Transcript Slide 1

Intermediate Macroeconomics
Chapter 3
Long-Run Economic Growth
Long-run Economic Growth
1.
2.
3.
4.
Growth accounting
Empirical results
Neoclassical growth model
Neoclassical growth model golden
rule
5. Endogenous growth model
6. Government policy and growth
Intermediate Macroeconomics
1. Growth Accounting
Growth in six countries
Real GDP per Worker, dollars
70,000
60,000
United States
50,000
40,000
Canada
30,000
U.K.
Hong Kong
20,000
Japan
Brazil
10,000
0
1950 1956 1962 1968 1974 1980 1986 1992 1998
Intermediate Macroeconomics
1. Growth Accounting
Growth accounting equation
ΔY = ΔA + εK ΔK + εL ΔL
Y
A
K
L
Output growth rate
= Productivity growth rate, ΔA/A
+ Capital growth rate, ΔK/K
x elasticity of output with respect to capital, εK
+ Labor growth rate, ΔL/L
x elasticity of output with respect to labor, εL
Intermediate Macroeconomics
2. Empirical Results
Solow and Denison studies
Solow
Denison
Period covered
1909 – 1949
1929 - 1982
Output growth
2.9%
2.9%
Capital growth
0.3%
0.6%
Labor growth
1.1%
1.3%
Productivity growth
1.5%
1.0%
Intermediate Macroeconomics
3. Neoclassical Growth Model
Growth in Actual and Potential U.S. GDP
Real GDP per Worker, dollars
70,000
Actual GDP cycles around the long-run GDP
growth rate (also called potential or fullemployment GDP)
60,000
Long run growth rate
50,000
40,000
Actual Real GDP
30,000
20,000
1950
1960
1970
1980
1990
Source: Penn World tables (http://datacentre.chass.utoronto.ca/pwt/alphacountries.html
Intermediate Macroeconomics
2000
3. Neoclassical Growth Model
Start with growth accounting equation
Assumption 1. No technological
change:
ΔY = εK ΔK + εL ΔL
Y
K
L
where,
Intermediate Macroeconomics
ΔA = 0
A
3. Neoclassical Growth Model
Steady State
Assumption 2. Steady State - a condition of
constant rates of growth in economic
measures. With no technological change,
a steady state is represented by identical
constant growth rates in population, total
output, and the level of capital.
ΔL = ΔK = n = population growth rate
L
K
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3. Neoclassical Growth Model
Constant returns to scale
Assumption 3. Constant returns to
scale production function.
εK + εL = 1
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3. Neoclassical Growth Model
Neoclassical growth equation result
ΔY = εK ΔK + εL ΔL
Y
K
L
= εK n + εL n
= (εK + εL ) n
=n
= population growth rate
The growth rate of output is independent
of savings or the level of capital.
Intermediate Macroeconomics
3.. Neoclassical Growth Model
Simple model implications
• Aggregate output grows at the same rate
as population.*
• Per worker output remains unchanged.*
• The level of capital has no effect of
aggregate or per worker output growth
rates in steady state.**
* Unless there is technological change, i.e. an increase in
productivity.
** An increase in the savings rate and capital-labor ratio
provides a temporary boost to aggregate output and per
worker output growth rates. Growth rates will return to
original steady state levels but at a permanently higher
output per worker level.
Intermediate Macroeconomics
3. Neoclassical Growth Model
Constant returns to scale
Production function:
Y = f(K, L)
If constant returns:
z Y = f(z K, z L)
If z = 1/L:
Y = f(K, 1)
L
L
Or,
Y/L = f(K/L)
Intermediate Macroeconomics
3. Neoclassical Growth Model
Per worker production function
Output per capita
Output
= f(K/L)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Capital-Labor Ratio, K/L
Intermediate Macroeconomics
0.8
0.9
1
Output and Savings per capita
3. Neoclassical Growth Model
Savings per worker
Output
= f(K/L)
Savings
= s • f(K/L)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Capital-Labor Ratio, K/L
Intermediate Macroeconomics
0.8
0.9
1
3. Neoclassical Growth Model
Investment per worker
Output and Savings per capita
Output
= f(K/L)
Steady
State
Equilibrium
Investment
= (n+d) • (K/L)
Slope = n + d
Savings
= s • f(K/L)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Capital-Labor Ratio, K/L
Intermediate Macroeconomics
0.8
0.9
1
3. Neoclassical Growth Model
Effect of an decrease in population growth rate
Output, Savings, and Investment
per capita
Investment Slope = n + d
gets smaller
Output
= f(K/L)
Investment 1
Investment 2
A
Savings
B
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Capital-Labor Ratio, K/L
Intermediate Macroeconomics
0.8
0.9
1
3. Neoclassical Growth Model
Effect of an decrease in population growth rate
Real GDP per worker, 2000
$120,000
$100,000
$80,000
U.S.
$60,000
$40,000
$20,000
$0
0%
1%
2%
3%
Average population growth rate, 1950-2000
Source: Penn World Tables (http://datacentre.chass.utoronto.ca/pwt/alphacountries.html)
International Monetary Fund, World Economic Outlook databases (www.imf,org).
Intermediate Macroeconomics
4%
3. Neoclassical Growth Model
Effect of an increase in the savings rate
Output, Savings, and Investment per
capita
Savings curve shifts upward
Output
Investment
Savings 2
B
Savings 1
A
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Capital-Labor Ratio, K/L
Intermediate Macroeconomics
0.8
0.9
1
3. Neoclassical Growth Model
Effect of an increase in the savings rate
Output per capita
12
Steady State 2
10
8
6
Steady State 1
4
2
0
0
1
2
3
4
5
6
7
8
9
Growth Rate
Time
Steady State 2
Steady State 1
Time
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10
3. Neoclassical Growth Model
Declining marginal productivity of capital
Output per capita
Output
= f(K/L)
Larger increase in output per
worker with one unit increase in
labor
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Capital-Labor Ratio, K/L
Intermediate Macroeconomics
0.8
0.9
1
3. Neoclassical Growth Model
Rich and Poor Convergence
• Poor countries:
– Low capital-labor ratio
– Each unit of new capital yields larger increase
in output per worker
• Best place to invest is in labor markets
with greatest marginal increase in output
for each new unit of capital.
• Investment and wealth should grow faster
in poor than rich countries.
Intermediate Macroeconomics
4. Neoclassical Growth Model Golden Rule
Summary
• Capital/Labor ratio that maximizes
consumption in steady state.
• Implies an optimal rate of savings – a
country can have too high a rate of
savings.
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4. Neoclassical Growth Model Golden Rule
Consumption
• Consumption is the difference
between output and investment in
steady state.
C=Y-I
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Output and Investment per capita
4. Neoclassical Growth Model Golden Rule
Consumption = Output - Investment
Output
= f(K/L)
Consumption
Investment
= (n+d) • (K/L)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Capital-Labor Ratio, K/L
Intermediate Macroeconomics
0.8
0.9
1
Consumption per capita
4. Neoclassical Growth Model Golden Rule
Consumption per worker
Consumption
Maximum
Consumption
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Capital-Labor Ratio, K/L
Intermediate Macroeconomics
0.8
0.9
1
5. Endogenous Growth Model
• Productivity growth:
– Neoclassical model: productivity growth
is exogenous; i.e., is given to us.
– Endogenous growth model attempts to
explain productivity growth within the
model.
• Marginal productivity of capital:
– Neoclassical model: decreasing
– Endogenous growth model: constant or
even increasing
Intermediate Macroeconomics
5. Endogenous Growth Model
Growth rate of output
• Output is proportional to the level of capital, which
implies non-decreasing marginal productivity of
capital:
Y=α٠K
• The change in output is proportional to the
change in capital:
ΔY = α ٠ ΔK
• The growth rate of output equals the growth rate
of capital:
ΔY = ΔK
Y K
Intermediate Macroeconomics
5. Endogenous Growth Model
Savings = Investment
• Savings = investment:
S=I
• Savings is proportional to output:
S=s٠Y
=s٠α٠K
• Investment equals additions to the level of
capital, ΔK, plus depreciation, d:
I = ΔK + d ٠ K
• Thus,
s ٠ α ٠ K = ΔK + d ٠ K
Intermediate Macroeconomics
5. Endogenous Growth Model
Savings versus Investment
Investment as share of real GDP
Annual averages, 1950 - 2000
35%
Venezuela
25%
Israel
15%
5%
Nicaragua
-5%
-5%
5%
15%
25%
Savings as share of real GDP
Source: Penn World Tables (http://datacentre.chass.utoronto.ca/pwt/alphacountries.html).
Intermediate Macroeconomics
35%
5. Endogenous Growth Model
Growth of output and rate of savings
• Rearrange to solve for the change in the capital
stock:
ΔK = s ٠ α ٠ K - d ٠ K
• Divide both side by K:
ΔK = s ٠ α – d
K
• Substitute into the equation for the growth rate of
output:
ΔY = s ٠ α – d
Y
The growth rate of output is now a
function of the savings rate.
Intermediate Macroeconomics
5. Endogenous Growth Model
Effect of investment rate on GDP growth
Growth rate real GDP per worker
Annual averages, 1950 - 2000
5%
4%
3%
2%
1%
0%
-1%
-5%
5%
15%
25%
Investment as share of real GDP
Source: Penn World Tables (http://datacentre.chass.utoronto.ca/pwt/alphacountries.html).
Intermediate Macroeconomics
35%
6. Government Policies and Economic Growth
Summary
• Policies that promote savings and
investment
– Temporary boost to aggregate growth rates in
simple model. Sustained boost in endogenous
growth model.
– Permanently higher output per worker as long
as higher savings rate is sustained.
– Current consumption sacrificed.
• Policies that raise productivity
– Temporary increase to aggregate growth rates
unless productivity growth rates sustained.
– Sustained increase in output per worker.
– No sacrifice of current consumption.
Intermediate Macroeconomics