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The Facts of
Growth
Chapter 10
Chapter 10 Outline
The Facts of Growth
10-1
10-2
10-3
10-4
Measuring the Standard of Living
Growth in Rich Countries since 1950
A Broader Look across Time and Space
Thinking about Growth: A Primer
The Facts of Growth
• Growth is the steady increase in aggregate output
over time.
• We now shift our focus from economic fluctuations
and the determination of output in the short and
medium run to growth and the determination of
output in the long run.
Figure 10-1 U.S. GDP since 1890. U.S. GDP per
person since 1890
Panel A
Panel A shows the enormous increase in U.S. output since 1890, by a factor of
46.
Figure 10-1 U.S. GDP since 1890. U.S. GDP per
person since 1890 (cont’d)
Panel B
Panel B shows that the increase in output is not simply the result of the large
increase in U.S. population from 63 million to more than 300 million over this
period. Output per person has risen by a factor of 9.
10-1 Measuring the Standard of Living
• We care about growth because we care about the
standard of living.
• Output per person, rather than output itself, is the
variable we compare over time or across countries.
• We need to correct for variations in exchange rates and
systematic differences in prices across countries.
• When comparing the standard of living across countries,
we use purchasing power parity (PPP) numbers
which adjust the numbers for the purchasing power of
different countries.
• The right measure on the production side is output per
worker or output per hour worked.
FOCUS: The Construction of PPP Numbers
• Consider this example:
– United States: Each year, people buy a new car for
$10,000, and spend another $10,000 on food.
– Russia: People spend 20,000 rubles on cars (each lasts for
15 years) a year, and 40,000 rubles on food.
• If the exchange rate is $1 = 30 rubles, consumption per
person in Russia is only 10% of U.S. consumption per
person.
• If we use U.S. prices for both countries and assume
people spending all money on food, then consumption
per person is $20,000 ($10,000+$10,000) in the U.S.,
but $10,700 [(1/15)x$10,000)=(1x$10,000)] in Russia,
so Russian consumption per person is 53.5% of U.S.
consumption per person.
10-2 Growth in Rich Countries since
1950
Table 10-1 The Evolution of Output per Person in Four Rich
Countries since 1950
•
There has been a large increase in output per person due in part to the
force of compounding.
•
There has been a convergence of output per person across countries.
FOCUS: Does Money Lead to Happiness?
Figure 1 Life Satisfaction and Income per Person
•
Easterlin paradox: Once basic needs are satisfied, higher income per
person does not increase happiness, and the level of income relative to
others, rather than the absolute level of income, matters
10-2 Growth in Rich Countries since 1950
Figure 10-2 Growth Rate of GDP Per Person since 1950 versus GDP per
Person in 1950; OECD Countries
Countries with
lower levels of
output per person
in 1950 have
typically grown
faster.
10-3 A Broader Look across Time and
Space
• From the end of the Roman Empire to roughly year
1500, Europe was in a Malthusian trap or
Malthusian era with stagnation of output per person
because most workers were in agriculture with little
technological progress.
• After 1500, growth of output per person turned
positive but still small.
• Between 1820 and 1950, U.S. growth was still
1.5% per year.
• Sustained growth was high since 1950.
10-3 A Broader Look across Time and
Space
Figure 10-3 Growth Rate of GDP per Person since 1960,
versus GDP Per Person in 1960 (2005 dollars); 85 Countries
There is no clear
relation between the
growth rate of output
since 1960 and the
level of output per
person in 1960.
10-3 A Broader Look across Time and
Space
• For the OECD countries, there is clear evidence of
convergence.
• Convergence is also visible for many Asian
countries, especially for those with high growth
rates, called the four tigers—Singapore, Taiwan,
Hong Kong, and South Korea.
• Most African countries were very poor in 1960, and
some of them had negative growth of output per
person between 1960 and 2011 due in part to
internal or external conflicts.
10-4 Thinking About Growth: A
Primer
• Aggregate production function F:
where Y is output, K is capital, and N is labor.
• The function F depends on the state of technology.
• Constant returns to scale:
• Decreasing returns to capital: Increases in capital
lead to smaller and smaller increases in output.
• Decreasing returns to labor: Increases in labor lead
to smaller and smaller increases in output.
10-4 Thinking About Growth: A
Primer
• The production function and constant returns to scale
imply a simple relation between output per worker
(Y/N) and capital per worker (K/N):
• Increases in capital per worker: Movements along the
production function.
• Improvements in the state of technology: Shifts (up)
of the production function.
• Growth comes from capital accumulation (a higher
saving rate) and technological progress (the
improvement in the state of technology).
10-4 Thinking About Growth: A
Primer
Figure 10-4 Output and Capital per Worker
Decreasing returns
to capital:
Increases in capital
per worker lead to
smaller and smaller
increases in output
per worker.
10-4 Thinking About Growth: A
Primer
Figure 10-5 The Effects of an Improvement in the State of
Technology
An improvement in
technology shifts
the production
function up, leading
to an increase in
output per worker
for a given level of
capital per worker.
Saving, Capital
Accumulation, and
Output
Chapter 11
Chapter 11 Outline
Saving, Capital Accumulation, and Output
11-1
11-2
Interactions between Output and Capital
The Implications of Alternative Saving
Rates
11-3
Getting a Sense of Magnitudes
11-4
Physical versus Human Capital
APPENDIX The Cobb-Douglas Production Function
and the Steady State
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11-2
Saving, Capital Accumulation, and
Output
• Since 1970, the U.S. saving ratio—the ratio of
saving to gross domestic product—has averaged
only 17%, compared to 22% in Germany and 30%
in Japan.
• Even if a lower saving rate does not permanently
affect the growth rate, it does affect the level of
output and the standard of living.
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11-3
11-1 Interactions between Output
and Capital
• Output in the long run depends on two relations:
– The amount of capital determines the amount of
output
– The amount of output being produced determines the
amount of saving, which in turn determines the
amount of capital being accumulated over time
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11-4
11-1 Interactions between Output
and Capital
Figure 11-1 Capital, Output, and Saving/Investment
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11-5
11-1 Interactions between Output
and Capital
• Recall Chapter 10:
or
• Assume that N is constant, and there is no technological
progress, so f does not change over time:
• Higher capital per worker leads to higher output per
worker.
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11-6
11-1 Interactions between Output
and Capital
• Assume:
– The economy is closed: I = S + (T − G)
– Public saving (T − G) is 0: I = S
– Private saving is proportional to income: S = sY
• So the relation between output and investment:
It = sYt
• Investment is proportional to output.
• The higher (lower) output is, the higher (lower) is
saving and so the higher (lower) is investment.
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11-7
11-1 Interactions between Output
and Capital
• The evolution of the capital stock is:
• Replace investment by the above expression and
divide both sides by N:
or
• The change in the capital stock per worker is equal
to saving per worker minus depreciation.
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11-8
11-2 The Implications of Alternative
Saving Rates
• Combining equations (11.1) and (11.2):
• If investment per worker exceeds (is less than)
depreciation per worker, the change in capital per
worker is positive (negative).
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11-9
11-2 The Implications of Alternative
Saving Rates
Figure 11-2 Capital and Output Dynamics
When capital and
output are low,
investment exceeds
depreciation and
capital increases.
When capital and
output are high,
investment is less
than depreciation
and capital
decreases.
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11-10
11-2 The Implications of Alternative
Saving Rates
• The state in which output per worker and capital
per worker are no longer changing is called the
steady state of the economy.
• The steady-state value of capital per worker is
such that the amount of saving per worker is
sufficient to cover depreciation of the capital stock
per worker.
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11-11
Focus: Capital Accumulation and Growth in
France in the Aftermath of World War II
• France suffered heavy losses in capital when World War II ended in
1945.
• The growth model predicts that France would experience high
capital accumulation and output growth for some time.
• From 1946 to 1950, French real GDP indeed grew at 9.6% per year.
Table 1 Proportion of the French Capital Stock Destroyed by the End
of World War II
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11-12
11-2 The Implications of Alternative
Saving Rates
• The saving rate has no effect on the long-run
growth rate of output per worker, which is equal to
zero.
• The saving rate determines the level of output per
worker in the long run.
• An increase in the saving rate will lead to higher
growth of output per worker for some time, but not
forever.
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11-13
11-2 The Implications of Alternative
Saving Rates
Figure 11-3 The Effects of Different Saving Rates
A country with a
higher saving rate
achieves a higher
steady-state level
of output per
worker.
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11-14
11-2 The Implications of Alternative
Saving Rates
Figure 11-4 The Effects of an Increase in the Saving Rate on Output
per Worker in an Economy Without Technological Progress
An increase in the
saving rate leads to
a period of higher
growth until output
reaches its new
higher steady-state
level.
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11-15
11-2 The Implications of Alternative
Saving Rates
Figure 11-5 The Effects of an Increase in the Saving Rate on Output
per Worker in an Economy with Technological Progress
An increase in the
saving rate leads to
a period of higher
growth until output
reaches its new
higher steady-state
level.
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11-16
11-2 The Implications of Alternative
Saving Rates
• What matters to people is not how many is
produced, but how much they consume.
• Governments can affect the saving rate by:
– changing public saving (budget surplus)
– using taxes to affect private saving
• Golden-rule level of capital: The level of capital
associated with the saving rate that yields the
highest level of consumption in steady state.
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11-17
11-2 The Implications of Alternative
Saving Rates
Figure 11-6 The Effects of the Saving Rate on Steady-State
Consumption per Worker
An increase in the
saving rate leads to
an increase, then to
a decrease in
steady-state
consumption per
worker.
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11-18
11-2 The Implications of Alternative
Saving Rates
• For a saving rate between zero and the golden-rule
level, a higher saving rate leads to higher capital
per worker, higher output per worker and higher
consumption per worker.
• For a saving rate greater than the golden-rule
level, a higher saving rate still leads to higher
capital per worker and output per worker, but
lower consumption per worker.
• An increase in the saving rate leads to lower
consumption for some time but higher
consumption later.
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11-19
11-3 Getting a Sense of Magnitudes
• Assume the production function f:
• so that equation (11.3) becomes:
• which describes the evolution of capital over time.
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11-20
FOCUS: Social Security, Saving, and
Capital Accumulation in the United States
• Social Security, introduced in 1935, has led to a lower
U.S. saving rate and thus lower capital accumulation
and lower output per person in the long run.
• Social Security is a pay-as-you-can system that taxes
workers and redistributes the tax contributions as
benefits to current retirees, resulting in lower private
saving as workers anticipate receiving benefits when
they retire.
• An alternative is a fully-funded system that pays back
the principal plus interest to the workers when they
retire, resulting in lower private saving but higher public
saving as the System invests their contributions in
financial assets.
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11-21
11-3 Getting a Sense of Magnitudes
• Equation (11.7) implies that capital per worker in
the steady state (K*/N) becomes:
• Combining equations (11.6) and (11.8) gives the
steady state output per worker:
• In the long run, output per worker doubles when
the saving rate doubles.
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11-22
11-3 Getting a Sense of Magnitudes
Figure 11-7(a) The Dynamic Effects of an Increase in the Saving
Rate from 10% to 20% on the Level and the Growth Rate of Output
per Worker
It takes a long time for output to adjust to its new higher level after an
increase in the saving rate. Put another way, an increase in the saving rate
leads to a long period of higher growth.
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11-23
11-3 Getting a Sense of Magnitudes
Figure 11-7(b) The Dynamic Effects of an Increase in the Saving
Rate from 10% to 20% on the Level and the Growth Rate of Output
per Worker
It takes a long time for output to adjust to its new higher level after an
increase in the saving rate. Put another way, an increase in the saving rate
leads to a long period of higher growth.
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11-24
11-3 Getting a Sense of Magnitudes
• In the steady state, consumption per worker is:
• Given equations (11.8) and (11.9), the steadystate consumption per worker is:
• Table 11-1 gives the steady-state values of capital
per worker, output per worker and consumption
per worker for different saving rates (given
δ=10%)
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11-25
11-3 Getting a Sense of Magnitudes
Table 11-1 The Saving Rate and the Steady-State Levels of Capital,
Output, and Consumption per Worker
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11-26
11-4 Physical versus Human Capital
• Human capital (H): The set of skills of the
workers in the economy built through education
and on-the-job training.
• The production function with human capital:
• As for physical capital (K) accumulation, countries
that save more or spend more on education can
achieve higher steady-state levels of output per
worker.
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11-27
11-4 Physical versus Human Capital
• Models of endogenous growth: Steady-state
growth in outpour per worker depends on variables
such as the saving rate and the rate of spending on
education, even without technological progress.
• However, the current consensus is that given the
rate of technological progress, higher rates of
saving or spending on education do not lead to a
permanently higher growth rate.
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11-28
APPENDIX: The Cobb-Douglas Production
Function and the Steady State
• The Cobb-Douglas production function:
which gives a good description of the relation between
output, physical capital, and labor in the United States
from 1899 to 1922.
• In steady state, saving per worker must be equal to
depreciation per worker, implying that:
s(K*/N)α = δ(K*/N)
where K* is the steady-state level of capital.
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11-29
APPENDIX: The Cobb-Douglas Production
Function and the Steady State
• The preceding expression can be rewritten as:
s = δ(K*/N) 1-α
• The steady-state level of capital per worker becomes:
(K*/N) = (s/δ) α/(1-α)
• If α = 0.5, then:
K*/N = s/δ
which implies that a doubling of the saving rate leads to
a doubling in steady-state output per worker.
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11-30
Question 3
Suppose that the production function is given by Y=K1/2L1/2
a. Derive the steady state levels of capital per worker and output per worker in
terms of the saving rate, s, and the depreciation rate, 8.
b. Suppose 8 = 0.05 and s = 0.2. Find out the steady state output per worker.
c. Suppose 8 = 0.05 but s increases to 0.5. Find out the steady state output per
worker and compare your result with your answer in part b. Explain the intuition
behind your results.