Lecture 1 of Eco 317
J.D. Han at King’s
Growth Theories
“Frame of Reference”
• General Neo-Classcial Model
Harrod-Domar Model
Solow Model
• Endogenous Growth Model
- Human Capital
- Others
• Lewis Model
• Rostow Model
Neo-Classical Economics
• Microeconomics that you have learned
• Aggregate Demand does not matter for longrun growth of income
• Macroeconomic Policies of Government
(controlling Money Supply, Government
Expenditures )do not matter for Y in the longrun – “You cannot pull yourself up by your own bootstrap”
1. Neo-classical Mode = Supply
Side Economics
• Economic growth
= Growth of Income
= Growth of aggregate output comes
from
an increase in labour L;
an increas in capital K; and/or
improvement of technology T
In General
• ‘production function’
Y = f (K, L; T)
• Growth function
dY = f (dK, dL; dT)
Specific Formula of Production
Function
Most Widely Used Production Fn is
• “Cobb-Douglas Production Function”:
Y=A K
a
L
1-a
, and a<1
*Realistic and Convenient Features of C-D function:
Diminishing Marginal Return
Constant Return to Scale
*Why are the two features
realistic in Economics?
• Diminishing Marginal Returns(DMR)
eg) Y = F(K,L )
10 = F(5, 5)
13 = F(10, 5)
Decreasing Marginal Productivity of Capital or Labor
dY/dK = MPk, d MPk/ dk <0 or dY2/d2K <0
dY/dL = MPL, d MPL / dL <0
• Constant Return to Scale (CRS)
If Y = F (K, L) is true, Y = F (2K, 2L) = 2 F (K, L) is attainable.
You do not have to take DRS 1.5 Y = F (2K, 2L)
**Diminishing Marginal Returns
as a Fact of Life
• Biological growth- “S curve”(upper part)
Stages of Acceleration (Youth) and Deceleration (Maturity)
Convergence
• Production Function
Stages of Increasing Marginal Return and Decreasing Marginal Return
inflection point between IMR and DMR
Why is IMR no substantive issue?
• Returns to Education/Efforts
2. Harrod-Domar Model
Income Growth Rate = Saving Rate x
Efficiency of Capital
dY/Y = S/Y x
dY/dK
( as S = I = dK )
=
Saving Ratio x Marginal Product of Capital
2. Harrod-Domar Model
Income Growth Rate = Saving Rate x Efficiency
of Capital
dY/Y = dY/dK x
dK/Y
( as S = I = dK )
= dY/dK x S/Y
=
Marginal Product(ivity) of Capital x Savings Ratio
=
=
S/Y
dK/dY
Average Propensity to Save
Incremetal Capital Output Requirement
• In general, eventually, the more amount
of capital, the Marginal Productivity of
capital decreases – “Convergence”
Recall: In the latter part of the S curve, the MP of capital is a
decreasing function of capital –“Decreasing Marginal Returns” or “Law
of Diminishing Marginal Return”
This happens as the size of capital grows in the natural course of
economic growth.
• It is a formidable task to keep the
weighted average Marginal Product of
Capital constant or even Increasing for
the entire economy.
Implications of the H-D model
-The key to economic growth is to expand the le
vel of investment: capital accumulation or
‘Mobilization of capital’

-Equally important is the productivity of capital:
the higher the marginal product(ivity) of capital,
the better, or the lower the required incremental
capital-output ratio, the better.
Limitation of the Harrod-Domar
Model
• difficult to stimulate the level of domestic savings
particularly in the case of developing countries
• One way of supplementing the low domestic savings
would be foreign savings/investment:
• However, borrowing from overseas causes debt
repayment problems later.
• The law of diminishing returns would suggest that as
investment increases the marginal productivity of the
capital will diminish, and the capital to output ratio rise.
Fighting this natural law is a formidable task.
• In a word, the model does not give any easy recipe
for a success of economic development while it can
explain the surface of the given economic growth.
How to enhance Efficiency of Capital:
Higher MP of Capital, or lower ICOR
• 1) Through Technological advances or
Technical innovations –
This can happen to any economic system: Market(economy) can
take care of this while government may promote it too.
• 2) Though resource allocation by ‘visible
hands’, government, channeling capital into
‘efficient areas’ –
- A specific Economic System/Institution
key words) Centrally planned economy; Economic Planning;
Resource Allocation Planning; Industrial Policy; Promotion of
National Strategic Industries; Key Industry
* Technical Innovation
Illusive
Difficult to measure
Hard to explain causes and impacts
- Refer to “Growth Accounting” later.
*To spark Growth,
we may need Institutions
• Institution
(as opposed to Market Economy)
covers Government; Economic System; Value System(ethics,religion)
- Mechanism to ‘Mobilize Capital’? How
to increase Saving Rate?
- Mechanism to raise the Efficiency of
Capital?
*East Asian Government’s Role
for Promotion of Economic
Growth
• Government Policies are needed to 1)
encourage/force savings;
• 2)and/or to enhance efficiency of
capital by allocating scarce capital
primarily to strategic area of
industry.
* Case Studies of Government’s Forced
Savings and Resource Allocation
1) Successes
-Japan
by Kozo Yamamura’s paper reports that
during the take-off stage of economic
growth of Japan, the capital output ratio fell
significantly due to Innovations(?) and
Government’s Industrial Policy”
-Korea
Promotion of chae-bol(s)
Strategic industries of Ship-building, Cars, Semiconductors, IT Industries, etc.
2) Debacles
Some countries have succeeded in
mobilization of capital, but failed in the
efficient use of capital.
Stalinist Economy
North Korea
Great Leap Movement in China
3. Solow Model
1) Per-capital Income
• Production function: Y = F(K, L)
• In “per worker” terms: y = f(k)
• Relationship between variables:
Y
y 
L
K
k 
L
From the above we can get:
• Per-person or per-capita income level
(y) depends on each worker’s capital
equipment(k).
• y=f(k) shows DMR.
Can you draw the graph with y and k?
– Growth rate is measured by the slope of the
tangent line of the y or f(k) curve.
– Growth rate decreases as the per-capita capital
stock rises. It is true for all countries“Convergence”
– Countries that start further away from the steady
state grow faster
2. Actual Supply of Capital
Assume FIXED SAVINGS RATE or APS: s
=S/N/Y/N = savings /income
• Given an income of y
– Actual savings= s · y = s f(k)
EXAMPLE
• Savings rate of 40%
– s = .4 (you save a fraction of your
income)
Can you draw the actual savings curve
in the previous graph you have drawn?
3. Required Capital for Just Keep-Up
Minimum Capital Requirement to just keep up for
each work is proportional to population growth
rate(n) and capital depreciation rate(d)
Minimumk  (d  n)k
*if you do not replenish the economy with the minimum
requirement of capital, then the level of capital and thus
the level of production or income fall.
• Example)
• Y = 100; L = 20; K = 10
y = Y/L = 5
k = K/L = 10/20 = 0.5
n = 3% ; d  5%
Then you need 8% of capital every year to keep
constant each worker’s capital equipment.
4. Equilibrium or Not
• The Change in capital per worker is the
actual supply of capital over the
minimum required capital
k  s  y  (d  n) k
k  s  f ( k )  (d  n) k
We may call this net investment.
• Thus:
– If k > 0: economy accumulates capital per
worker
– If k < 0: economy reduces capital per
worker
– If k = 0: constant capital per worker:
steady state
Graphically
f(k)
(d+n)k
k < 0
s f(k)
k > 0
k0
k*
k
• Steady-state Per-capita Income or y* =
Y/N is determined where s f(k*) =
(d+n)k*.
Implications of the model
• The economy converges, over time, to
its steady state.
– If the economy starts BELOW the steady
state, it accumulates capital until it reaches
the steady state.
– If the economy starts ABOVE the steady
state, it reduces capital until it reaches the
steady state.
• Growth rates
– Capital per worker grows at rate 0
– Output per worker grows at rate 0
– Total capital: K = k · L grows at rate n
– Total output: Y = y · L grows at rate n
Comparative statistics
Parameters of the model: s, n, d
Predictions of the model:
• In steady state:
– Higher savings rate implies higher income per worker
– Higher population growth implies lower income per
worker
Savings rate and growth
(d+n)k
s2f(k)
s1f(k)
kss
kss2
k
• Note that an increase in savings rate do
increase the level of income, but not
the rate of growth of income.
Population growth rate and
growth
(d+n2)k
(d+n1)k
sf(k)
kss2
kss
k
Technical Innovations
• How is technical innovation different for the y curve
from an increase in savings rate?
-answer: In the case of technical innovation, the whole
y curve goes up; the level of equilibrium y goes up
and the rate of an increase in y goes up for a given
level of y. So in the end, the rate of economic growth
does not fall; a long-term sustainted economic
growth(rates)
In the case of an increase in savings rate, y goes up
but the rate of a change in y falls.
• Continuous Technical Innovations
4. Lewis Model:
Dual Sector Model of Economic Growth
• many LDCs had dual economies with a
traditional agricultural sector and a modern
industrial sector
• Traditional Sector has too much labor at
subsistence level
MPlabour = 0; Y = C + S + T = C + I + G
• Modern Sector absorbs labor and becomes
the source of economic surplus or savings
How does the Mechanism work?
• The lack of development was due to a lack of
savings and investment. The key to development was
to increase savings and investment.
• Lewis saw the existence of the modern industrial
sector as essential if this was to happen. A growing
industrial sector requiring labour provided the incomes
that could be spent and saved. This would in itself
generate demand and also provide funds for
investment. Income generated by the industrial sector
was trickling down throughout the economy.
• Urban migration from the poor rural areas to the
relatively richer industrial urban areas gave workers
the opportunities to earn higher incomes and crucially
save more providing funds for entrepreneurs to
investment.
Policy Implications of Lewis model
• Induced Displacement of Population from
Rural to Urban Sector
• Government may use push and pull factors
using Institutions or System
-‘Vanity Effect’ as a magnet:
Glamorous/modernized Urban Sector versus
Backward/‘Suppressed’ Rural Area
-Income Inequality is as a ‘magnet’
Lewis Model is Unbalanced Economic Growth Strategy
(不均衡的经济发展战略）
• This is a practical strategy.
• Let’s reflect on side-effect/problems
-Sustainability in the long-run: Ravaging impacts of labor saving
technology; How much and how long is the modern sector
absorb the surplus labor? What will happen to no-longerneeded surplus labor?
-Inequality between agricultural – industrial sectors
Income Inequality; Urbanization issues
- Urban/Modern Sector may not Save but Spend: Urban
‘Consumerism’
- Rural-Urban Migration is larger than what the urban sector can
absorb: Rural Poverty simply becomes Urban Poverty
Case Studies: Casual Analysis
• England in 18th Century
Enclosure Movement
• U.S. in 19th century
Slave-Emancipation
• Japan
• Korea in the 1970s and the 1980s
*New Village Movement (Sae-Ma-Eul-Un-Dong)
• Taiwan (part of China)
• China
*Quantitative Analysis:
Income (Distribution) Inequality and Economic
Growth
• Income Inequality is measured by Gini-Coefficient
• Some international comparisons argue as economy
grows, Gini Coefficient generally rises first and then
fall
• It is in line with Lewis’ theory: Income inequality is not
only inevitable, but also necessary for economic
growth
- Case studies of Korea, Japan, and China
(presentation)
5. Rostow's Modelthe Stages of Economic Development
.
• In 1960, the American Economic
Historian, WW Rostow suggested that
countries passed through five stages of
economic development
•
Stage 1 Traditional Society
-dominated by subsistence (defined as no economic surplus, meaning output being consumed by producers
rather than traded);
-trade being carried out by barter, meaning goods being exchanged directly for other goods;
-Agriculture being the most important industry;Production being labor intensive using only limited
quantities of capital.
•
Stage 2 Transitional Stage (the preconditions for takeoff)
-Increased specialization starting to generate surpluses for trading.
-an emergence of a transport infrastructure to support trade; External trade also occurs concentrating on
primary products; Entrepreneurs emerge
-savings and investment grow.
•
Stage 3 Take Off
-Rapid Industrialization or Industrial Revolution
- Growth concentrated in a few regions of the country and in one or two manufacturing industries.
- The level of investment reaches over 10% of GNP.
- The economic transitions are accompanied by the evolution of new political and social institutions that
support the industrialization.
- The growth is self-sustaining: investment leads to increasing incomes in turn generating more savings to
finance further investment.
•
Stage 4 Drive to Maturity
-Industrial Diversification; producing a wide range of goods and services; reliance on exports and imports
may start decreasing
•
Stage 5 High Mass Consumption
- Mass Consumption（大众消费）; Domestic Aggregate Demand is the major determinant of Business
(Cycles)
- Consumer durable industries; Service sector
Limitations
• Deterministic Path for All?
Rostow predict that every economy is going through the same
stage.
However, some economies are stuck in the first stage forever
while other economies “take off”.
-leaving a room for ‘cultural explanation’
• It does not set down the detailed nature of the pre-conditions
for growth; What sparks the take-off?
-Exogenous Shocks as a Catalyst for Great Transformation?
• It is not very helpful as a policy prescription. Perhaps its main
use is to highlight the need for investment.
* Explaining the fast is always easier than Predicting
the future
Major Contribution of Rostow’ Model
Emphasis of ‘Take-Off’
-Economic Development is
not a continuous process;
-There should be
some Event for Great Transformation.
*Case Studies: Catalyst for Take off
Catalysis for Take Off= Exogenous Shocks
Japan
Meiji Revolution; Korean War
Korea
President Park, Jeong Hee; Vietnam War
China
Deng Xiao Ping’s Reform
Jiang Ze Min’s “Southern Journey(Nan Xun)”
Iraq War?
6. Endogenous Growth Theory
-Excellent Summary http://www.ncl.ac.uk/ncihe/r8_117.htm
All seem to converge on the importance of Human capital->
education -> knowledge
-Implications:
“Institutions Matter” : only institution guarantees repetitive human
behaviours.
-Criticism:
Not so specific about the fundamental institutions that make
differences across countries
Analytical focus is still mainly on human capital(individual) rather
than on institution(collective and social).
How can we attempt to explain a deeper factor –institutional
difference across countries?
*Value System as a ‘Foundation’ Institution for Economic
Growth:
• Max Weber arguned that
“Protestant Work Ethic” sanctioned
hard work, frugality and wise
investment.
• Rodney Stark is one of the most
highly regarded sociology of religion
scholars alive today. He recently
published The Victory of Reason:
How Christianity Led to Freedom,
Capitalism, and Western Success.
• Professor Tu Wei-Ming at Harvard
University said that NeoConfucianism of the Far East is
similar to protestant ethic.
- refer to the essence of his idea