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Copyright © 2020, 2015 Michael P. Todaro and Stephen C. Smith
Economic Development
Thirteenth Edition
Chapter 3
Classic Theories of
Economic Growth and
Development

3.1 Classic Theories of Economic Development:
Four Approaches
• Linear stages of growth model
• Theories and patterns of structural change
• International-dependence “revolution”
• Neoclassical, free market “counterrevolution”

3.2 Development as Growth and Linear-
Stages Theories
• A Classic Statement: Rostow’s Stages of Growth
• Harrod-Domar Growth Model
• (Also referred to as the AK model, because the
capital stock is multiplied by a constant factor,
sometimes called “A”)

Simplified Harrod-Domar Growth Model
• Sometimes called the “AK model”
• Harrod-Domar Growth Model Derivation
• Y = (1/c)*K
• Linear relationship assumed, so,
• ΔY = (1/c)*ΔK; or,
• ΔY = SNet/c
• Dividing by Y: ΔY/Y = (SNet/Y)/c; so,
• Growth = (sNet)/c; that is,
• Growth = Net savings rate/ICOR

The Harrod-Domar Model – Simplified
Version, Alternate Derivation

The Harrod-Domar Model – Simplified Version

• Equation 3.7 is also often expressed in terms of gross savings, in
which case the growth rate is given by
(3.7’)
where δ is the rate of capital depreciation
The derivation follows in the next two slides:
The Harrod-Domar Model – Incorporating
Capital Depreciation

And,
Harrod-Domar (or “AK”) Model: Derivation of
disaggregated treatment of depreciation

IG
º SG
( )
So,
Harrod-Domar (or “AK”) Model: Derivation of
disaggregated treatment of depreciation
(Continued)

Illustrative Exercise on Growth Potential
‘Back-of-the-envelope’ calculations with the H-D
(or AK) growth model.
Suppose sG = .125, =.04, c =2.5
gTOT
=
.125
2.5
-.04 = .01
Then,
But if sG = .175,  =.03, c =2.5
gTOT
=
.175
2.5
-.03 = .04
Then,

Illustrative Exercise: Growth Targets
• Suppose a country has a gross savings rate of 20%, a depreciation
rate of 3%, and an lCOR of 2.5
• Using the Harrod-Domar growth model, find the implied rate of
growth of total GDP in the country
• Answer: Growth = .2/2.5 - .03 = .05 (i.e., 5%)
• How much would the rate of savings have to increase to raise the
growth rate of total GDP to 9% (a target discussed in India)?
• Answer: Now the savings rate is your unknown.
• Growth = s/2.5 - .03 = .09 , so s/2.5 = .12 or s = .3 (that is, up 10
percentage points from 20% to 30%)
• Targeted growth rates and required savings are considered further
in Chapter 11

Criticisms of the Stages Model
• Necessary versus sufficient conditions

3.3 Structural-Change Models
• The Lewis two-sector model

Figure 3.1
The Lewis Model of Modern-Sector Growth in a
Two-Sector Surplus-Labour Economy

Criticisms of the Lewis Model
• Rate of labor transfer and employment creation may
not be proportional to rate of modern-sector capital
accumulation
• Questionable assumption of surplus labor in rural
areas and full employment in urban
• Questionable assumption of diminishing returns in
modern industrial sector, at least in some cases
• Institutional factors have a small (if any) role in this
approach

Figure 3.2
The Lewis Model Modified by Laborsaving
Capital Accumulation: Employment Implications

Empirical Patterns of Development -
Examples
• Some processes are very typical but not universal; so
these are often referred to as “stylized facts”:
‒ Switch from agriculture to industry (and services)
‒ Rural-urban migration and urbanization
‒ Steady accumulation of physical and human
capital
‒ Population growth first increasing and then
decreasing with decline in family size

3.4 The International-Dependence “Revolution”
• The neocolonial dependence model
– Legacy of colonialism, Unequal power, Core-periphery
• The false-paradigm model
– Pitfalls of using “expert” foreign advisors who misapply
developed-country models
• The dualistic-development thesis
– Superior and inferior elements can coexist; Prebisch-Singer
Hypothesis
• Criticisms and limitations
– Accumulating counterexamples; the framework does little
to show how to achieve development in a positive sense

3.5 The Neoclassical Counterrevolution, or
“Market Fundamentalism”
• Challenging the Statist Model: Free Markets, Public Choice, and
Market-Friendly Approaches
– Free market approach
– Public choice approach
– Market-friendly approach
• Main Arguments
– Denies efficiency of intervention
– Points up state owned enterprise failures
– Stresses government failures
– Urges reliance upon the “magic of the marketplace”
– Associated with a different (Solow) formal model of growth:

3.5 The Neoclassical Counterrevolution, or
“Market Fundamentalism”
• Associated with a different (Solow) formal model of
growth
‒ Traditional neoclassical growth theory (Solow model)
‒ Includes labor as a separate input
‒ Shows that with diminishing returns, growth cannot be
sustained by capital accumulation alone
‒ Adds separate, explicit accounting of the role of
technological change
‒ The model details are presented in Appendix 3.2

From the Appendix:
Interpreting the Solow equilibrium equation
• Interpreting of the Solow Equilibrium in Equation (A3.2.5) and
the preceding figure (A3.2.1),
• sf(k*) is savings per worker, and is just equal to the sum of:
• δk*, the amount of capital (per worker) needed to replace
depreciating capital, and,
• nk*, the amount of capital (per worker) that needs to be added
due to population (labor force) growth.
sf (k*) = (d +n)k * (A3.2.5)

Contributions and Limitations of the
Four Schools
• Capital Fundamentalism
– Points up importance of investment, and of efficiency of capital allocation
– Investment may be necessary but is not sufficient. Broader context matters
• Structural/Empirical Patterns of Development
– Careful empirical evidence can remove theories from contention
– But, still need theory to interpret data, avoid cart-before-horse policies
• Dependency
– Existing international relations/ trade/ investment can place constraints on pattern
of development
– But, growing number of counter-examples of stronger versions of dependency
theory; good performance of “globally” integrated countries
• Market Fundamentalism
– Governments fail (e.g. in SOEs, planning) and we must account for this
– But, markets also fail in developing countries; the East Asia experience shows that
government role can be constructive

3.6 Classic Theories of Development:
Reconciling the Differences
• Governments do fail, but so do markets; a balance is
needed
• Must attend to institutional and political realities in
developing world
• Development economics has no universally accepted
paradigm
• Insights and understandings are continually evolving
• Each theory has some strengths and some
weaknesses

Appendix 3.1: Components of Economic
Growth
• Capital Accumulation, investments in physical and
human capital
– Increase capital stock
• Growth in population and labor force
• Technological progress
– Neutral, labor/capital-saving, labor/capital augmenting

Figure A3.1.1
Effect of Increases in Physical and Human
Resources on the Production Possibility Frontier

Figure A3.1.2
Effect of Growth of Capital Stock and Land on
the Production Possibility Frontier

Figure A3.1.3
Effect of Technological Change in the Agricultural
Sector on the Production Possibility Frontier

Figure A3.1.4
Effect of Technological Change in the Industrial
Sector on the Production Possibility Frontier

Appendix 3.2: The Solow Neoclassical
Growth Model
• Notation
‒ f(k*) is the production function relating capital per worker
to output; the function has diminishing returns; s is the
savings rate; So,
‒ sf(k*) is savings per worker;
‒ δ is the rate of capital depreciation;
‒ n is the rate of growth of the labor force;
‒ Savings per worker sf(k*) is just equal to the sum of:
‒ δk*: the amount of capital (per worker) needed to replace
depreciating capital, and,
‒ nk*: the amount of capital (per worker) that needs to be
added - due labor force growth – to keep capital per
worker from falling

Appendix 3.2 The Solow Neoclassical
Growth Model: The Solow Equation
Dk = sf (k)-(d +n)k (A3.2.4)
Equilibrium is found where Δk = 0, as in equation A3.2.5 on the next slide.
Note: We can also use equation A3.2.4 above to provide a “heuristic” proof
by contradiction – making use of Figure A3.2.1 – to see that the equilibrium
must be where Δk = 0: otherwise k is growing to the left of k* and shrinking
if to the right of k*.

Equilibrium Condition in the Solow
Neoclassical Growth Model
Again:
s is the savings rate;
f(k*) is the production function relating capital per worker to output; the
function has diminishing returns; So,
sf(k*) is savings per worker
δ is the rate of capital depreciation; n is the rate of growth of the labor force;
Savings per worker sf(k*) is just equal to the sum of:
δk*: the amount of capital (per worker) needed to replace depreciating
capital, and,
nk*: the amount of capital (per worker) that needs to be added - due labor
force growth – to keep capital per worker from falling
Details of the model are examined in Appendix 3.2

Figure A3.2.1
Equilibrium in the Solow Growth Model

Figure A3.2.2
The Long-Run Effect of Changing the Saving
Rate in the Solow Model

The Solow Equation:
A Heuristic Numerical Example
• Note: This heuristic example addresses the capital per worker component,
not production (output per worker)
• Income depends upon capital (K) per worker (L): i.e., K/L
• Before K/L can grow we must invest to make allowance for a) depreciation;
and b) growth of the labor force L
• To illustrate, consider a 10-worker economy growing to 12 workers;
initially K/L = 2; and depreciation = .05
• To increase K/L to 2.5 we must invest:
‒ 1 unit of K for depreciation allowance: (20)*(.05) = 1
‒ 4 units of K for “capital widening” (equipping the new workers with the
same capital as the existing workers)
‒ 6 units of K for “capital deepening,” to finally increase the K/L ratio, up
to where each worker has 2.5 units of capital to work with
‒ Overall, the K stock grows from 20 to 30, i.e., 30/12 = 2.5

Supplementary Note: The Role of
Technology*
• If there is technological progress, income per worker can
increase proportionately
• Think of K in the Solow production function as multiplied by a
constant, A, “AK”:
• So far we have implicitly set A to 1; but it can grow over time,
representing productivity growth
• In equilibrium, if the “effective workforce” increases at rate l,
then the Solow equilibrium is:
• sf(k*) = ( + n + l)k*
• The “effective workforce” then grows faster than the (actual)
workforce, corresponding to an increase in output per worker
*This slide addresses a topic not explicitly explained or currently formalized in the text

Concepts for Review
• Autarky
• Average product
• Capital-labor ratio
• Capital-output ratio
• Center
• Closed economy
• Comprador groups
• Dependence
• Dominance
• Dualism
• False-paradigm model
• Free market
• Free-market analysis
• Harrod-Domar growth
model
• Lewis two-sector model
• Marginal product
• Market failure

Concepts for Review (Continued)
• Market-friendly approach
• Necessary condition
• Neoclassical counterrevolution
• Neocolonial dependence
model
• Net savings ratio
• New political economy
approach
• Open economy
• Patterns-of-development
analysis
• Periphery
• Production function
• Public-choice theory
• Self-sustaining growth
• Solow neoclassical growth model
• Stages-of-growth model of
development
• Structural-change theory
• Structural transformation
• Sufficient condition
• Surplus labor
• Underdevelopment

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