Macroeconomics
Sixth Edition, Global Edition
Chapter 7
Economic Growth:
Malthus and Solow
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Learning Objectives, Part I
7.1 List the seven key economic growth facts, and explain their
importance.
7.2 Construct the steady state in the Malthusian model, and
analyze the effects of changes in exogenous factors on
population, per capita consumption, and land per worker.
7.3 Explain the usefulness of the Malthusian model.
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Learning Objectives, Part II
7.4 Construct the competitive equilibrium in the Solow growth
model.
7.5 Use the Solow growth model to analyze the effects of changes
in exogenous factors on income per worker, capital per worker,
and the economy’s growth rate.
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Learning Objectives, Part III
7.6 List the facts about growth in real GDP, employment, the
capital stock, and total factor productivity in the United States
over the period 1950–2014.
7.7 Determine the Solow residual and growth rates in real GDP,
capital stock, employment, and the Solow residual from data
on real GDP, capital stock, and employment.
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U.S. Per Capita Real Income Growth
• Except for the Great Depression and World War II,
growth in U.S. per capita real income has not strayed
far from 2% per year since 1900.
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Figure 7.1 Natural Logarithm of Per
Capita Real GDP
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Real Per Capita Income and the
Investment Rate
• Across countries, real per capita income and the
investment rate are positively correlated.
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Figure 7.2 Real Income Per Capita vs.
Investment Rate
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Real Per Capita Income and the Rate of
Population Growth
• Across countries, real per capita income and the
population growth rate are negatively correlated.
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Figure 7.3 Real Income Per Capita vs.
the Population Growth Rate
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Real Per Capita Income and Per Capita
Income Growth
• There is no tendency for rich countries to grow faster
than poor countries, and vice-versa.
• Rich countries are more alike in terms of rates of
growth than are poor countries.
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Figure 7.4 Growth Rate in Per Capita
Income vs. Level of Per Capita Income
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A Malthusian Model of Economic
Growth
• This model predicts that a technological advance will
only increase population, with no long-run change in
the standard of living.
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Production Function
Output is produced from land and labor inputs.
Y = zF (L, N)
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Evolution of the Population
• Population growth is higher the higher per-capita
consumption is.
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Equilibrium Condition
• In equilibrium, consumption equals output produced.
C = zF (L, N)
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Equilibrium Evolution of the Population
• This equation describes how the future population
depends on current population.
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Figure 7.5 Population Growth Depends on
Consumption per Worker in the Malthusian Model
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How Population Evolves in Equilibrium
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Figure 7.6 Determination of the Population in the
Steady State
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The Per-Worker Production Function
y = zf (l),
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Equilibrium Condition in Per-Worker Form
c = zf (l)
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A Steady State Condition
• Population growth is increasing in consumption per
worker, c
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Figure 7.7 The Per-Worker Production Function
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Figure 7.8 Determination of the Steady
State in the Malthusian Model
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An Increase in z in the Malthusian Model
• If z increases, this shifts up the per-worker production
function.
• In the long run, the population increases to the point
where per capita consumption returns to its initial
level.
• There is no long-run change in living standards.
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Figure 7.9 The Effect of an Increase in
z in the Malthusian Model
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Figure 7.10 Adjustment to the Steady State in
the Malthusian Model When z Increases
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Population Control in the Malthusian
Model
• Population control alters the relationship between
population growth and per-capita consumption.
• In the long run, per capita consumption increases, and
living standards rise.
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Figure 7.11 Population Control in the
Malthusian Model
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How Useful is the Malthusian Model?
• The model provides a good explanation for pre-1800
growth facts in the world.
• Malthus did not predict the effects of technological
advances on fertility.
• Malthus did not understand the role of capital
accumulation in growth.
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Solow Growth Model
• This is a key model which is the basis for the modern
theory of economic growth.
• A key prediction is that technological progress is
necessary for sustained increases in standards of living.
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Population Growth
• In the Solow growth model, population is assumed to
grow at a constant rate n.
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Consumption-Savings Behavior
• Consumers are assumed to save a constant fraction s of
their income, consuming the rest.
C = (1 − s)Y
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Representative Firm’s Production Function
Y = zF(K, N),
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Constant Returns to Scale
• Constant returns to scale implies:
Y
K
= zF
,1
N
N
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Evolution of the Capital Stock
• Future capital equals the capital remaining after
depreciation, plus current investment.
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Figure 7.12 The Per-Worker Production Function
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Income-Expenditure Identity
• The income expenditure identity holds as an equilibrium
condition.
Y=C+I
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Equilibrium
• In equilibrium, future capital equals total savings (= I)
plus what remains of current K.
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Next Step
Substitute for output from the production function.
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Then,
Rewrite in per-worker form.
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Next,
Rearrange, to get:
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Figure 7.13 Determination of the Steady
State Quantity of Capital per Worker
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Figure 7.14 Determination of the Steady
State Quantity of Capital per Worker
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An Increase in the Savings Rate s
• In the steady state, this increases capital per worker
and real output per capita.
• In the steady state, there is no effect on the growth
rates of aggregate variables.
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Figure 7.15 Effect of an Increase in the
Savings Rate on the Steady State Quantity
of Capital per Worker
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Figure 7.16 Effect of an Increase in the
Savings Rate at Time T
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Figure 7.17 Steady State Consumption
per Worker
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Figure 7.18 The Golden Rule Quantity
of Capital per Worker
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An Increase in the Population Growth
Rate n
• Capital per worker and output per worker decrease.
• There is no effect on the growth rates of aggregate
variables.
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Figure 7.19 Steady State Effects of an
Increase in the Labor Force Growth Rate
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Increases in Total Factor Productivity z
• Sustained increases in z cause sustained increases in
per capita income.
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Figure 7.20 Increases in Total Factor
Productivity in the Solow Growth Model
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Growth Accounting
• An approach that uses the production function and
measurements of aggregate inputs and outputs to
attribute economic growth to: (1) growth in factor
inputs; (2) total factor productivity growth.
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Cobb-Douglas Production Function (1 of 2)
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Cobb-Douglas Production Function (2 of 2)
A labor share in national income of 70% gives:
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Solow Residual
The Solow residual is calculated as:
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Figure 7.23 Natural Log of the Solow Residual
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Average Annual Growth Rates in the
Solow Residual
Years
1950-1960
1960-1970
1970-1980
1980-1990
1990-2000
2000-2009
2009-2014
Average Annual Growth Rate
1.7
1.8
0.6
1.3
1.7
0.7
1.1
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Average Annual Growth Rates
Years
1950-1960
1960-1970
1970-1980
1980-1990
1990-2000
2000-2009
2009-2014
Y
3.6
4.3
3.2
3.3
3.5
1.4
2.1
K
3.7
3.9
3.0
2.6
2.4
2.1
0.9
N
1.1
1.8
2.4
1.8
1.4
0.2
0.9
z
1.7
1.8
0.6
1.3
1.7
0.7
1.1
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