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CHAPTER
4
The Economy in the Very Long
Run: The Economics of Growth
Learning objectives




Understand that economic growth is due to growth in
inputs, and to improvements in technology.
Understand that capital accumulates through savings and
investment.
Understand that the long run level of output per person
depends on the savings rate and the rate of population
growth.
Understand that the basic economic growth model
predicts that standards of living in different countries will
eventually converge.
PowerPoint® slides prepared by Marc Prud’Homme, University of Ottawa
Copyright 2005 © McGraw-Hill Ryerson Ltd.
Growth Accounting
Y = AF(K, N)
(1)
o This chapter uses the Growth accounting
equation: A summary of the contributions
of input growth and changes in
productivity to the growth of output.
Y/Y = [(1-) (N/N)] + [(K/K)] + A/A (2)
o Total factor productivity: Rate at which
productivity of input increases; also a
measure of technological progress.
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Chapter 4: The Economy in the Very Long Run
o In Chapters 2 and 3, the general
production function used was:
Slide 2
Growth Accounting
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Chapter 4: The Economy in the Very Long Run
Figure 4-1: GDP per Capita for Four Countries, 1820 - 2002
Slide 3
BOX
4-1
Human Capital
The higher the rate of investment (physical capital or
human capital) the higher the GDP.
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Slide 4
Growth Accounting
Year
(1-) (N/N) (K/K)
A/A
Y/Y
19621973
2.1
1.4
1.9
5.4
19741992
1.6
1.1
0.0
2.8
19932002
0.9
1.0
1.5
3.4
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Chapter 4: The Economy in the Very Long Run
Table 4-1: Accounting for Growth in Canada, 1962 and 2002 (Averages)
Slide 5
BOX
The Post-1973 Productivity Slowdown
4-2
• A measurement problem
• Oil price shocks
• The pace of innovation slowed
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Slide 6
Growth Theory: The Neoclassical Model
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Chapter 4: The Economy in the Very Long Run
o Neoclassical growth theory: Focuses on capital
accumulation and its link to savings decisions
and the like.
Y = AF(K, N)
(1)
Assumptions: No technological change and per
capita form.
Y/N = f(K/N, 1)
(4)
If y = Y/N is per capita output and k = K/N is the
capital-labour ratio, then
y = f(k)
(5)
o Capital-labour ratio: Number of machines per
worker.
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Growth Theory: The Neoclassical Model
The production function y =
f(k) is the relationship
between per capita output
and the capital-labour ratio...
Per capita output
y
… it exhibits two
important
characteristics: 1)
As k increases, y
increases, so that
the marginal
product of labour is
positive; 2) Output
rises less at high
levels of k because
of diminishing
marginal product of
capital.
y = f(k)
y*
k*
Chapter 4: The Economy in the Very Long Run
Figure 4-2: Per Capita Production Function
k
Capital-labour ratio
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Slide 8
Growth Theory: The Neoclassical Model
Copyright 2005 © McGraw-Hill Ryerson Ltd.
Chapter 4: The Economy in the Very Long Run
o Marginal product of capital: Increment of output obtained
by adding one unit of capital with another factor input
held constant.
Assumptions: No government and no foreign trade, then
y=c+I
(6)
Where c = C/N and i = I/N
Assumption: per capita consumption is a function of
income, then
c = (1 - s)y
(7)
s is marginal propensity to save and (1 - s) is marginal
propensity to consume.
In the long run, I = S, therefore propensity to consume.
i = sy
(8)
i = s f(k)
(9)
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Growth Theory: The Neoclassical Model
o Steady-state equilibrium: The combination of
per capita GDP and the capital-labour ratio
where the economy will remain at rest (i.e.
where per capita economic variables are no
longer changing.)
Assumption: Population growth increases
exogenously, then
10) n = N/N, and that depreciation each year equal
d, then
11) k = i = (n + d)k and 12) sy = (n + d)k
In equilibrium:
13) sf (k*) = (n + d)k*
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Chapter 4: The Economy in the Very Long Run
Steady-State Equilibrium
Slide 10
Growth Theory: The Neoclassical Model
Per capita output
y
y = f(k)
=c
i = sf(k)
=i
Capital-labour ratio
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Savings is a
constant proportion
of income given by
sk(k). In the long
run equilibrium,
savings equals
investment. The
remainder of
income is
consumption, given
that we assume no
government and
foreign trade.
Chapter 4: The Economy in the Very Long Run
Figure 4-3: Consumption and Investment in the Neoclassical Growth Model
Slide 11
Growth Theory: The Neoclassical Model
o Figure 4-4 studies the adjustment
process that leads the economy from
some initial capital-labour ratio over time
to the steady state.
o Critical element in the transition process:
rate of saving and investment compared
with the rate of depreciation and
population growth.
Copyright 2005 © McGraw-Hill Ryerson Ltd.
Chapter 4: The Economy in the Very Long Run
The Growth Process
Slide 12
Growth Theory: The Neoclassical Model
Figure 4-4: Steady State Output and Investment
y
D
y*
y = f(k)
Per capita output
y0
(n + d)k
C
A
sy0
B
k0
k*
sy
The economy starts
at k0…
… saving (A)
exceeds investment
(B) to hold k
constant…
… k increases.
The adjustment
process continues
until point C is
reached, i.e., the
Steady State where
k and y are
constant.
Capital-labour ratio
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Slide 13
Growth Theory: The Neoclassical Model
Figure 4-5: Increase in Savings Rate Moves Steady State
y
C’
y**
C
s’y
Per capita output
Y*
f(k)
sy
(n + d)k
K*
Capital-labour ratio
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K**
The economy starts
in steady-state
equilibrium at point
C where saving
equals investment
requirement.
An increase in the
fraction of income
that is saved leads
to sy to s’y…
…saving is higher
than investment
required and the
capital stock per
head will increase
until point C’ is
reached.
Slide 14
Growth Theory: The Neoclassical Model
Copyright 2005 © McGraw-Hill Ryerson Ltd.
Chapter 4: The Economy in the Very Long Run
Figure 4-6: Adjustment to a New Steady State
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Growth Theory: The Neoclassical Model
Figure 4-7: The Golden Rule May Not be the Steady State
Per capita output
y
f(k)
(n + d)k
The Steady-State capital
stock is at k* but at this
level of capital per head
saving is too too high.
sy
The Golden Rule level of
capital stock is k**
where consumption per
head is maximized.
s*y
To attain the Golden Rule
level of capital stock, the
saving rate, s, would
need to change to s*.
The Golden Rule may not
be the Steady State.
k**
k*
Capital-labour ratio
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Slide 16
Growth Theory: The Neoclassical Model
(n + d)k
Figure 4-8: Exogenous Technical Change
y
y1
A1
A0
y1
Per capita output
A2
sy2
y0
sy1
sy0
k*0
k*1
k*2
An exogenous
increase in
technology causes
the production
function and the
savings curve to rise.
This results in a new
steady-state point at
a higher per capita
output and a higher
capital labour-ratio.
Capital-labour ratio
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Slide 17
Growth Theory: The Neoclassical Model
o Endogenous growth: Self-sustained growth.
o Assume a production function with a constant marginal
product of capital (a) and with capital as the only factor.
Y = aK
(14)
o Assume the savings rate is constant and at s and that
there is neither population growth nor depreciation of
capital.
K = sY = saK
K/K = sa
(15)
o Since output is proportional to capital, the growth rate of
output is
Y/Y = sa
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(16)
Chapter 4: The Economy in the Very Long Run
Endogenous Growth
Slide 18
Growth Theory: The Neoclassical Model
Copyright 2005 © McGraw-Hill Ryerson Ltd.
Chapter 4: The Economy in the Very Long Run
Figure 4-9: (a) Solow Growth Model vs. (b) Endogenous Growth
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Growth Theory: The Neoclassical Model
o Absolute Convergence: Tendency of
both the levels and growth rates of
output in different countries to approach
each other over time, and for their
steady-state values to be the same.
o Conditional Convergence: Tendency of
growth rates of output in different
countries to approach each other over
time, and for their steady-state values to
be the same.
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Chapter 4: The Economy in the Very Long Run
Convergence
Slide 20
BOX
A Nobel Laureate’s Words
4-4
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Slide 21
Growth Theory: The Neoclassical Model
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Chapter 4: The Economy in the Very Long Run
Table 4-2: GDP Declines in Formerly Socialist Economies, 1989-1994
Slide 22
Growth Policy
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Chapter 4: The Economy in the Very Long Run
Figure 4-10: Personal and Government Savings, 1961-2002
Slide 23
Chapter Summary
Copyright 2005 © McGraw-Hill Ryerson Ltd.
Chapter 4: The Economy in the Very Long Run
• Neoclassical growth theory accounts for
growth in output as a function of growth in
inputs, particularly capital labour.
• Each input contributes to growth by an amount
equal to its factor share times its growth rate.
• Long run growth can result from
improvements in technology.
• Steady-State output per person depends
positively on the savings rate and negatively
on the rate of population growth.
Slide 24
The End
Chapter 4: The Economy in the Very Long Run
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