economic development chapter 3 concepts and patterns

1. Chapter 3
Economic growth :
concepts and patterns
Rasheed zedan

2. introduction
• Note : a small differences in the
growth rate can cause a huge
difference overtime.
• The difference b/w 1 percent growth
and 2 percent growth is huge : is not
a 1 percent difference but it a 100
percent difference.

3. How to calculate growth rate
• How to calculate the expected level of income after
a t years at growth rate=r?
• To answer this question we use the following rule:
• 𝑿 𝒕= 𝑿 𝟎 × (𝟏 + 𝒓) 𝒕
where:
• 𝑿 𝒕 = the expected level of income.
• 𝑿 𝟎= the current level of income.
• 𝒓 = the growth rate.
• 𝒕 = numbers of years.

4. How to calculate growth rate
• Example: suppose that country A has in income per
capita equal to $1492 , ant its historical growth rate
equal 1 percent per year , if we want to project this
country level of income after 10 years . calculate
• Answer
• 𝑿 𝒕 = ?
• 𝑿 𝟎= $1492
• 𝒓 = 1 percent
• 𝒕 = 10
• Accordingly:

5. How to calculate growth rate
• 𝑿 𝒕= 𝑿 𝟎 × (𝟏 + 𝒓) 𝒕
=
• $𝟏𝟒𝟗𝟐 × (𝟏 + 𝟎. 𝟎𝟏) 𝟏𝟎= $𝟏𝟔𝟒𝟖
• So if this country continue to grow at this
rate (1percent) its per capita income after 10
years will be $1648

6. How to calculate growth rate
• Question 2 : instead of calculating the future value of
income , we want to calculate the growth rate.
• If we know the current value of income (𝑿 𝟎) and the
future value of income (𝑿 𝒕 ) we now want to calculate
the growth rate (𝒓). To calculate 𝒓 we can use the
following rule:
• 𝒓 =(
𝑿 𝒕
𝑿 𝟎
)
1
𝑡 -1
• Regarding to the previous example: 𝑿 𝒕 = $1648 , 𝑿 𝟎
= $1449 , 𝒕 = 10 calculate 𝒓 .
• 𝒓 = (
$1648
$1449
)
1
10 -1
• =0.01 (approx.)

7. How to calculate growth rate
• Question 3: calculating the doubling time.
• To calculate the doubling time we use the rule of 70
• 𝑿 𝒕 = 𝑿 𝟎 × 𝒆 𝒓𝒕
• We use this formula to calculate the time it takes to
double by setting 𝑿 𝒕 = 𝟐 and 𝑿 𝟎 = 𝟏.then
• 𝟐 = 𝟏 × 𝒆 𝒓𝒕
• If we transform this equation by taking the natural
logarithms of both sides we can get
• 𝐥𝐧 𝟐 = 𝐥𝐧 𝟏 + (𝒓 × 𝒕)
• Because 𝐥𝐧 𝟏 = 𝟎 so that term drops out .this
calculation is called the rule of 70 because
ln 𝟐 = 𝟎. 𝟕𝟎
•

8. How to calculate growth rate
• So if we know the value of 𝒓 we can
calculate the doubling time by using the
following :
• Doubling time(𝒕)=
𝟎.𝟕𝟎
𝒓
• Regarding the previous example : if country A
remains to grow at the rate of 𝒓 = 𝟏𝒑𝒆𝒓𝒄𝒆𝒏𝒕 it will
70 year to double its income level.
• 𝒕 =
𝟎.𝟕𝟎
𝟎.𝟎𝟏
= 𝟕𝟎

9. Factor accumulation, productivity,
and economic growth
• Economists have been trying to understand the
determinants of economic growth and the
characteristics that distinguish fast-growing from
slower growing countries.
• Many factors can be used to refer to economic
growth such as the amount and type of
investments, education, and health care systems.
• At the core of most theories of economic growth is
the relationship b/w the basic factors of
production (labor, capital) and the total economic
production

10. Factor accumulation, productivity, and
economic growth
• Some countries also depend on its natural
resources assets such as petroleum deposits, gold,
etc.
• These assets are often included in the definition of
capital stock but sometimes are treated separately.
• We focus our analysis mainly on labor, capital
depending on the products being produced.
• A country’s total output (total income) is
determined by how much capital and labor it has
available and how productivity it uses those assets.

11. Factor accumulation, productivity, and
economic growth
• In turns increasing the amount of production
(economic growth) depends on increasing the
amount of capital and labor available and increasing
the productivity of those assets. In other words
economic growth depends on two basic
processes(factor accumulation, productivity
growth)
• Factor accumulation : increasing the size of capital
stock and labor force. Producing more goods and
services requires more machines, factories, roads
along with better educated workers.

12. Factor accumulation, productivity, and economic
growth
• Productivity growth: increasing the amount of output
produced by each machine or worker. Productivity can
increased by two ways (improve the efficiency,
technological change)
• Efficiency: by reorganizing workers each specialize in
one task this might lead to increase the productivity.
• Technological change: through which new ideas, new
machines, or new ways of organizing production can be
used
• Note: Countries that can invent new technology or
quickly adopt technologies can achieve more rapid
economic growth than other countries.

13. Saving, investments, and capital
accumulation
• Understanding that factor accumulation and
productivity growth are at the heart of the economic
growth process is important but takes us so far.
• We now must know what drive factor accumulation
and economic growth themselves.
• The most influential model of economic growth is the
solow growth model.
• Capital accumulation is the most influential factor on
the growth process.
• Most of models of economic growth pay much less
attention to the process of expanding the labor force
(assumed to grow in line with the population)

14. Saving, investments, and capital
accumulation
• The key ideas in these kinds of models (classical,
neoclassical model) are relatively straightforward:
• New investments increase the capital stock:
investment in new factories and machines directly
increase the capital stock.
• for the capital stock to grow the value of new
investment must be grater than the amount of the
depreciation in the existing capital.
• Investments that are greater than the amount of
the depreciation directly add to the capital stock.

15. Saving, investments, and capital
accumulation
• Note: New investments must be greater than the
amount of the depreciation and the growth of the
labor force in order to increase capital per worker.
• Investment is financed by saving: we know
previously that in the case of closed economy
investment is equal to saving.
• so that the main factor to increase investment is to
increase the amount of saving.
• Saving come from current income: people save
whatever they do not consume.
• Corporation save in the form of retained earnings
after distribution of dividends to stockholders.

16. Saving, investments, and capital
accumulation
• Government add to saving if it receives taxes that are
greater than government expenditure (budget surplus)
.
• Government deducts from saving when the received
taxes is lower than government expenditure(budget
deficit).
• The main decision facing households, corporations,
governments is how much to save and how much to
consume.
• Individuals do not care about the level of output or
capital but they care about the amount of goods and
services they can consume.

17. Saving, investments, and capital
accumulation
• The more is the amount consumed now the less is
the amount available to be saved.
• Additional saving provide the base for higher
income in the future.
• Increasing saving and investments is necessary for
growth but not sufficient (because there are many
investments that are non-productive).
• Economic growth requires both generating new
investments and ensuring that the investments are
productive.

18. Sources of growth analysis
• There is one way to explore how factor
accumulation and productivity growth affect output
and economic growth is by using production
function.
• Production function: explain how inputs (capital,
labor)are combined to produce a various level of
output.
• Figure 3-1 shows an example of common
production function .the horizontal axis shows one
measure of factor inputs(capital per worker) and
the vertical axis shows output per worker.

19. Sources of growth analysis

20. Sources of growth analysis
• We combine capital and labor in one single
term(capital per worker) to simplify the analysis.
• Factor production in figure 3-1(a) any movement to
the right along the horizontal axis mean that the
economy increase the amount of capital per worker
which will lead directly to increase the amount of
output per worker shown by the upward slope of
the production function.
• As the value of capital per worker increase from
$10,000 to $15,000 this will cause output per
worker to increase from 2,500 to 2,800.

21. Sources of growth analysis
• This movement from point a to point b along the
production function represents the growth process.
• Figure 3-1(b) represent the relationship b/w
productivity change and economic growth.

22. Sources of growth analysis
• As factors of production are used more efficiently or
new technology is adopted the production function
shift upward.
• This mean that if the same amount of capital per
worker ($10000) is used more efficiently this will
lead to economic growth(increasing output from
2,500 to 3,000)
• In this case moving from point a to point c
represent the economic growth through
productivity gains.

23. Sources of growth analysis
• Solow’s procedure for measuring these
relationships usually is referred to as growth
accounting or sources of growth analysis.
• He starts with a standard production function
relating the contribution of labor and capital to
aggregate production, then adds a term to capture
total factor productivity (TFP).
• TFP is meant to measure the contribution to
production of efficiency, technology, and other
influences on productivity.

24. Sources of growth analysis
• This production function is then converted into a
form that makes it possible to measure the
contribution of changes in each term—expansion
of the labor force, additions to the capital stock,
and growth in TFP—to overall growth. The resulting
equation is:
• 𝒈 𝒚=(𝑾 𝒌 × 𝒈 𝒌)+(𝑾𝒍 × 𝒈𝒍)+a. Where:
• 𝒈 𝒚=the growth of total income.
• 𝒈 𝒌=the growth rate of capital stock(k).
• 𝒈𝒍=the growth rate of labor force (L).

25. Sources of growth analysis
• both 𝑾𝒍and 𝑾 𝒌 = the share in total income of
wages and returns to capital. respectively
• a=the rate of change in TFP.
• For example, if 60 percent of all income comes from
wages and the remaining 40 percent comes from
returns on capital.
• then 𝑾𝑙 = 0.60 and 𝑾 𝒌 = 0.40. These two shares
must add up to 100 percent because all income
must be allocated to either workers or the owners
of capital.

26. Sources of growth analysis
• The equation should make intuitive sense: It shows us
how the growth in output depends on the growth in
inputs (K and L) and the growth in the productivity of
those inputs (a).
• Equation 3–1 simply summarizes the two effects
illustrated in Figure 3–1.
• Figure 3–1a shows the effect of factor accumulation on
output.
• Figure 3–1b illustrates productivity growth as a vertical
shift of the production function.
• Equation 3–1 combines these two dimensions of
growth in a way that allows us to distinguish between
them.

27. Sources of growth analysis
• The first two terms on the right-hand side of the
equation, (𝑾 𝒌 *𝒈 𝒌 ) + (𝑾𝒍 *𝒈𝒍), describe
movements along the production function (that is,
using more inputs to increase output).
• TFP growth (indicated by a in equation 3–1)
measures the upward shift in the production
function in Figure 3–1b.
• The basic procedure is to substitute actual data for
all the variables in equation 3-1 except a, which
cannot be measured directly.

28. Sources of growth analysis
• then calculate a as the residual. This is the famous
Solow residual.
• Example: From the statistical records of a
developing country, we find the following values for
the variables in the equation:
• 𝒈 𝒚= 0.05 (GDP growth rate of 5 percent a year).
• 𝒈 𝒌= 0.07 (capital stock growth of 7 percent a year).
• 𝒈𝒍= 0.02 (labor force growth of 2 percent a year).
• 𝑾𝒍= 0.6 (the share of labor in national income is 60
percent).
• 𝑾 𝒌=0.4 (the share of capital is 40 percent).

29. Sources of growth analysis
• By substituting these figures into equation 3–1, we get:
• 0.05 = (0.4 * 0.07) + (0.6 * 0.02) + a
• Solving for a, we find that a = 0.01, meaning that TFP
growth is 1 percent per year.
• TFP growth of 1 percent counts for one fifth (20
percent) of total growth.
• The growth in the capital stock accounts for slightly
more than half (56 percent) the total growth: (0.4 *
0.07)>0.05
• . Finally, growth in the labor force accounts for the
remaining 24 percent of total growth: (0.02 * 0.6)>0.05.

30. Sources of growth analysis
• In this particular example, capital accumulation is the
main driver of growth, with labor accumulation and
TFP growth each contributing similar amounts.
• This type of accounting analysis has been used widely
in many countries to examine the sources of growth.
• with particular attention paid to calculating TFP growth.
• however, it is important to recognize the limits of this
kind of study.
• arising from the fact that we can estimate productivity
growth only as the residual output growth unexplained
by having used more input.

31. Sources of growth analysis
• There are at least two kinds of problems in
estimating the value of productivity growth TFP:
• First, a represents a combination of influences that
this analysis cannot entirely disentangle.
• Should improvements in a be attributed to
efficiency gains stemming from improved trade
policies, reduced corruption, or streamlined
bureaucratic procedures?
• Or are they due to the introduction of faster
computers, new seed varieties for agricultural
crops, or other technologies?

32. Sources of growth analysis
• The limited growth accounting framework cannot
definitively answer these questions without
adding many more variables for which data do not
exist.
• Second, a is measured inaccurately because it is the
residual in the equation.
• All economic data are measured with some
inevitable errors, including all the data used in
equation 3–1.
• As a result, in addition to TFP, a captures the net
effect of all the errors and omissions in the other
data.

33. Sources of growth analysis
• In summary, sources of growth analyses suggest that
capital accumulation is the main source of growth for
developing countries, consistent with the Solow
growth model.
• TFP can play an important part in the growth process in
the appropriate policy and structural context.
• In rapidly growing economies, both factor
accumulation and TFP growth appear to play an
important role.
• TFP growth tends to become more important as
income rises and is a major contributor to growth in the
high income industrialized countries.

34. CHARACTERISTICS OF RAPIDLY
GROWING COUNTRIES
• There six factors represent the characteristics of
rapidly growing countries. These are:
• 1) MACROECONOMIC AND POLITICAL STABILITY:
• 2) INVESTMENT IN HEALTH AND EDUCATION:
• 3) EFFECTIVE GOVERNANCE AND INSTITUTIONS.
• 4) FAVORABLE ENVIRONMENT FOR PRIVATE
ENTERPRISE.
• 5) TRADE, OPENNESS, AND GROWTH.
• 6) FAVORABLE GEOGRAPHY