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10TopicECONOMIC GROWTH
U.S. real GDP per person and the standard of living tripled
between 1960 and 2010.
We see even more dramatic change in China, where
incomes have tripled not in 50 years but in the 13 years
since 1999.
Incomes are growing rapidly in some other economies of
Asia, Africa, and South America.
What are the forces that make real GDP grow?
The Basics of Economic Growth
The Basics of Economic Growth
Economic growth is the sustained expansion of production
possibilities measured as the increase in real GDP over a
given period.
Calculating Growth Rates
The economic growth rate is the annual percentage
change of real GDP.
The economic growth rate tells us how rapidly the total
economy is expanding.
The Basics of Economic Growth
The standard of living depends on real GDP per person.
Real GDP per person is real GDP divided by the
population.
Real GDP per person grows only if real GDP grows faster
than the population grows.
The Basics of Economic Growth
Economic Growth Versus Business Cycle Expansion
Real GDP can increase for two distinct reasons:
1. The economy might be returning to full employment in an
expansion phase of the business cycle.
2. Potential GDP might be increasing.
The return to full employment in an expansion phase of the
business cycle isn’t economic growth.
The expansion of potential GDP is economic growth.
The Basics of Economic Growth
This Figure illustrates the
distinction.
A return to full employment
in a business cycle
expansion is a movement
from inside the PPF (point
A) to a point on the PPF
(point B).
Economic growth is the
outward shift of the PPF
from PPF0 to PPF1 and the
movement from point B on
PPF0 to point C on PPF1.
Growth Rates Matter
Compound Interest
We all know the power of compound interest, but it is worth
reminding ourselves of it.
Consider a fifty year time period. The table below shows
what happens to output per head at different growth rates:
2.1% per annum Increases 182.7%
1.5% per annum Increases 110.5%
3.0% per annum Increases 338.4%
1.0% per annum Increases 64.5%
4.0% per annum Increases 610.7%
Growth Rates Matter
The Magic of Sustained Growth
The Rule of 70 states that the number of years it takes for
the level of a variable to double is approximately 70 divided
by the annual percentage growth rate of the variable.
Growth Rates Matter
Applying the Rule of 70
This Figure shows the doubling time for growth rates.
A variable that grows at 7 percent a year doubles in 10 years.
A variable that grows at 2 percent a year doubles in 35 years.
A variable that grows at 1 percent a year doubles in 70 years.
Long-Term Growth Trends
Real GDP Growth in the World Economy
This Figure shows the growth in the rich countries.
Japan grew rapidly in
the 1960s, slower in the
1980s, and stagnated
during the 1990s.
Growth in Europe Big 4,
Canada, and the United
States has been similar.
Economic Growth Trends
This Figure shows the
growth of real GDP per
person in a group of
poor countries.
The gaps between real
GDP per person in the
United States and in
these countries have
widened.
The Causes of Economic Growth:
A First Look
Preconditions for Economic Growth
The basic precondition or prerequisite for economic growth is an
appropriate incentive system.
Three institutions that help with the creation of appropriate incentives
are:
Competitive Markets
Monetary exchange, i.e., proper Flow of liquidity
Clear and certain property rights together with strong liability rule
The Causes of Economic Growth:
A First Look
For economic growth to persist, society somehow needs to
ensure these three activities:
Saving and investment in new capital
Investment in human capital
Discovery of new technologies
Appropriate incentives allow these activities to occur in a
decentralized market, society.
The Causes of Economic Growth:
A First Look
Note that, Potential GDP, Y = F(L, K, T )
Saving and Investment in New Capital
The accumulation of capital dramatically increases output and productivity;
one US farmer can feed many, many households.
Investment in Human Capital
Human capital acquired through education, on-the-job training, and learning-
by-doing can also dramatically increase output and productivity.
Discovery of New Technologies
Technological advances contribute immensely to increasing productivity; think
what you can do with a PC, things that were impossible for your parents
without months of work.
Growth Accounting
The quantity of real GDP supplied, Y, depends on the
quantity of labor, L, the quantity of capital, K, and the state
of technology, T.
The purpose of growth accounting is to estimate how
much real GDP growth comes from growth of labor and
capital inputs, and how much is apparently because of
technological change
Growth accounting is based on the aggregate production
function,
Y = F(L, K, T ).
Growth Accounting
Labor Productivity
Labor productivity is real GDP per hour of labor or per
unit of labor; it equals real GDP divided by aggregate
hours or real GDP divided by total number of labor.
So, Labor productivity = 𝑌
𝐿
Growth Accounting
Growth accounting divides growth in productivity into two
sources:
Growth in capital per unit of labor
Technological change
Any productivity growth not accounted for by growth in
capital is allocated to technological change, so this
category is a broad catch-all concept, which also includes
for example efficiency improvements from better
organization, economic system, or management.
Growth Accounting
For any 𝑋, denote
𝑋
𝐿= 𝑥
Assume a Cobb-Douglas CRTS Production Function:
𝑌 = 𝑇𝐾𝛼𝐿1−𝛼
⇒𝑌
𝐿= 𝑇
𝐾𝛼𝐿1−𝛼
𝐿
= 𝑇𝐾𝛼𝐿1−𝛼
𝐿𝛼𝐿1−𝛼= 𝑇
𝐾
𝐿
𝛼
⇒ 𝑦 = 𝑇𝑘𝛼
Equation of the productivity curve
𝑦 = 𝑇𝑘𝛼
Taking ′ln′ on both sides
⇒ ln 𝑦 = ln 𝑇 + 𝛼 ln 𝑘
Differentiating both sides with respect to ′𝑡′
⇒1
𝑦
𝑑𝑦
𝑑𝑡=1
𝑇
𝑑𝑇
𝑑𝑡+ 𝛼
1
𝑘
𝑑𝑘
𝑑𝑡
⇒ሶ𝑦
𝑦=
ሶ𝑇
𝑇+ 𝛼
ሶ𝑘
𝑘
𝑔𝑦 = 𝑔𝑇 + 𝛼𝑔𝑘
Growth Accounting
For any 𝑥, denote 𝑑𝑥
𝑑𝑡= ሶ𝑥
Growth Accounting
Equation
R & D Private investments
Intensive
growth
Extensive
growth
Productivity Curve
The Productivity Curve
The productivity curve is the relationship between output
per worker and capital per worker, with technology held
constant.
𝑦 = 𝑇𝑘𝛼𝑘 and 𝑦 are positively related
The relationship is governed by 𝛼
𝑦
𝑘
𝑦
𝑘
𝛼 = 1 𝛼 > 1 𝛼 < 1
linear Convex
𝑦
𝑘
Concave
Productivity Curve
𝑦 = 𝑇𝑘𝛼
Slope:𝑑𝑦
𝑑𝑘= 𝛼𝑇𝑘𝛼−1 > 0
Change in Slope:𝑑2𝑦
𝑑𝑘2= 𝛼(𝛼 − 1)𝑇𝑘𝛼−2
= 0 𝑖𝑓 𝛼 = 1
> 0 𝑖𝑓 𝛼 > 1
< 0 𝑖𝑓 𝛼 < 1
𝑦
𝑘
𝑦
𝑘
𝑦
𝑘
linear
Convex
Concave
Productivity Curve
Micro-level analysis using firm-level data reveals: 𝛼 =1
3
𝑦
𝑘
Concave
Productivity Curve
𝑦 = 𝑇𝑘𝛼
⇒ ln 𝑦 = ln 𝑇 + 𝛼 ln 𝑘
⇒𝑑 ln 𝑦
𝑑 ln 𝑘= 𝛼
⇒%Δ𝑦
%Δ𝑘= 𝛼 =
1
3
Note that:𝑑
𝑑𝑥ln 𝑥 =
1
𝑥
𝑑 ln 𝑥 =𝑑𝑥
𝑥= %Δ𝑥
Productivity Curve
Micro-level analysis using firm-level data reveals: 𝛼 =1
3
𝑦
𝑘
Concave
Productivity Curve
Note that:
𝑦 = 𝑎 + 𝑏𝑥 ⇒ 𝑏 =𝑑𝑦
𝑑𝑥
𝑦 = 𝑎𝑥𝑏 ⇒ 𝑏 =%Δ𝑦
%Δ𝑥
𝑦 = 𝑇𝑘𝛼
⇒ 𝛼 =%Δ𝑦
%Δ𝑘=1
3
𝑏: Slope
𝑏: Elasticity
Productivity Curve
This Figure illustrates the productivity curve.
An increase in capital
per worker brings a
movement along the
productivity curve. The
slope of the productivity
curve reflects the rate
of return or the real
interest rate earned on
capital.
Technological
improvement shifts the
productivity curve
upward.
Productivity Curve
The shape of the productivity curve reflects the law of
diminishing returns.
The law of diminishing returns states that, as the
quantity of one input increases with the quantities of all
other inputs remaining the same, output increases but
eventually by ever smaller increments.
Robert Solow discovered that diminishing returns are well
described by the one-third rule: with no change in
technology, on the average, a 1 percent increase in capital
per hour of work brings a one-third of 1 percent increase in
output per hour of labor.
Growth Theories
Classical Growth Theory
Classical growth theory came to the conclusion that real
GDP growth was temporary; when real GDP per person
rises above the subsistence level, a population explosion
brings real GDP per person back to the subsistence level.
This may sound stupid now, but in the early 1800s it was a
not unreasonable conclusion – it was not clear that living
standards in most of the world were any higher than in
Roman times.
Growth Theories
Growth Theories
The basic classical idea
There is a subsistence real wage rate, which is the
minimum real wage rate needed to maintain life and match
births to deaths.
Advances in technology shifts the productivity curve up.
Labor productivity increases and the real wage rate rises
above the subsistence level.
When the real wage rate is above the subsistence level,
the population grows – births exceed deaths.
Population growth increases the supply of labor, which
lowers the real wage rate.
Growth Theories
The population continues to increase until the real wage
rate has been driven back down to the subsistence real
wage rate, where deaths match births again.
At this real wage rate, both population growth and
economic growth stop.
Contrary to the assumption of the classical theory, the
historical evidence is that population growth is not tightly
linked to income per person, and rising incomes do not
result in population growth driving incomes back down to
subsistence levels.
Growth Theories
This Figure
illustrates
the
classical
growth
theory.
Growth Theories
Neoclassical Growth Theory
Neoclassical growth theory posits that real GDP per
person grows because technological change induces a
level of saving and investment that makes capital per hour
of labor grow.
Growth ends only if technological change stops.
Growth Theories
The neoclassical economics of population growth
The neoclassical view is that the population growth rate is independent of both real GDP per person and its growth rate.
The population growth rate equals the birth rate minus the death rate.
The birth rate is influenced by the opportunity cost of a woman’s time.
As women’s wage rates have increased, the opportunity cost of having children has also increased and the birth rate has fallen.
Growth Theories
The death rate is influenced by nutrition, sanitation, public
health policy, and the quality and availability of health care.
As the quality and availability of health care has improved,
the death rate has fallen.
The falls in both the birth rate and the death rate have
tended to offset each other and to make the population
growth rate independent of the level of income; in most
high-income societies the death rate exceeds the birth rate
and population is tending to fall [immigration and an
unusually high birth rate make the US an exception].
Growth Theories
Target Rate of Return and Saving
Ceteris paribus, the higher the real interest rate, the greater is the amount that people save. To decide how much to save, people compare the real interest rate with a target rate of return. If the real interest rate exceeds the target rate of return, saving is sufficient to make capital per hour of labor grow. If the target rate of return exceeds the real interest rate, saving is not sufficient to maintain the current level of capital per hour of labor, so capital per hour of labor shrinks. And if the real interest rate equals a target rate of return, saving is just sufficient to maintain the quantity of capital per hour of labor at its current level.
Growth Theories
The basic neoclassical idea
Technology begins to advance more rapidly.
New profit opportunities arise.
Investment and saving increase.
As technology advances and the capital stock grows, real
GDP per person rises.
Diminishing returns to capital per hour of labor lower the
real interest rate and eventually growth stops unless
technology keeps on advancing.
Growth Theories
This
Figure
illustrates
neo-
classical
growth
theory.
Growth Theories
New Growth Theory
“New growth theory” holds that real GDP per person grows because of choices that people make in the pursuit of profit and concludes that growth can persist indefinitely.
The theory emphasizes that
People are always in pursuit of profit
Discoveries bring profit
In a market economy, profit brings competition and competition destroys profit
People look for more profit, more discoveries take place, more knowledge is gathered, more growth takes place
Knowledge is not subject to diminishing returns
Growth Theories
This
Figure
illustrates
new
growth
theory.
Growth Theories
This Figure summarizes the ideas of new growth theory as
a perpetual motion machine.