Growth Models and Developement Strategies.

1. Chapter 3: 2
Growth Models in the Context of
Development Economics
1.Endogenous and Exogenous Model
2.Balanced and Unbalanced Models
3.Inward and Outward Looking Models
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2. A) Exogenous Growth Model
(The Solow-Swan Growth Model)
• The Solow growth model allows us a dynamic view of how savings
affects the economy over time.
• We begin with a production function and assume constant returns.
Y=F(K,L) so… zY=F(zK,zL)
• By setting z=1/L we create a per worker function.
Y/L=F(K/L,1)
• So, output per worker is a function of capital per worker. We write
this as,
y=f(k)
• Given a savings rate (s) and a consumption rate
(1–s) we can generate a consumption function.
c = (1–s)y …which makes our identity,
y = (1–s)y + I …rearranging,
i = s*y …so investment per worker
equals savings per worker
2

3. Steady State Equilibrium
• The Solow model long run equilibrium occurs at
the point where both (y) and (k) are constant.
These are the endogenous variables in the model.
The exogenous variable is (s).
• By substituting f(k) for (y), the investment per
worker function (i = s*y) becomes a function of
capital per worker (i = s*f(k)).
• To augment the model we define a depreciation
rate (δ).
• To see the impact of investment and depreciation
on capital we develop the following (change in
capital) formula,
Δk = i – δk …substituting for (i) gives us,
Δk = s*f(k) – δk
3

4. • If our initial allocation of (k) were too high, (k) would decrease
because depreciation exceeds investment. If our initial allocation
were too low, k would increase because investment exceeds
depreciation. At the point where both (k) and (y) are constant it must
be the case that,
• Δk = s*f(k) – δk = 0 …or,
• s*f(k) = δk
…this occurs at our equilibrium point k*. At k* depreciation equals
investment.
4
•s*f(k)
•δk
•khigh
•k*
•s*f(k*)=δk*
•k
•s*f(k),
•δk

5. • We What happens if we increase savings?. This would increase the
slope of our investment function and cause the function to shift up.
know that steady state is at the point where s*f(k)=δk. This would lead
to a higher steady state level of capital. Similarly a lower savings rate
leads to a lower steady state level of capital.
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•The Solow Growth
model is a dynamic
model that allows us to
see how our
endogenous variables
capital per worker and
output per worker are
affected by the
exogenous variable
savings. We also see
how parameters such
as depreciation enter
the model, and finally
the effects that initial
capital allocations have
on the time paths
toward equilibrium.
•k
•s*f(k),δ
k
•δk
•s*f(k)
•k*
•s*f(k*)=δk*
•s*f(k*)=δk*

6. The golden rule level of capital, maximizing
consumption per worker.
• As mentioned above, the Solow growth
model allows us a dynamic view of how
savings affects the economy over time.
We also learned about the steady state
level of capital.
• Now, we assume policy makers can set
the savings rate to determine a steady
state level of capital that maximizes
consumption per worker. This is known as
the golden rule level of capital (k*gold)
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7. 7
• .
• Because, consumption per worker is the
difference between output and
investment per worker we want to
choose k* so that this distance is
maximized.
• This is the golden rule level of capital
k*gold
• We begin by finding the steady state
consumption per worker.
From the national income accounts identity,
y = c + i
we get c = y – i
• We want steady state “c” so we substitute
steady state values for both output (f(k*))
and investment which equals depreciation
in steady state (δk*) giving us
• c*=f(k*) – δk*
• A condition that characterizes the
golden rule level of capital is
MPK = δ
•k*gold
•f(k*),δk
*
•f(k*)
•k
*
•δk
*
•Below k*gold,
increasing k*
increases c*
•Above k*gold,
increasing k*
reduces c*

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• While the economy moves toward a steady state it is not
necessarily the golden rule steady State. Any increase or
decrease in savings would shift the sf(k) curve and would result
in a steady state with a lower level of consumption.
•k*gold
•k*
•δk*
•f(k*)
•sgoldf(k*)
•sgoldf(k*)
•f(k*),δk*
•To reach the golden
rule steady state…
•The economy needs
the right savings rate.

9. The augmented model that includes population growth
and technological progress.
• As mentioned above, the Solow growth model allows
us a dynamic view of how savings affects the
economy over time. We learned about the steady
state level of capital and how a golden rule steady
state level of capital can be achieved by setting the
savings rate to maximize consumption per worker.
We now augment the model to see the effects of
population growth and technological progress.
• By expanding our model to include population growth
our model more closely resembles the sustained
economic growth observable in much of the real world.
• To see how population growth affects the steady state
we need to know how it affects the accumulation of
capital per worker.
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10. • When we add population growth (n) to our model
the change in capital stock per worker becomes…
Δk = i – (δ+n)k
• As we can see population growth will have a
negative effect on capital stock accumulation. We
can think of (δ+n)k as break-even investment or
the amount of investment necessary to keep
capital stock per worker constant.
• Our analysis proceeds as in the previous
presentations. To see the impact of investment,
depreciation, and population growth on capital we
use the (change in capital) formula from above,
Δk = i – (δ+n)k …substituting for (i) gives us,
Δk = s*f(k) – (δ+n)k
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11. Steady State Equilibrium with population growth
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• At the point where both (k) and (y) are constant it must be the case
that, Δk = s*f(k) – (δ+n)k = 0 or, s*f(k) = (δ+n)k…this occurs at our
equilibrium point k*.
•At k* break-even
investment equals
•Investment
Break-even
Investment
•s*f(k*)=(δ+n)k* •s*f(k)
Investment
•Break-even
investment
(δ+n)k
•Like depreciation, population growth is
one reason why the capital stock per
worker shrinks.

12. The impact of population growth
• Suppose population growth changes from n1 to n2.This shifts the line
representing population growth and depreciation upward. At the new steady
state k2* capital per worker and output per worker are lower
• The model predicts that economies with higher rates of population growth
will have lower levels of capital per worker and lower levels of income.
12
•(δ+n1)k
•An increase in
“n”
•k2*
•Investment
Break-even
Investment
•s*f(k)
•(δ+n2)k
•k1*
•…reduces k*

13. The efficiency of labour
• We rewrite our production function as…
Y=F(K,L*E)
where “E” is the efficiency of labour. “L*E” is
a measure of the number of effective
workers. The growth of labour efficiency is
“g”.
• Our production function y=f(k) becomes
output per effective worker since…
y=Y/(L*E) and k=K/(L*E)
• With this augmentation “δk” is needed to
replace depreciating capital, “nk” is needed to
provide capital to new workers, and “gk” is
needed to provide capital for the new
effective workers created by technological
progress.
13

14. Steady State Equilibrium with population
growth and technological progress
• At the point where both (k) and (y) are constant it must be the case
that, Δk = s*f(k) – (δ+n+g)k = 0 or,s*f(k) = (δ+n)k.…this occurs at our
equilibrium point k*.
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•At k* break-even
investment equals
investment.
•Investment
Break-even
Investment
•s*f(k)
Investment
•Break-even
investment
(δ+n+g)k
•Like depreciation and population
growth, the labour augmenting
technological progress rate causes the
capital stock per worker to shrink.
•s*f(k*)=(δ+n)k*

15. The impact of technological progress
• Suppose the worker efficiency growth rate changes from g1 to
g2.This shifts the line representing population growth, depreciation,
and worker efficiency growth upward. At the new steady state k2*
capital per worker and output per worker are lower.
• The model predicts that economies with higher rates of worker
efficiency growth will have lower levels of capital per worker and
lower levels of income.
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•k1*
•…reduces k*
•k2*
•Investment
Break-even Investment
•s*f(k)
•(δ+n+g2)k
•An increase in “g”

16. Effects of technological progress on the golden rule
• With technological progress the golden rule level
of capital is defined as the steady state that
maximizes consumption per effective worker.
Following our previous analysis steady state
consumption per worker is…
c* = f(k*) – (δ + n + g)k*
• To maximize this…
MPK = δ + n + g
or
MPK – δ = n + g
• That is, at the Golden Rule level of capital, the net
marginal product of capital MPK – δ, equals the
rate of growth of total output, n+g.
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17. Steady State Growth Rates in the Solow
Model with Technological Progress
• .
17
Variable Symbol Steady-State Growth
Rate
Capital per
effective worker
k=K/(E*L) 0
Output per
effective worker
y=Y/(E*L)=f(k) 0
Output per
worker
Y/L=y*E g
Total output Y=y(E*L) n+g

18. “New Growth Theories”
Endogenous Growth Models
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19. Endogenous Growth Model
• Motivation: Traditional neoclassical growth theory failed
to explain long term growth. There is convergence, MPK
eventually declines.
• Technological Advances may eliminate convergence, but
they are Exogenous in the model
• Solow residual: is responsible for about 50% of historical
growth in DCs.
• In a rather ad hoc manner, neoclassical theory credits the
bulk of economic growth to an exogenous or completely
independent process of technological progress.
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20.  No diminishing returns to capital assumption in the new theory
sustained long-term growth resulting from increasing returns to scale.
 The potentially high rates of return on investment offered by LDCs
with low K/L ratios are greatly eroded by lower levels of
“complementary investments” in human capital, infrastructure, or
research and development.
 In turn, poor countries benefit less from the broader social gains
associated with each of these alternative forms of capital expenditure.
 Shortcoming of the new growth theory: it remains dependent on a
number of traditional neoclassical assumptions that are often
inadequate for LDCs.
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21. • Endogenous growth theory tries to overcome the shortcoming of exogenous
growth model by building macroeconomic models out of microeconomic
foundations.
• Firms maximize profits so that they tend to invest on technology to
maximize their profit.
• The engine for growth can be as simple as a constant return to scale
production function (the AK model) or a Romer model of more
complicated set ups with spillover effects.
• The new growth theory provides a theoretical framework for analyzing
endogenous growth, persistent growth that is determined by the system
governing the production process rather than by forces outside that system.
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22. • The EGT discards the classical assumption of diminishing marginal
return on capital investments,
• It assumes that public and private investment in human capital
generate external economies and production improvement that offset
the natural tendency for diminishing returns and explain the
existence of increasing returns to scale.
• In particular, the Romer model addresses technological spillovers
that may be present in the process of industrialization.
• It starts from the firm or industry level for growth process
considering economy- wide capital stock, positively affects output at
the industry level so that there may be increasing return to scale at
the economy wide level.
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23. 23
• Reemphasizes the importance of saving for fast economic growth
(similar to neoclassical approaches)
• Suggest active role of public policy (government) to provide
public goods (infrastructure) so as to encourage private
investment and efficient allocation of resources (contrast to the
neoclassical approaches that adhere strict dogma of free market
and passive governments).
• Underlines that the potentially high rate of returns to investment
in LDC is hindered by low level of complementary investments in
human capital (education), infrastructure and research.
N.B: However, the both endogenous and exogenous models
fail to look into the growth problems of LDCs that arise
mainly from inefficiencies due to inadequate institutional
structure, and imperfect capital and goods markets.

24. Endogenous Growth Model and
New Explanatory Variable
• Endogenous Economic Growth Model
• New Explanatory Variables
- Human Capital with Knowledge; we can have
an accumulation/evolution function for Human
Capital
• No convergence – MPK does not have to
decline if there is an increase in Human
Capital
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25. • The contribution of this model is that it emphasizes the link
between technical innovation, Human Capital, and Institutions
including Government.
• The previous Neo-Classical economists emphasized the
close relationship between Technical Innovation and
Physical Capital.
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26. Formal EG Model:
Romer-Mankiew-Weil Model
• Technological change is the result of the intentional
actions of people, such as Invention, and Research and
Development
• Some institutions promote innovation and R & D, and
others inhibit R & D.
• Romer supports Government-funding for Educational
Institution and R & D.
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27. Growth, Technology and Education
Engelbrecht
– At an early stage of economic development, the
level of education plays important role in technological
catch-up
– Productivity growth is more rapid where countries
have higher levels of average schooling
– Human capital has largest effects when specific to
sub categories important for technological diffusion
(science, math, engineering)
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28. 28
2) Balanced versus Unbalanced Growth
• Balanced and unbalanced growth models are
opposite sides of the same coin
• The choice is either maintaining a balance of
development of sectors throughout the development
process or creating imbalances first and moving
toward a balanced path eventually

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A. Balanced growth Model…
(Nurske, Rosenstein Rodan, Myint)
 The BG model is also referred to as the big push or
critical minimum effort model.
 Big push – a concerted, economy-wide and probably
public policy-led, effort to initiate or accelerate
economic development across a broad spectrum of
new industries and skill.
 Development of many sectors parallel to avoid supply
crises for inputs and to create domestic demand and
thus induce the willingness to invest.
 It agrees that countries have to develop a wide range
of industries at all & at the same time if they are ever to
prosper in attaining sustainable growth (assuming
people have enough wealth to buy goods produced). It
assumes everyone will prosper from the industry.

30. 30
Balanced growth Model…
BG assumes that simultaneous development of a wide
range of industries mitigate the problems associated
to market failures (coordination failures) that work
against development; e.g. pecuniary externalities -
positive or negative spillover effects on an agents
cost or revenues
• If the growth rate in the sectors is equal to the
growth rate of demand, then the Say Theorem is
valid, that is production growth creates its own
demand.

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Balanced model…
Complementarities in balanced growth models
Balanced growth On the demand side:
• Balanced growth in - industries developed are determined
by the demand/expenditure patterns or purchasing power
for consumers and investors
Balanced growth on the supply side:
- the need to build a number of industries simultaneously to
prevent supply bottlenecks
- Necessity to maintain balance between development of
agriculture and industry at the aggregate level
– Needs horizontal and vertical linkages among industries
– Support of infrastructure
– incremental capital-output ratio
Hence investment is key variable in the process (Rostow,
Harrod & Domar):
– ability to save and invest (s = savings)
– ability to convert capital into output

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Shortcomings of the Balanced model
• Market failures/coordination failures work against
development and is likely high or unavoidable in
LDC.
• A country lacks resources to finance balance
growth, i.e., capital is scarce to invest in all sectors
of an economy
• Hirschman: If a country were ready to apply the
doctrine of balanced growth, then it would not be
underdeveloped in the first place (Hemmer1988:
447ff).

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B. Unbalanced Growth Model (Albert Hirschman)
• The theory argues that sufficient resources cannot be mobilized by
government to promote widespread, coordinated investments in all
industries.
• Similar to the theorists of balanced growth, they agree that free market
alone cannot generate development, but differ in that government
planning or market intervention is required just in strategic industries.
• Nations should concentrate their energies on a few sectors during the
early stages of development
• Shortages of savings and capital, entrepreneurship, education 
concentrate on economic activities that will raise demand for social
capital most effectively  induced decision-making:
•  stimulate people to go for education, to save because they get high
interest rates, etc..  leave less to governments and more to markets.
• Identify activities with highest potential  select industries with
strongest forward and backward linkages

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Unbalanced growth Model…
• Lack of willingness to invest is not the true result of narrow
markets. The real reason lies in the socio-psychological
area of entrepreneurship.
– Management capacity of producer is important;
“Learning by doing”.
– Entrepreneurs are forced to pass the required maturity
process, thereby acquiring the necessary capabilities
for making investments (hence unbalance).

35. 35
Unbalanced growth Model…
• For this strategy, it is important to create inter-sectoral
dependencies, thereby the unbalance takes momentum.
• Resources are therefore need to be concentrated on
strategic industries with significant forward and backward
linkages.
• Government identify strategically important areas with
significant backward and forward linkages to
– Subsidize; e.g., State owned banks finance priority
investment projects chosen for their contribution to
growth and development.

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Unbalanced growth Model…
• Central concept point in this model is linkages; i.e.,
connection between (among) firms usually based on sales:
industries should be linked to other industries and must be
taken into account in development strategies
• Forward linkages: Firms creating essential inputs for other
key firms in the domestic economy. i.e., availability of
products that call for investments in further activities to the
production chain.
 E.g. investment in iron and steel industry  stimulate
setting-up of machinery industry.
 Backward linkages: Key firms buy industrial inputs from a
large number of domestic firms. Economic activities that
require inputs that can be supplied by other industries
(enterprises). Often replace imports of particular goods
that are later supplied by local industries.

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Unbalanced growth Model…
• Both linkages create pressures that lead to the
establishment of new industries. Pressures – new profit
opportunities; political process that forces government
to act.
• Problem:
– Only one or few industries prosper giving wealth to
those only working in those areas, i.e., a selected few
will achieve any gains

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(3) Inward & Outward Looking Development
Policies/ Strategies
Description:
 Inward-looking means inward-oriented or import
substitution (Trade Pessimists or Protectionists approach)
• Encourages indigenous “learning by doing” in
manufacturing and the development of indigenous
technologies.
• Greater reliance by restricting trade (tariff and quota)
and communication.
 Outward-looking means outward-oriented or export
promotion (Trade Optimists approach)
• Advocates that there is economic gains from trade for
all participants
• Encourages free trade, free movement of capital, labor
and enterprises

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A. Inward looking strategy
Inward looking strategy is also called import substitution
strategy. It has both economic and political
implications.
Definition:
• Import substitution is a policy that agrees with export
pessimism. The strategy requires government
information to safeguard local manufacturers, and
assume that markets would now work effectively for
rapid progress. It refers to developing domestic
industries to replace imports and so improves the
balance of payments.

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Inward looking strategy…
• Imports are substituted if the domestic production of
previously imported goods covers the additional
demand caused by the economic development
process and thus, the relative share of imports in the
domestic supply decreases (Hemmer, 1988, S. 527f).
• An attempt to replace imported manufactured
consumer goods with domestic sources of
production and supply
• The principle of inward-looking is national self-
sufficiency (autarky) & is associated with
independence from the international trade, albeit at
some cost in terms of efficiency in production.

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Weaknesses of Inward looking Strategies
• However, sustained import substitution can be damaging
– May result in inefficient allocation of resource use and
large loss in economic development, i.e., establishment
of high cost, inefficient local industries
– Because of small market in a small country, industries
operate a less than optimal capacity (inefficient).
– Tariffs and quotas to protect against imports force
consumers to pay a higher price for the product.
– Risk of creating domestic monopolies
– Foreign exchange argument
• import of essential goods (investments, intermediate
products, may increase with increasing economic
development
• Loss of technological advantage of late comers

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B. Outward Looking Development Strategies
Ground for the of market or trade is the existence
differences in resource endowment and technology
among individuals, regions and countries. So one
cannot produce everything he/she needs => exchange
• International trade is necessary:
– to get those goods that the country cannot or can
only produce at relatively high costs (argument of
comparative costs).
– To pay for imports, goods must be exported (foreign
exchange argument).
• The root for international trade is the theory of
comparative advantage.

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Problems with outward-looking
Export of primary commodities has the following
critical limiting factors:
Demand side problems:
Low per capita elasticity of demand for agricultural
food stuffs and raw materials (<0.5)
Low price elasticity of demand for the primary
goods
Low or no population growth in DC (importers)
Development of synthetic substitutes

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• Supply side Problems: Structural rigidity
– Limited resource, poor climate, bad soils, obsolete
rural institutions, poor social and economic structure.
– Hence, whatever, demand situation is in the world
market, there will be little possibility export
expansion
– Success in promotion of export is possible only
through restructuring social and economic aspects of
the rural of the LDC are first reorganized with the
primary objectives of providing sufficient food
• Benefits from comparative advantage could be exploited
If LDCs cooperate with one another, and being assisted
by the DCs for better access to markets of developed
countries (?????)

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Problems of Outward Looking…
Other problems:
– Worsening real exchange relations (terms of trade) b/c
of inelastic supply and demand.
– Severe variability in export revenues because of short-
run price instability resulted from inelastic demand for
primary products; and inelastic supply (because of
heavily weather dependence)
– Poor competitiveness of products of LDC because of:
• Inefficiency and low productivity in production
• Imperfections in the operation of factor and
product markets that leads to technological
fossilization
• Weak port management & difficult bureaucratic
administration
– infant industry argument

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Problems with outward-looking…
• Protection by industrialized countries
– subsidization of textiles, agriculture
– tariffs on imports from less developed countries
– non-tariff barriers
– tariff escalation (Very high tax for processed goods,
and low tax for unprocessed goods)
• Increasing private and social disparities (e.g., increase
unemployment Vs. increasing benefits of capitalists)

47. Thanks
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