1

Fall 2009

Economics of Development

Throughout the course, appendices discuss some

technical topics. You are not required to read the
appendices, although you will benefit from reading
them.

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1. Lectures

3:00-5:45pm, Fridays (Room 209)

2. Office hours

Immediately before or after class on Friday or by

appointment (kchu@khu.ac.kr)

3. Broad objectives of the course

Exploration of the causes and consequences of

economic development

Use of models of neoclassical and new institutional

economics to understand the process of economic
development

Discussion of selected country experiences in selected

aspects of economic development

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4. Key topics

Economic growth and economic development:

processes and underlying factors

Role of institutions = providing rules of the game for

economic agents

5. Textbooks

Michael P. Todaro and Stephen C. Smith (2006),

Economic Development, 9th ed., Addison-Wesley

Statistical yearbooks of the IMF, UNDP, World Bank,

and World Economic Forum.1

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In addition, you may find the following books useful: (1) Meier, Gerald
M., and James E. Rauch (2000), Leading Issues in Economic Development,
7th ed., Oxford University Press and (2) Charles I. Jones, Introduction to
Economic Growth, 2nd ed., W. W. Norton. Please also check the syllabus
for useful book chapters and papers.

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6. Grades

Attendants 5%
A quiz (before the mid-term) 10%
Mid-term 35%
Paper (5%) and presentation (5%) 10%
Final 40%

7. Weekly topics

(1) Economic Development

i. Ultimate and proximate causes of economic

development
ii. Relationship between growth, development,
and poverty and prosperity.

(2) Theories of Economic Growth and

Development

i. Basic mathematical and statistical tools

ii. Growth models and broader approaches to
studying economic growth and development

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(3) Economic Development and Institutions

i. Relationship between institutions and

economic development
ii. Simple game models and transaction
institutions.

Quiz

(4) Institutions and Values

i. Values underlying institutions

ii. Societal values, particularly collectivist values,
and institutions.

(5) Human Resources

i. Human resources economics

ii. Relationship between population, labor force,
and growth
iii. Role of human capital formation in economic
development

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(6) Labor Market Institutions

i. Labor market institutions

ii. Their role in development.

(7) Capital and Technology

i. Role of capital and technology for

development
ii. Schumpeterian model of development and the
role of innovation.

(8) Mid-term

(9) Institutions for Technological Innovation and

Capital Formation

i. Capital market institutions

ii. Institutional requirement for technological
innovations

(10) Role of Government

i. Role of government in a market economy

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ii. Implications for promoting economic

development

(11) Income Distribution and Poverty

i. Relationship between income distribution and

development
ii. Economic development and poverty

(12) International Dimensions of Economic

Development

i. Trade and international capital movements

ii. Their role for development.

(13-14) Selected additional topics

A selection of one or two, time permitting, from the

following topics:

i. Informal sector and micro-credits

ii. Grameen Bank: Bangladesh
iii. East Asian growth: miracle or myth?

(15) Presentation of the students‘ papers

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(16) Final exam

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1. Economic Development

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1.1. Economic growth and development

1.1.1. Human history and economic development

(1) Limited scope of human prosperity

Throughout human history, economic growth and

development have been very recent phenomena.

Throughout the world, prosperity is geographically

very limited.

Douglass North (1994, p. 364):

―Throughout most of history and for most societies in

the past and present, economic performance has been
anything but satisfactory…

―Human beings have, by trial and error, learned how

to make economies perform better;

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but not only has this learning taken ten millennia …

the radical improvement in economic performance…
is a modern phenomenon of a past few centuries.‖

(2) Civilization and economic development

North has observed that civilization is a very recent

phenomenon of human existence.

i. BC 4-5,000,000 Human race emerged.

ii. BC 8000 Civilization (agricultural
society, settled life) began.

A comparison of human history to one day is as

follows:

i. If the era of human

existence 24 hours
ii. the era of civilization
(10,000 years) 3~4 minutes

Most of the human civilization era was marked by

economic stagnation.

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i. From the beginning of human civilization—

1750: economic stagnation
ii. 1750 to now: limited economic growth only in
industrial countries

A comparison of the civilization era to one day will be

as follows:

i. If the civilization era = 24 hours,

ii. the era of economic growth = 35 minutes.

1.1.2. Economic growth and economic development:

meanings

(1) Economic growth

Economic growth means ―sustained growth of per

capita output and income‖ of a society.

Output and income are measured by GDP or GNP

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(2) Economic development

Economic development is conceptually broader than

economic growth and often means improvements of
social indicators, such as

i. life expectancy
ii. educational attainment
iii. living standards

In a broader conceptualization, economic

development means

i. economic, social, and political development

ii. advancement in economic, social, and political
freedom and opportunities

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Todaro and Smith (2006), p. 15-18.

―In strictly economic terms, development has

traditionally meant the capacity of a national
economy, whose initial economic condition has been
more or less static for a long time, to generate and
sustain an annual increase in its gross national income
(GNI) at rates of 5% to 7% or more.

―A common alternative economic index of

development has been the use of rates o growth of
income per capita to take into account the ability of a
nation to expand its output at a rate faster than the
growth rate of its population….

‖… Development must therefore be conceived of as a

multidimensional process involving major changes in
social structures, popular attitudes, and national
institutions, as well as the acceleration of economic
growth, the reduction of inequality, and the
eradication of poverty…

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1.2. Other dimensions of economic

development: improvements in a
society‘s economic achievement

1.2.1. Economic development, environment, and

human learning

(1) Economic development as a learning process

Economic development is a human learning process

through which humans achieved greater control of
their environment.

In this process, they established institutions (rules of

the game) to structure their interactions.

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North (1994, p. 364):

―The key to the foregoing story [improvement in

economic performance through time] is the kind of
learning that the individuals in a society acquired
through time…‖

―Collective learning consists of those experiences that

have passed the slow test of time and are embodied in
our language, institutions, technology, and ways of
doing things….‖

(2) Importance of incentive and beliefs for

economic development

Efficient institutions provide efficient incentive for

human actions.

Underlying efficient institutions are beliefs that

nurture such institutions.

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North (1994, p. 364):

―Incentives embodied in belief systems as expressed in

institutions determine economic performance through
time…‖

1.2.2. Lucas‘ questions about development

Robert Lucas looked at the data below and

formulated the problems as follows:

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GDP per capita

----------------------------------------------------------------------------
Cumulative
1990 dollars growth, %
-------------------
1950 1992
------------------------------------
US 9,570 21,560 125
Bangladesh 550 720 31
China 610 3,100 405
Egypt 520 1,930 273
India 600 1,350 126
Indonesia 870 2,750 215
South Korea 850 10,010 1,042
Taiwan 920 11,590 1,157
Zaire 640 410 -36
---------------------------------------------------------------------
Source: Lucas (1988), ―On the Mechanics of Economic
Development,‖ Journal of Monetary Economics.

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Lucas (1988)2:

―I do not see how one can look at figures like these

without seeing them as possibilities. Is there some
action a government of India could take that would
lead the Indian economy to growth like Indonesia‘s or
Egypt‘s?‖

―If so, what, exactly? If not, what is it about the

‗nature of India‘ that makes it so? The consequences
for human welfare involved in questions like these are
simply staggering: Once one starts to think about
them, it is hard to think anything else.‖

2
Quoted in Dornbusch, Rudi, Stanley Fischer, and Richard Startz (2001),
Macroeconomics, The McGraw-Hill.

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1.3. Basic concepts

1.3.1. Different GDPs

(1) Potential GDP vs. actual GDP

Q = F(K, hL)
QC = F(KS, hSLF)

Q = actual GDP
QC = potential GDP
L = employed labor service
K = utilized capital service
h = average human capital of employed
workers
LF = labor force
KS, hS = physical, (per worker) human capital
stocks

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(2) Nominal GDP vs. real GDP

Y = PQ
= nominal GDP
P = GDP deflator
Q = real GDP

1.3.2. International comparison of GDPs

(1) GDP expressed in dollars by using a market

exchange rate

Two measures of GDP in a domestic currency may be

distinguished:

i. nominal GDP Y
ii. real (at constant prices) GDP Q = Y/P

For international comparison, GDPs are measured in

dollars.

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(2) Two measures of GDP in dollars

i. One measure of GDP in dollars is derived by

converting GDP in a domestic currency to a
dollar measures by using an exchange rate
(usually the market rate) between the
domestic currency and the dollar.
ii. Another, purchasing power parity (PPP) GDP,
is measured by valuing, for each country, the
quantities of the categories of values added on
the basis of international prices.

(3) Illustration of GDPs: exchange rate

conversion and PPP

The following table offers numerical illustrations of

the two methods:

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International price of an apple = $0.2

----------------------------------------------------------------
GDP
in
Annual domes- Ex-
apple tic change
output & cur- PPP rate
Country price rency GDP GDP
------------------------------------------------------------------
A 100 500 $20 $20
5 som som
Exchange
rate = 25 som/$

B 100 1,000 $20 $20

10 lira lira
Exchange
rate = 50 lira/$

C 100 100 $20 $20

1 yuan yuan
Exchange
Rate = 5 yuan/$
-------------------------------------------------------------------------

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The following table illustrates the effects of changes in

the countries‘ exchange rates.

International price of an apple = $0.2 (no change)

-------------------------------------------------------------------
GDP
in
Annual domes- Ex-
apple tic change
output & cur- PPP rate
Country price rency GDP GDP
--------------------------------------------------------------------
A 100/ 500 $20 $20
5 som som
Exch 25 som/$
rate no change

B 100 1,000 $20 from $20

10 lira lira to $10
Exch from 50 lira/$
rate to 100 lira/$

C 100 100 $20 from $20

1 yuan yuan to $40
Exch from 5 yuan/$
rate to 2.5 yuan/$
----------------------------------------------------------------------

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1.3.3. International comparison of living standards

(1) Gross domestic product (GDP) and gross

national income (GNI)

Gross national income (GNI) is GDP adjusted for

changes in the international terms of trade, which is
the ratio of the average export price to the average
import price of a country.

Two methods (exchange rate and PPP) may yield

different measures of income.

(2) Two measures of GNI

Following are statistical data on per capita (PC)

GNIs:

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Per capita incomes: exchange rate conversion vs.

PPP (2004 US$)
-------------------------------------------------------------------------------

Countries PC GNI PC PPP GNI

-------------------------------------------------------------------------------
Korea 13,980 20,400

Ethiopia 110 810

Burundi 90 660
Kenya 460 1,050
India 620 3,100

Singapore 24,220 26,590

Hong Kong, SAR 26,810 31,510
Sweden 35,770 29,770
Japan 37,180 30,030
U.S. 41,400 39,710
Norway 52,030 38,550
---------------------------------------------------------------------
World Bank, World Development Indicators, 2006
SAR = special administrative region.

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1.4. Faces of poverty

1.4.1. Absolute poverty

Of the 6 billion people of the world, the following

survive with incomes below $1 a day.

----------------------------------------------------------------------
1987 1998
----------------------------------------------------------------------
Total 1,170 1,168

East Asia and the Pacific 420 278

(other than China) (110) (60)
South Asia 470 520
Latin America 60 80
Sub-Saharan Africa 220 290
-----------------------------------------------------------------
World Bank, World Development Report 2003.

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1.4.2. Cross-country income distribution (2004)

Only 14 of the world‘s countries have achieved

income levels exceeding $30,000/year.

In more than 60 countries, the per capita income level

is below $5,000.

Distribution of countries by per capita income

-----------------------------------------------------------------------
Number of
Per capita GDP (US$) countries
-----------------------------------------------------------------------
-1,000 14
1,000-4,000 47
4,000-10,000 54
10,000-20,000 26
20,000-30,000 16
30,000- 14
Total 171
--------------------------------------------------------------------------
Compiled form UNDP, Human Development Report 2006.

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1.4.3. Meaning of economic affluence

What is the meaning of getting out of poverty? What

is the meaning of economic affluence. People may
have different views. Following is one of such views:3

Francis Hackett—Irish-born American writer,

literary critics, and historian:

―I believe in materialism. I believe in all the proceeds

of a healthy materialism—good cooking, dry houses,
dry feet, …

baths, electric lights, automobiles, good roads, bright

streets, long vacations away from the village pumps,
new ideas, fast horses, …, theaters, operas, …

―The man who dies without knowing these things

may be as exquisite as a saint, and as rich as a poet;
but it is in spite of, not because of, his deprivation.‖

3
As quoted in Paul Samuelson, Economics.

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1.5. Stages of economic growth

1.5.1. Extensive, intensive growth

(1) Extensive growth

Extensive growth means the growth of aggregate

output (Q), without the growth of per capita output (q
= Q/N). Therefore, this is not economic growth as
defined in the course.

At first, both aggregate output (Q) and population (N)

remain constant.

a. High death rates

b. Low productivity

Next, both N and Q growth, but q remains stagnant.

Population growth limited by food production

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(2) Intensive growth

Intensive growth means the growth of per capita

income. This is economic growth as defined in this
course.

Intensive growth arises as a country achieves

i. nation building and

ii. development of manufacturing

Productivity of society increases as a result of a large

number of small technical progresses--―the
importance of the unconspicuous.‖

1.5.2. Rostow‘s theory of stages of economic growth

American economic historian W.W. Rostow has

described that a society‘s economy goes through the
following stages of growth, with the main features of
the society‘s and its change listed for each stage:

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(1) Traditional society

i. Limited production based on pre-Newtonian

technology
ii. Pre-Newtonian attitudes toward the physical
world

(2) Satisfaction of preconditions for take-off

i. Changes in attitudes toward growth—

emergence of the realization that growth is
possible and necessary
ii. Emergence of a political coalition interested in
modernization
iii. Entrepreneurs, leading sectors (e.g., textile
industry), improved institutions (e.g., laws,
banking system)

(3) Take-off into self-sustained growth

i. Acceleration of growth
ii. Increases in savings and investments

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(4) Drive to maturity & high mass-consumption

i. Maturing of industrial structure

ii. Broad spreading of the benefits of growth

1.5.3. Growth and structural change

(1) Changes in industrial structure

Economic growth of an economy is accompanied by

broad structural changes of the society.

Historically, economic growth has led to

changes in a country‘s industrial structure:

i. Decline of primary industries and expansion

of manufacturing
ii. Underlying factors: income elasticity of
demand and progress in production
technology

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Industrial composition of values added

---------------------------------------------------------------------

Agri- Manu-
culture factures Services
--------------------------------------------------------------------------
Mozambique 26 31 43
Ethiopia 46 10 44
Tanzania 45 16 39

China 15 51 35
Korea 3 35 62

Singapore 0 35 65
Japan 1 30 68
United Kingdom 1 27 72
Denmark 2 26 71
---------------------------------------------------------------------
World Bank, World Development Report (2006).

(2) Changes in income distribution: Kuznets‘

inverted-U hypothesis

The hypothesis states that as a country grows, the

country‘s income inequality rise and falls.

How is income inequality measured?

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i. A country‘s income inequality is often

measured by a Gini coefficient, which
measures a country‘s income inequality (more
later) and whose values approaches
i1. 1 for extreme inequality and
i2. 0 for extreme equality
ii. Gini may be measured for
ii1. market incomes of households (incomes
earned (e.g., wages, interests, rents)
through market activities or
ii2. disposable incomes (i.e., market income +
income transfers received from
government – direct taxes paid to
government).

Many researchers have conducted empirical tests of

the hypothesis.

Paukert has conducted an international comparison

of Gini coefficients (1965 US$). The study shows the
following average Gini coefficients for country groups
with different average per capita incomes:

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Per capita income Average Gini coefficient

------------------------------------------------------------
less than 100 0.42
100-200 0.47
200-300 0.50  highest number
300-500 0.49
500-1000 0.44
1000-2000 0.40
2000- 0.36
-----------------------------------------------------------------

Why are market incomes are unequal in poor

countries?

i. In very poor countries, virtually all are very

poor. Incomes are fairly equal.
ii. Growth results from expanded income-
earning opportunities of a limited number of
individuals. Income become unequal.
iii. It takes time for all the members of a society
to join this process. Incomes become
relatively equal at higher income levels.

Why are disposable incomes more unequal in poor

countries than in rich countries?

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It takes time for poor countries to acquire

financial and institutional resources for
redistributive social programs.

1.5.4 Income inequality and economic growth

On one hand,

i. high-income households‘ saving rates are high,

and
ii. a high saving rate in a country tends to enable
the country to mobilize resources for
investment.

On the other hand, a high income inequality may

i. destroy social cohesion,

ii. promote political instability, and
iii. undermine the environment for productive
long-term investment.

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1.6. Broader characterization of

development

1.6.1. Two dimensions of development

There are two types of characterization of

development.

(1) Development as a ―fierce‖ process, with blood,

sweat and tears

Economic development in China and Korea may fit

this description. In these countries, government
imposed beliefs that, during the process of
development,

i. ―political freedom is a luxury‖ and

ii. ―strict discipline is required.‖

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(2) Development as a ―friendly‖ process

Sen argues that development should be a friendly

process.

1.6.2. Amartya Sen‘s characterization of

development as a friendly process

Freedom is an objective and an instrument of

development.

(1) An individual‘s capability

An individual‘s capability depends on the following

factors:

i. economic opportunities
ii. political liberties
iii. social facilities
iv. enabling conditions of good health, basic
education, and the encouragement and
cultivation of initiatives.

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(2) 5 instrumental freedoms

There are 5 freedoms as instruments

i. political freedom: opportunities to decide on

rulers and legal order
ii. economic opportunities: opportunities to use
resources for production, consumption, and
exchange
iii. social facilities: opportunities to receive
educational and medical benefit
iv. transparency: freedom to maintain clear
transaction relations
v. protective security: opportunities to be
protected by social safety nets (pensions,
unemployment benefits, social assistance)

Political freedom has enabled poor countries (e.g.,

India) to avoid famines.

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1.6.3. United Nations Development Program

(UNDP)‘s Human Development Index (HDI)

(1) Definition

An HDI is the average of

i. the per capita GDP index,

ii. educational attainment index(adult literacy +
primary, secondary, and tertiary enrolment
rate),
iii. life expectancy at birth

x index = (x – minimum x)/(maximum x –

minimum x)

(2) Economic growth and social development

Economic growth leads to improved social indicators.

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GDPs and social indicators (2004)

------------------------------------------------------------------
GDP Life Adult
per capita expectancy literacy
PPP at birth above 15
$US years %
------------------------------------------------------------------------
Korea 20,499 77.3 90.8

Norway 38,454 79.6 …

United States 39,676 77.5 …
Singapore 28,077 78.9 92.5

Sierra Leone 561 41 35.1

Niger 779 44.6 28.7
Burundi 677 44 59.3
-----------------------------------------------------------------------
UNDP, Human Development Report 2006.
… = close to 100%.

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Country groups with higher PPP GNIs, on average,

have improved social development indicators.
-------------------------------------------------------------------------------
Per capita Social
(PC) GNI development
PPP, indicators,
Popu- amount adult literacy/
lation, PC GDP life expec-
Country million growth tancy
groups persons rate% at birth (female)
2004/ 1998-2004/
2004 2003-04 2003
-----------------------------------------------------------------------
Low- 2,338 $2,260/4,4% 64%/59yrs.
income 4.4% 59yrs.

Middle- 3,006 $6,480/6.0% 90%/72yrs.

income
Lower 2,430 $5,640/6.2% 89%/72yrs.
Upper 576 $10,090/ 5.9% 93%/73yrs.

High- 1,001 $30,970/2.8% 91%/75yrs.

income
---------------------------------------------------------------------
Source: World Bank, World Development Report 2006.
Low income: $825 or less in 2004; middle income: $826-$10,065; high-
income: $10,066 or higher.

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While an increase in per capita income generally

means a high HDI, there are exceptions.

Statistics (2004)
-----------------------------------------------------------------------
Adult School Avg.
PC liter- enroll- life Avg.
PPP acy ment expec- HDI
GDP rate rate tancy or
US$% % % yrs. HDI
-------------------------------------------------------------------------
Low-income 2,297 62.3 54 58.7 0.556
Middle-income 6,756 89.9 73 70.3 0.768
High-income 31,331 99.0 … 78.8 0.942

Low HDI 1,113 57.9 46 45.8 0.427

Middle HDI 4,901 80.5 66 67.3 0.701
High HDI 26,563 … 91 78.0 0.923

Sierra Leone 561 35.1 65 41 0.335

Sri Lanka 4,390 90.7 63 74.3 0.755
China (2002) 4,580 90.9 68 70.9 0.745
(2004) 5,896 90.9 70 71.9 0.768
Brazil 8,195 88.6 86 70.8 0.792

Korea 20,499 98.0 95 77.3 0.912

--------------------------------------------------------------------
UNDP, Human Development Report (2006, 2004).

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(3) Economic growth and social development:

complementarity and trade-off

Statistics (2004)
----------------------------------------------------------------------------
Adult School Average
PC liter- enroll- life
PPP acy ment expec-
GDP rate rate tancy
US$% % % yrs. HDI
--------------------------------------------------------------------
Sri Lanka 4,390 90.7 63 74.3 0.755
Brazil 8,195 88.6 86 70.8 0.792
---------------------------------------------------------------------

Sri Lanka has a per capita GDP only half of Brazil‘s,

but has high social indicators.

High social attainment may help Sri Lanka to

promote its growth.

But Sri Lanka‘s growth

i. might have been higher

ii. if it had invested

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ii1. for economic growth (e.g., for building

roads and factories)
ii2. some of the resources it has devoted to
social development (e.g., for building
schools and hiring teachers

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1.7. U.N. Millennium Development

Goals

1.7.1. Goals and targets

In 2000, the heads of state of the 189 U.N. member

countries signed a document that declared the
following:

―We have a collective responsibility to uphold the

principles of human dignity, equality and equity at
the global level. As leaders we have a duty therefore
to all the world‘s people, especially the most
vulnerable and, in particular, the children of the
world, to whom the future belongs.

The Millennium Development Goals (MDGs)

comprise the following 8 goals aimed at the
eradication of poverty and the achievement of other
human development goals by 2015:

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(1) Eradicate extreme poverty and hunger.

Target for 2015: Halve the proportion of the people

living on less than $1 a day.

(2) Achieve universal primary education

Target for 2015: Ensure that all boys and girls

complete primary education.

(3) Promote gender equality.

Target for 2005: Eliminate gender inequality in

primary and secondary schools.

Target for 2015: Eliminate all gender disparities.

(4) Reduce child mortality.

Target for 2015: Reduce the under-5 mortality by 2/3.

(5) Improve maternal health.

Target for 2015: Reduce the ratio of women dying in

child birth by 3/4.

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(6) Combat HIV/AIDS, malaria, and other

diseases.

Target for 2015: Begin to reverse the spread of

HIV/AIDS and the incidence of malarias and other
major diseases.

(7) Ensure environmental sustainability.

General target: Integrate environment sustainability

into country policy framework.

Target for 2015: Reduce the proportion of people

without access to safe drinking water by 1/2.

Target for 2020: Achieve significant improvement in

the lives of at least 100 million slum dwellers.

(8) Develop a global partnership for development

Develop further an open treading and financial

system that includes a commitment to good
governance, development and poverty reduction,
nationally and internationally.

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Address the least developed countries‘ special needs

and the special needs of landlocked and small-island
developing states….

1.7.2. Progress report

A comprehensive progress report was published by

the United Nations in 2006. Selected findings:

Proportion (%) of people living on leas than $1 a day

---------------------------------------------------------------------------
1990 2002
--------------------
Sub-Sahara Africa 44.6 44.0
Southern Asia 39.4 31.2
South-Eastern (SE) Asia and Oceania 33.0 14.1
Latin America and the Caribbean 19.6 7.3
Northern Africa and Western Asia 2.2 2.4
Transition countries of SE Europe 0.4 1.8
---------------------------------------------------------------------------
UN, The MDGs Progress Report, 2006.

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Net enrolment ratio (%) in primary education

---------------------------------------------------------------------------
1990/91 2003/04
---------------------------
Sub-Saharan Africa 53 64
Western Asia 74 80
Southern Asia 72 89
CIS, Asia 91 90
SE Asia 84 92
Eastern Asia 98 94
Northern Africa 81 94
L.A. and the Caribbean 86 95
----------------------------------------------------------------------------
UN, The MGGs Progress Report, 2006.

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1.8. Economic development and

development economics

Economic development is a multifaceted phenomenon.

Development studies must be multifaceted, as well.

Todaro and Smith (2006), pp. 10.

― Because of the heterogeneity of the developing

world and the complexity of the development process,
development economics must be eclectic, attempting
to combine relevant concepts and theories from
traditional economic analysis along with new models
of broader multidisciplinary approaches derived from
studying the historical and contemporary
development experience of Africa, Asia, and Latin
America…‖

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p. 13.

―It is necessary to recognize from the outset that

ethical or normative value premises about what is or
is not desirable are central features of the economic
discipline and general and of development economics
in particular…

p. 20

―… at least three basic components or core values

serve as a conceptual basis and practical guideline for
understanding the inner meaning of development…

―Sustenance: The ability of Meet Basic Needs…

Self-Esteem: To Be a Person…
Freedom from Servitude: To Be Able to Choose…‖

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Appendix to Lecture 1

Initial income levels, growth rates, and

catching up and falling behind

This note discusses the relationship between initial income levels

of per capita income, growth rates, and catching up.

1. If two countries‘ (country A‘s and country B‘s)

i. initial per capita income levels are the same,

and
ii. the growth rate of A‘s per capita income is higher than
B‘s permanently,

B will be unable to catch up with A.

To see this, let the two countries‘

i. initial incomes (e.g., for time = 0), respectively, are Y(0)

and X(0), and
ii. growth rates, respectively, are g and h,

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where

i. Y(0) = X(0) and

ii. g > h.

Then,

Y(t) = Y(0)egt
X(t) = X(0)eht

and the ratio between Y(t) and X(t) will be

Y(t)/X(t) = Y(0)egt/X(0)eht
= [Y(0)/X(0)]e(g-h)t
= [1]e(g-h)t , since Y(0) = X(0).

Since g>h, this means that Y(t)/X(t) will grow at the rate of g–h
and that Y(0) will continue to be higher than X(0).

For example, if

Y(0) = X(0) = 100, and

g = 0.05 = 5% per year
h = 0.04 = 4% per year

Y(t)/X(t) = [1]e(0.05-0.04)t = e0.01t

This means that Y(t)/X(t) will grow at 1% per year.

X(t) will never be able to catch up Y(t).

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2. Suppose, however, that

g > h, but
Y(0) < X(0)

In this case,

Y and X, respectively, will increase by

Y(0)g and
X(0)h

If X(0) is much larger than Y(0), X may initially increase more

than Y, and the gap between X and Y may increase when

X(0)g > Y(0)h

For example, suppose

Y(0) = 100
X(0) = 200 and

g = 0.05
h = 0.04

In this case, the initial annual increases in Y and X, respetively,

will be

Y(0)g = 100(0.05) = 5
X(0)h = 200(0.04) = 8

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Thus, the gap between X and Y will increase initially.

As time goes by, however, Y(t) will eventually catch up with X(t).
This can be shown as follows:

The ratio between Y(t) and X(t) will be

Y(t)/X(t) = Y(0)egt/X(0)eht
= [Y(0)/X(0)]e(g-h)t

Initially, Y(0)/X(0) will be less than 1, but Y(t)/X(t)

Will grow to be larger than 1, meaning that Y(t) will become
larger than X(t).

In the numerical example given above, initially,

Y(0)/X(0) will be 0.5, but

Y(t)/X(t) will grow at the annual rate of 0.01 (=1%), and Y(t) will
eventually catch up with X(t) when

Y(0)egt = X(0)eht that is, when

e(g-h)t = X(0)/Y(0)

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