to pay more for a
mail-room clerk.
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The O-Ring Theory
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Reading and Outline
Readings:
KB Chapter 3
DR Chapter 3.
Banerjee and Newman, “Occupational Choice and the Process of
Development”
Solow, “Perspectives on Growth Theory”; Romer, “The Origins of
Endogenous Growth”
Outline
Growth, Distribution and Development.
Harrod-Domar
Solow
(Distribution)
Note: The role of distribution in development (and how it motivates or
stifles it) is important but the model that I was going to present is easily
adapted and discussed in the case of child labour so I’m going to wait until
that lecture to present it.
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Growth
We are interested in growth because of the benefits and access to
more services that income tends to bring people.
Furthermore, per capita income tends to be highly correlated with
many measures of well-being; such as life expectancy, adult literacy,
and infant mortality.
Human Development is multifaceted but having a proxy for measures
of well-being, such as per capita income, means that we should be
interested in what effects growth (especially in terms of per capita
income growth).
The following models give us an idea of growth and what can play a
part in determining the growth, or lack of growth, within a country.
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Harrod-Domar Model
Let a society’s production function be Yt = min {vK , bL} where Y is
total output, K is aggregate capital and L is aggregate labour.
Furthermore v , b > 0 are fixed coefficients.
K=(b/v)*L
K
L
In developing economies there is usually a surplus of labour.
Therefore, the binding constraint if typically K . With that in mind
we can rewrite the production function as Yt = vKt = c1 Kt .
Note that the lower the output-capital ratio is the better.
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Harrod-Domar Model
Let s be the marginal propensity to save (MPS). That means the
amount of income saved in a year is sYt .
Assuming that all saved money is invested then, if there is no
depreciation, we know that ∆K = Kt +1 − Kt = sYt which means
that Kt = Kt −1 + sYt −1 .
Now define K̇t = Kt +1 − Kt = sYt = svKt and we can now, discuss
the growth of capital!
The growth rate of capital
Kt +1 −Kt
Kt
=
K̇t
Kt
=
svKt
Kt
= sv = cs .
For ease of exposition define K̂t as the growth rate, which means that
K̇t
K̂t = K
= cs
t
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Harrod-Domar Model
Now lets find out what the growth rate of the economy is, i.e. Ybt
Ŷt =
Ẏt Yt +1 − Yt vKt +1 − vKt Kt +1 − Kt K̇t
s
=
=
=
= = K̂t =
Yt
Yt
vKt
Kt
Kt
c
Therefore the economy grows at a rate equal to the savings rate
divided by the capital-output ratio.
To increase growth then we could:
Try to increase the savings rate.
Hope to change the capital-output ratio.
We have come to this result assuming that capital, K , is the binding
constraint. What if the population is the binding constraint? i.e. We
do not have excess labour...
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Harrod-Domar Model
With no excess labour then Yt = bLt .
As above we would have Ybt = Lbt because:
Ŷt =
Ẏt Yt +1 − Yt bLt +1 − bLt Lt +1 − Lt L̇t
=
=
=
= =L̂t
Yt
Yt
bLt
Lt
Lt
So if n was the rate of growth of the population then that would also
be the rate of growth in the economy, that is Ŷt = L̂t = n
This would suggest that, if labour were the binding constraint, we
should increase population growth to increase the total output in the
economy.
Major criticism of this model:
s is exogenously given.
Savings rates depend on the wealth of a country.
Therefore we want to look at an endogenous model.
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Solow Growth Model (Neoclassical)
This model will be very general so we will go through it thoroughly.
Let output be a function of capital and labour:
Yt = F (Kt , Lt )
Where the function F has three conditions that are satisfied
1
It exhibits constant returns to scale (CRS).
That means that for all λ ≥ 0, F (λK , λL) = λF (K , L). We assume
that λ = L1 so Yt = F (Kt , Lt ) = Lt F (kt , 1) or, as we will write
Yt
t
yt = f (kt ). Where kt = K
Lt and yt = Lt . Note that per capita
output can grow only if the capital-labour ratio increases.
2
3
Fk , FL > 0 and that FKK , FLL < 0 (diminishing returns).
The Inada conditions hold. That is lim Fk (K , L) = lim FL (K , L) = ∞
K →0
L→0
and lim Fk (K , L) = lim FL (K , L) = 0
K →∞
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L→ ∞
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Solow Growth Model
These three conditions, though complicated, are what are needed simply
so we have a nicely shaped production function such as the one below.
Y
K
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Solow Growth Model
Let labour grow at a rate of n =
L̇t
Lt .
Let the MPS be s.
Let the depreciation rate be δ.
We have, from before, that K̇t = Kt +1 − Kt so, using substitution we
have K̇t = sLt f (kt ) − δKt or that K̇Ltt = sf (kt ) − δkt .
·
It would be great if we could solve for what k t is... and
k̇t =
K̇t
Kt L̇t
K̇t
−
=
− nkt
Lt
Lt Lt
Lt
So we end up with the fact that k̇t = sf (kt +1 ) − (δ + n ) kt
Which means that k̂t =
the capital-labour ratio.
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sf (kt )
kt
− (δ + n) . This is the growth rate for
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Solow Growth Model
To get an idea of the what this means lets look at the growth rate of
k, i.e. k̂t
This shows us that things are tending to a steady state.
What happens if the MPS, s, changes? In the new steady state per
capita income is higher but the growth rate of per capita income is
exactly the same as before.
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Solow Growth Model
This means that raising the s or any other policy for that matter will
bring little benefit because in the steady state the growth rate will
always be the same.
If you think of developing countries, though, you can quickly come up
with examples of countries that have maintained a strong level of
growth, i.e. their growth level has not decreased as they approached a
steady state and in fact may have even accelerated.
Given those examples, is there anyway that the Solow growth model
could explain sustained growth or maybe even a “poverty trap?”
The answer is YES but we have to let go of the Inada conditions, (3)
from above, and allow y = f (k ), to not be concave.
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Solow Growth Model
f(k)
f(k)
s*f(k)/k
f(k)
δ+n
k'
k
k''
k
The graph on the left hand side shows the functional form of the
production function and the graph on the right shows that sustained
growth is possible in this situation.
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Solow Growth Model
f(k)
f(k)
s*f(k)/k
f(k)
δ+n
k'
k
k''
k
The graph on the left hand side shows the functional form of the
production function and the graph on the right shows that “poverty
trap”is possible in this situation.
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Conclusions
We have seen two models in which we are able to derive poverty traps:
The MSV model
The O-Ring model
Both models show us how poverty traps can develop and, when
possible, what type of policies are possible to remove an economy
from that poverty trap.
In the growth section we have gone through two famous growth
models:
The Harris-Domar Model
The Solow Growth Model
Both of these models take the savings rate as important and the
Solow model shows that growth is possible only in the short run
because everything returns to the steady state.
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