CHAPTER Neoclassical Growth Model

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CHAPTER Neoclassical Growth Model
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Neoclassical Growth Model

• An Example of Economic Growth
• A History of Growth
• The Solow Growth Model
• The Production Function
• Forces that Change Capital
• Balanced Growth Investment
• Equilibrium in the Solow Model

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Neoclassical Growth Model

• Implications of the Solow Growth Model
• Increase in the Saving Rate
• Change in Population Growth or Depreciation Rate
• Change in Technological Progress
• Incentives for Saving and Investment

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Why Growth Rates Matter
Country A 2500 income growing at 1.5 for 100
years
Grows to 2500(1.015)100
11,080
Grows to 2500(1.015)100
Country B 2500 income growing at 2.5 for 100
years
27,534
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A History of World Economic Growth
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A History of World Economic Growth

• The Japanese and European economies grew rapidly
  after World War II into the 1970s.
• From 1950 to 1995 the Asian tigers grew faster
  than most other economies.
• In North America output grew at
• 2.5 from 1950 to 1973
• 1.5 from 1973 to 1995
• 2.5 after 1995

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The Modern Era of Growth 1820-2000
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Economic Policies to Promote Growth

• Maintain stable political, social, and market
  environments that give individuals freedom to
  operate.
• Save and invest to build up the capital stock.
• Educate the people in the society.

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Stable Political, Social, and Market Environments

• Growth increased tremendously when markets
  developed
• Markets allow specialization and division of
  labor
• Specialization and division of labor increase
  productivity (output per unit of labor)
• Increased productivity leads to a higher standard
  of living

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Save and Invest to Increase the Capital Stock

• Capital is the stock of physical goods used along
  with labor and raw materials in the production
  process
• Capital allows people to specialize
• Creating capital - investing - requires some of
  current production be diverted from consumption
  to investment

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Educate the Population

• Human capital is the set of skills and the
  knowledge that enable individuals to produce.
• Higher human capital leads to more productive
  research and technological advances.
• More knowledge and technology lead to faster
  economic growth.

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The Solow Growth Model

• The Solow growth model shows how economic growth
  is determined by
• Technology
• Saving
• Population growth
• The model assumes that aggregate supply creates
  an equal amount of aggregate demand.

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Firms and Production

• Firms use labor (L), capital (K), and technology
  (A) to produce goods and services.
• The relationship between inputs and outputs is
  shown in the production function
• Y AF(K, L)

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Attributes of Production Functions

• Output increases as the quantity of inputs
  increases
• Constant returns to scale - output increases in
  the same proportion as inputs
• Diminishing marginal product - output will
  increase by smaller amounts as more of one input
  is added, holding all others constant

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Per-Person Production Function
Since Y AF(K, L) Y/L
AF(K/L,1) or y Af(k)
Where y output per person k capital per
person
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A Per-Person Production Function
y2
y1
y0
Output per person
The slope of the production function is the
marginal pro- duct of capital per person
Capital per person
k0
k02
k01
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Saving and Investment Increase Capital

• Saving and investment are assumed to be a
  constant fraction, v, of income.
• Investment per person, i, is related to the
  capital stock through the production function and
  the investment rate.

I S vY
i s vy
I/L S/L vY/L
y Af(k)
i vAf(k)
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Saving per Worker
Af(k) production function
y0
Output and Investment per Person
consumption
vAf(k) investment function
vy0
saving investment
Capital per person
k0
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Depreciation Decreases in Capital per Person

• Depreciation is the wear and tear on capital.
• The rate of depreciation is assumed to be a
  constant fraction, d, of existing capital.
• Depreciation reduces capital per person, k, by
  the rate of depreciation times capital per
  person, dk.

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Depreciation Decreases Capital per Person
If capital per person is currently 50,
and capital depreciates at a rate of 12
percent, how much capital will depreciate?
Depreciation dk 1250 6
How much capital remains for next period?
Capital remaining 50 - 6 44
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Population Growth Decreases Capital per Person

• Population growth, n, reduces capital per person
  by the rate of population growth times capital
  per person.
• If total capital is 8000 and initial population
  is 400, capital per person is 20.
• If population grows by 1 to 404, capital per
  person decreases to 8000/404 19.8

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Population Growth and Depreciation Decrease
Capital per Person
Loss of capital per person per period
(n d) k
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Balanced Growth Investment

• Investment increases capital per person.
• Depreciation and population growth reduce capital
  per person.
• Balanced growth investment is the amount of
  investment i (nd)k that keeps capital per
  person constant.

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Balanced Growth Investment Line
Balanced growth investment line when n .02 and
k .08
i (nd)k
Investment per person
?
300
?
200
2000
3000
Capital per person
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Steady State Equilibrium
At k, investment i adds just enough capital to
offset depreciation and population growth
balanced growth investment line
Investment per Person
A
investment function
i
?
Capital per person
k
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Movement to Steady State
Af(k) production function
y
C
Output and Investment per Person
?
vAf(k) investment function
y0
A
?
i
B
e
?
?
i0
?
d
k
k0
Capital per person
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A Numerical Example of Steady State
(I) (II) (III) (IV) - (V) (VI)
Period k i0.4y nk.1k
?k capital output
investment(i) balanced
excess i

growth i 1 9.0 3.0
1.2 0.9 0.3 2 9.3 3.05
1.22 0.93 0.29 3 9.59 3.097
1.239 0.959 0.28 4 9.87 3.142
1.257 0.987 0.27 5 10.139 3.184
1.274 1.014 0.26 200 16.000
4.000 1.600 1.600 0.00
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Solving for Steady State Capital
Assume that v 0.4, y , n.1, and d0. In
steady state equilibrium i (nd)k and i
vy so vy (nd)k By substitution .4
.1k .16k .01k2 k 16
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Increase in the Saving Rate
y1
Af(k)
y0
(nd)k
Output and Investment per Person
i1
v1Af(k)
v0Af(k)
i0
k0
Capital per person
k1
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Transition Period
y1
output per person
transition period
y0
Income, output per person
t0
time
t1
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Conclusions About Saving

• A higher saving rate will lead to a higher level
  of capital per person and a higher income per
  person, but it will not lead to persistent growth
  per person.
• In the steady state, the economy will grow at the
  rate the population is growing.
• Income per person does not grow in the steady
  state.

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Golden Rule Level of Capital Accumulation
y
Af(k)
Maximum steady-state consumption
(nd)k
Income and Investment per Person
vAf(k)
v1Af(k)
i1
k1
Capital per person
k
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Increase in Population Growth
y0
Af(k)
y1
(n1d)k
Output and Investment per Person
i2
(n0d)k
A
i0
?
?
v Af(k)
i1
B
k1
Capital per person
k0
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Conclusions About Population Growth and
Depreciation

• A rise in population growth leads to a
  permanently higher growth rate in total output.
• A rise in population growth leads to a lower
  output per person.
• A rise in the rate of depreciation does not
  change the growth rate of total output, but leads
  to lower output per person.
• A rise in population does not lead to a sustained
  increase in output per person.

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Technological Innovation
A1f(k)
y1
A0f(k)
y0
(nd)k
Income and Investment per Person
i1
vA1f(k)
v A0f(k)
i0
k0
Capital per person
k1
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Conclusions About Technological Progress

• A technological advance increases income per
  person.
• A technological advance does not lead to an
  increase in the growth rate of income per person
  in the long run.
• Continual increases in technological advances can
  lead to continuous growth of output per person.

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Incentives for Saving and Investment

• Consumption-based tax
• Accelerated depreciation
• Investment tax credit