Transcript The Solow Model of Economic Growth

Economic Growth
The World Economy
• Total GDP: $31.5T
• GDP per Capita:
$5,080
• Population Growth:
1.2%
• GDP Growth: 1.7%
The World Economy by Region
Region
GDP
GDP
per cap
Sub-Saharan Africa
$318B $450
2.2%
3.2%
East Asia & Pacific
$1.8T
.9%
6.7%
Middle East & N.
Africa
$693B $2,220 2%
3.2%
Europe & C. Asia
$1.1T
4.7%
South Asia
$655B $450
Latin America
$1.7T
$950
Pop
GDP
Growth Growth
$2,160 .1%
1.7%
4.3%
$3,280 1.5%
-.5%
US vs. Europe
United States
GDP: $10.1T
GPD/Capita: $35,500
Pop Growth: .9%
GDP Growth: 2.1%
European Union
GDP: $6.6T
GDP/Capita: $20,230
Pop Growth: .2%
GDP Growth: .7%
High Income vs. Low Income
Countries
• As a general rule, low income (developing)
countries tend to have higher average rates
of growth than do high income countries
Income vs. Growth
Income
GDP/Capita
Pop
Growth
GDP
Growth
Low
$430
1.7%
4.1%
Middle
$1,840
.9%
3.2%
High
$26,310
.5%
1.3%
High Income vs. Low Income
Countries
• As a general rule, low income (developing)
countries tend to have higher average rates
of growth than do high income countries
• However, this is not always the case
Exceptions to the Rule
Haiti
GDP/Capita: $440
Pop Growth: 1.8%
GDP Growth: -.9%
Hong Kong (China)
GDP/Capita: $24,750
Pop Growth: .8%
GDP Growth: 2.3%
High Income vs. Low Income
Countries
• As a general rule, low income (developing)
countries tend to have higher average rates
of growth than do high income countries
• However, this is not always the case
• So, what is Haiti doing wrong? (Or, what is
Hong Kong doing right?)
Sources of Economic Growth
• Recall, that we assumed three basic inputs
to production
– Capital (K)
– Labor (L)
– Technology (A)
Growth Accounting
Step 1: Estimate capital/labor share
of income
K = 30%
L = 70%
Growth Accounting
Step 1: Estimate capital/labor share
of income
K = 30%
L = 70%
Step 2: Estimate capital, labor, and
output growth
%Y = 5%
%K = 3%
%L = 1%
Growth Accounting
Step 1: Estimate capital/labor share
of income
K = 30%
L = 70%
Step 2: Estimate capital, labor, and
output growth
%Y = 5%
%K = 3%
%L = 1%
Productivity growth will be the
residual output growth after
correcting for inputs
Growth Accounting
Step 1: Estimate capital/labor share
of income
K = 30%
L = 70%
Productivity growth will be the
residual output growth after
correcting for inputs
%A = %Y – (.3)*(%K) – (.7)*(%L)
Step 2: Estimate capital, labor, and
output growth
%Y = 5%
%K = 3%
%L = 1%
Growth Accounting
Step 1: Estimate capital/labor share
of income
K = 30%
L = 70%
Productivity growth will be the
residual output growth after
correcting for inputs
%A = %Y – (.3)*(%K) – (.7)*(%L)
Step 2: Estimate capital, labor, and
output growth
%A = 5 – (.3)*(3) + (.7)*(1)
%Y = 5%
%K = 3%
%L = 1%
= 3.4%
Sources of US Growth
1929 - 1948
1948 - 1973
1973-1982
1982-1997
Output
2.54
3.70
1.55
3.45
Capital
.11
.77
.69
.98
Labor
1.42
1.40
1.13
1.71
Total Input
1.53
2.17
1.82
2.69
Productivity 1.01
1.53
-.27
.76
The Solow Model of Economic
Growth
• The Solow model is basically a “stripped down”
version of our business cycle framework (labor
markets, capital markets, money markets)
– Labor supply (employment) is a constant
fraction of the population ( L’ = (1+n)L )
– Savings is a constant fraction of disposable
income: S = a(Y-T)
– Cash holdings are a constant fraction of income
(velocity is constant)
The Solow Model
• Labor Markets
– (w/p) = MPL(A,K,L)
– L’ = (1+n)L
– Y = F(A,K,L) = C+I+G
The Solow Model
• Labor Markets
– (w/p) = MPL(A,K,L)
– L’ = (1+n)L
– Y = F(A,K,L) = C+I+G
• Capital Markets
– r = (Pk/P)(MPK(A,K,L) – d)
– S = I +(G-T)
– K’ = K(1-d) + I
The Solow Model
• Labor Markets
– (w/p) = MPL(A,K,L)
– L’ = (1+n)L
– Y = F(A,K,L) = C+I+G
• Capital Markets
– r = (Pk/P)(MPK(A,K,L) – d)
– S = I +(G-T)
– K’ = K(1-d) + I
• Money Markets
– M = PY
The Solow Model
• Step #1: Convert everything to per capita
terms (For Simplicity, Technology Growth
is Left Out)
– x = X/L
Properties of Production
• Recall that we assumed
production exhibited
constant returns to scale
• Therefore, if Y = F(K,L),
the 2Y = F(2K,2L)
• In fact, this scalability
works for any constant
Properties of Production
• Recall that we assumed
production exhibited
constant returns to scale
• Therefore, if Y = F(K,L),
the 2Y = F(2K,2L)
• In fact, this scalability
works for any constant
Y = F(K,L)
(1/L)Y = F((1/L)K, (1/L)L)
Y/L = F(K/L, 1) = F(K/L)
y = F(k)
Properties of Production
• Recall that we assumed
production exhibited
constant returns to scale
• Therefore, if Y = F(K,L),
the 2Y = F(2K,2L)
• In fact, this scalability
works for any constant
Y = F(K,L)
(1/L)Y = F((1/L)K, (1/L)L)
Y/L = F(K/L, 1) = F(K/L)
y = F(k)
MPL is increasing in k
MPK is decreasing in k
Labor Markets
• w/p = MPL(k) and MPL is increasing in k
• y = F(k) = c + i + g
• L’ = (1+n)L
Capital Markets
• r = MPK(k) – d with MPK declining in k
• s = i + (g-t) = a(y-t) = a(F(k)-t)
• k’(1+n) = k(1-d) + i
The Solow Model
• Step #1: Convert everything to per capita
terms (For simplicity, Technology Growth is
left out)
– x = X/L
• Step #2: Find the steady state
– In the steady state, all variables are constant.
Steady State Investment
• In the steady state, the capital/labor ratio is
constant. (k’=k)
k’(1+n) = (1-d)k + i
Steady State Investment:
• In the steady state, the capital/labor ratio is
constant. (k’=k)
k’(1+n) = (1-d)k + i
k(1+n) = (1-d)k + i
Steady State Investment
• In the steady state, the capital/labor ratio is
constant. (k’=k)
k’(1+n) = (1-d)k + i
k(1+n) = (1-d)k + i
Solving for i gives is steady state
investment
i = (n+d)k
Steady State Investment n =.20,
d = .10
35
30
25
20
Investment
15
10
5
0
0
10
20
30
40
50
60
70
80
90
100
Steady State Output/Savings
• Given the steady state capital/labor ratio,
steady state output is found using the
production function
y = F(k)
• Recall that MPK is diminishing in k
Steady State Output
500
450
400
350
300
250
200
150
100
50
0
output
0
10
20
30
40
50
60
70
80
90
100
Steady State Net Income (t=100)
500
450
400
350
300
250
200
150
100
50
0
output
net income
0
10
20
30
40
50
60
70
80
90 100
Steady State Savings (a=.05)
500
450
400
350
300
250
200
150
100
50
0
40
35
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90 100
Output
Net income
Savings
In Equilibrium, (g-t)=0.
Therefore, s=i
24
21
18
15
Investment
Savings
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90
100
Steady State
•
•
•
•
In this example, steady state k (which is K/L) is 50.
Steady state investment (i) = steady state savings(s) = 15
Steady state output (y) equals F(50) = 400
Steady state government spending (g) = steady state taxes
(t) = 100
• Steady state consumption = y – g – i = 285
• Steady state factor prices come from firm’s decision rules:
– W/P = MPL(k) , r = MPK(k) – d
• The steady state price level (P) = M/Y
Growth vs. Income
• Suppose that the economy is currently at a capital/labor
ratio of 20.
In Equilibrium, (g-t)=0.
Therefore, s=i
24
21
18
15
Investment
Savings
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90 100
Growth vs. Income
• Suppose that the economy is currently at a capital/labor
ratio of 20.
– Investment = Savings = 7.5. This is higher than the
level of investment needed to maintain a constant
capital stock (6).
– With the extra investment, k will grow.
– As k grows, wages will rise and interest rates will fall.
Growth vs. Income
• Suppose that the economy is currently at a capital/labor
ratio of 20.
– Investment = Savings = 7.5. This is higher than the
level of investment needed to maintain a constant
capital stock (6).
– With the extra investment, k will grow.
– As k grows, wages will rise and interest rates will fall.
• Suppose the economy is at a capital/labor ratio of 70.
In Equilibrium, (g-t)=0.
Therefore, s=i
24
21
18
15
Investment
Savings
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90 100
Growth vs. Income
• Suppose that the economy is currently at a capital/labor
ratio of 20.
– Investment = Savings = 7.5. This is higher than the
level of investment needed to maintain a constant
capital stock (6).
– With the extra investment, k will grow.
– As k grows, wages will rise and interest rates will fall.
• Suppose the economy is at a capital/labor ratio of 70.
– Investment = Savings = 6.5. This is less than the
investment required to maintain a constant capital
stock.
– Without sufficient investment, the economy will shrink.
– As k falls, interest rates rise and wages fall.
Growth vs. Income
• Poor (developing) countries (low capital/income ratio) are
below their eventual steady state. Therefore, these
countries should be growing rapidly
• Wealthy (developed) countries (high capital/labor ratio) are
at or above their eventual steady state. Therefore, these
countries will experience little or no growth.
Growth vs. Income
• Poor (developing) countries (low capital/income ratio) are
below their eventual steady state. Therefore, these
countries should be growing rapidly
• Wealthy (developed) countries (high capital/labor ratio) are
at or above their eventual steady state. Therefore, these
countries will experience little or no growth.
• The implication is that we will all end up in the same place
eventually. This is known as absolute convergence
Growth vs. Income
• Poor (developing) countries (low capital/income ratio) are
below their eventual steady state. Therefore, these
countries should be growing rapidly
• Wealthy (developed) countries (high capital/labor ratio) are
at or above their eventual steady state. Therefore, these
countries will experience little or no growth.
• The implication is that we will all end up in the same place
eventually. This is known as absolute convergence
• So, what’s wrong with Haiti?
Conditional Convergence
• Our previous analysis is assuming that every country will
eventually end up at the same steady state. Suppose that
this is not the case.
For example, suppose that a country experiences a decline
in population growth. How is the steady state affected?
A Decline in Population Growth
24
21
18
15
n=20
Savings
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90
100
A Decline in Population Growth
24
21
18
15
n=20
Savings
n=10
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90
100
Conditional Convergence
• Our previous analysis is assuming that every country will
eventually end up at the same steady state. Suppose that this is
not the case.
For example, suppose that a country experiences a decline in
population growth. How is the steady state affected?
• With a lower population growth, the steady state increases from
50 to 85. With an increase in the steady state, this country finds
itself further away from its eventual ending point. Therefore,
growth increases.
• Conditional convergence states that a country’s growth rate is
proportional to the distance from that county’s steady state
Another Example
• Suppose that savings rate in a country
declines. How is the steady state effected?
A Decline in the Savings Rate
24
21
18
15
a=.05
n=10
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90
100
A Decline in the Savings Rate
24
21
18
15
a=.045
a=.05
n=10
12
9
6
3
0
0
10
20
30
40
50
60
70
80
90
100
Another Example
• Suppose that savings rate in a country
declines. How is the steady state effected?
• With a lower steady state (the steady state
falls from 85 to 75), the country finds itself
closer to its finishing point. Therefore, its
growth rate falls.
Possible Income/Growth
Combinations
Growth
Low
Income
High
Low
Haiti
Dem.Rep.Congo
Niger
Zimbabwe
Angola
Bangladesh
China
Ghana
High
Canada
Great Britain
Germany
France
Hong Kong
USA
S. Korea
Malaysia
Low Income/Low Growth
Countries
• This combination is a symptom of a very low steady state.
Therefore, the solution would be
– Lower Population Growth
– Higher Domestic Savings (Or Open up country to
foreign savings)
Low Income/Low Growth
Countries
• This combination is a symptom of a very low steady state.
Therefore, the solution would be
– Lower Population Growth
– Higher Domestic Savings (Or Open up country to
foreign savings)
• Another possibility could be the existence of barriers to
capital formation
– Encourage enforcement of property rights.
Low Income/Low Growth
Countries
• This combination is a symptom of a very low steady state.
Therefore, the solution would be
– Lower Population Growth
– Higher Domestic Savings (Or Open up country to
foreign savings)
• Another possibility could be the existence of barriers to
capital formation
– Encourage enforcement of property rights.
• Foreign Aid?
High Income/Low Growth
Countries
• These countries are probably nearing their (high) steady
state. Therefore, recommendations would be:
– Consider lowering size/scope of government
– Promote the development of new technologies