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Figure 10-1
U.S. GDP Since 1890
Aggregate U.S. output has increased by a factor of 43 since 1890.
Source: 1890–1929: Historical Statistics of the United States; 1929–2000: National Income and Product Accounts.
6,400
GDP in billions of 1992 dollars
U.S. GDP
3,200
1,600
800
400
200
1890
Oliver Blanchard
Macroeconomics, 3E
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Table 10-1 The Evolution of Output per Capita in Five Rich Countries
Since 1950
Annual Growth Rate
Output per Capita (%)
Real Output per Capita
(1996 dollars)
1950–1973
1974–2000
1950
2000
2000/1950
France
4.1
1.6
5,489
21,282
3.9
Germany
4.8
1.7
4,642
21,910
4.7
Japan
7.8
2.4
1,940
22,039
11.4
United Kingdom
2.5
1.9
7,321
21,647
3.0
United States
2.2
1.7
11,903
30,637
2.6
Average
4.3
1.8
6,259
23,503
3.7
Source: 1950–1992: Penn World Tables, constructed by Robert Summers and Alan Heston (pwt.econ.upenn.edu).
Extended from 1992 to 2000 by using rates of real GDP growth from the OECD Economic Outlook, and
population growth rates from the IMF International Financial Statistics (IFS). The average in the last line is a simple
(unweighted) average.
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 10-2
Growth Rate of GDP per Capita Since 1950 Versus GDP per Capita in 1950; OECD Countries
Annual growth rate of GDP per capita 1950–1992 (percent)
Countries that had a lower level of output per capita in 1950 have typically grown faster.
Source: See Table 10-1. South Korea, the Czech Republic, Hungary, and Poland are not included because of missing data.
Oliver Blanchard
Macroeconomics, 3E
6
Japan
5
Portugal
4
Greece
Germany
Turkey
3
2
United States
United Kingdom
New Zealand
1
0
4000
8000
GDP per capita in 1950 (1992 dollars)
12000
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 10-4
Growth Rate of GDP per Capita, 1960–1992,Versus GDP per Capita in 1960; OECD, Africa, and Asia.
Annual growth rate of GDP per capita 1960–1992 (percent)
Asian countries are converging to OECD levels. There is no evidence of convergence for African countries.
Source: See Figure 10-2.
Oliver Blanchard
Macroeconomics, 3E
7.5
OECD
Africa
Asia
5.0
2.5
0.0
2.5
0
5000
10000
GDP per capita in 1960 (1992 dollars)
15000
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 10-5
Output and Capital per Worker
Output per worker, Y/N
Increases in capital per worker lead to smaller and smaller increases in output per worker.
D9
C9
Y/N F (K/N , 1)
B9
A9
A
Oliver Blanchard
Macroeconomics, 3E
B
C
Capital per worker, K/ N
D
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 10-6
The Effects of an Improvement in the State of Technology
An improvement in technology shifts the production function up, leading to an increase in output per worker for a given level of capital per worker.
Output per worker, Y/ N
F (K/N , 1)
B9
F (K/N , 1)
A9
A
Capital per worker, K/ N
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 11-1
Capital, Output, and Saving/Investment
Capital
stock
Output/income
Change in
the capital
stock
Saving/investment
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
The Solow Model III: The Steady State
• We are in the steady state when Kt+1 =
Kt .
• Recall: kt+1 − kt = syt − δkt
syt = δkt
sAf (kt) = δkt
sAf (k∗) = δk∗
• Example: Assume Af (k) =
√
k
µ ¶2
√
√
s
s
s k = δk ⇒ = k ⇒ k∗ =
δ
δ
4
Figure 11-2
Capital and Output Dynamics
When capital and output are low, investment exceeds depreciation, and capital increases.
When capital and output are high, investment is less than depreciation and capital decreases.
Output per worker, Y/N
Depreciation per worker
Kt /N
Output per worker
f (Kt /N )
Y */ N
Investment per worker
s f (Kt /N )
B
C
D
A
(K0/ N)
Oliver Blanchard
Macroeconomics, 3E
K */ N
Capital per worker, K/ N
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 11-3
The Effects of Different Saving Rates
Output per worker, Y/N
A country with a higher saving rate achieves a higher level of output per worker in steady state.
Depreciation per worker
Kt /N
Output per worker
f (Kt /N )
Y1/ N
Investment per worker
s1f (Kt /N )
Y0/ N
Investment per worker
s0f (Kt /N )
K0/ N
Oliver Blanchard
Macroeconomics, 3E
K1/ N
Capital per worker, K/ N
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 11-4
The Effects of an Increase in the Saving Rate on Output per Worker
An increase in the saving rate leads to a period of growth until output reaches its new higher steady-state level.
Output per worker, Y/N
(Without technological progress)
Associated with saving rate s1 >s0
Y1/ N
Y0/ N
Associated with saving rate s0
t
Time
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 11-6
The Effects of the Saving Rate on Consumption per Worker in Steady State
An increase in the saving rate leads to an increase, then to a decrease in consumption per worker in steady state.
Consumption per worker, C/N
Maximum steady state
consumption per worker
0
sG
1
Saving rate, s
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
The Solow Model V: Human Capital and
Technological Progress
• Sources of growth
1. Physical Capital Accumulation F (K, N )
2. Human Capital Accumulation F (K, H)
3. Technological Progress F (K, N, A)
• (3): The GDP per effective worker
ŷ = Y /N A = f (K/AN ) = f (k̂)
where k̂ is now capital per effective worker.
• NB: We can use the same graph as before
in k̂ but now if ŷ = Y /AN is constant then
y = Y /N grows as long as A grows.
6
Figure 12-1
Output per Effective Worker Versus Capital per Effective Worker
Output per effective worker, Y/AN
Because of decreasing returns to capital, increases in capital per effective worker lead to smaller and smaller increases in output per effective worker.
f (K/AN)
Capital per effective worker, K/AN
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 12-2
Dynamics of Capital per Effective Worker and Output per Effective Worker
Output per effective worker, Y/AN
Capital per effective worker and output per effective worker converge to constant values in the long run.
Required investment
( gA gN )K/AN
Production
f (K/AN)
(ANY )*
Investment
sf (K/AN)
B
C
D
A
(K/AN)0
(K/AN)*
Capital per effective worker, K/AN
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Table 12-1 The Characteristics of Balanced Growth
Rate of growth of:
1
Capital per effective worker
0
2
Output per effective worker
0
3
Capital per worker
4
Output per worker
5
Labor
6
Capital
gN
gA + gN
7
Output
gA + gN
Oliver Blanchard
Macroeconomics, 3E
gA
gA
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 12-3
The Effects of an Increase in the Saving Rate: I
Output per effective worker, Y/AN
An increase in the saving rate leads to an increase in the steady-state levels of output per effective worker and capital per effective worker.
f (K/AN )
(ANY )
(ANY )
1
( gA gN )K/AN
s1f (K/AN )
0
s0f (K/AN )
(K/AN)0
(K/AN)1
Capital per effective worker, K/AN
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458
Figure 12-4
The Effects of an Increase in the Saving Rate: II
The increase in the saving rate leads to higher growth until the
economy reaches its new, higher, balanced growth path.
B
Capital, K (log scale)
Associated with s1 > s0
A
B
slope (gA gN )
A
Associated with s0
t
Time
B
Output, Y (log scale)
Associated with s1 > s0
A
B
slope (gA gN )
A
Associated with s0
t
Time
Oliver Blanchard
Macroeconomics, 3E
© 2003 Prentice Hall, Inc
Upper Saddle River, NJ 07458