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MACROECONOMICS
UNDERSTANDING THE GLOBAL ECONOMY
Capital Accumulation and Economic
Growth
1
Copyright © 2012 John Wiley & Sons, Inc. All rights reserved.
4-2
Key Concepts
 Definition of Capital and Investment
 Decreasing Marginal Return
 Convergence in Rates of Growth
 The Steady State
 The Golden Rule
4-3
Growth Transitions
Labor Growth
Capital Growth
TFP Growth
4-4
Real GDP
(billions of 1996 $)
Decreasing marginal product
An increase in the
quantity of labor But growth
increases Real
rate
GDP
decreases
as labor
increases
15
12
6
500 1000
1500
Labor Hours
4-5
Real GDP
(billions of 1996 $)
Decreasing marginal product
An increase in the
quantity of capital But growth
increases Real
rate
GDP
decreases
as capital
increases
15
12
6
500 1000
1500
Quantity of Capital
4-6
Capital (K)
 Total value of the machines and buildings used to produce output
 Capital depreciates (wears out)


Assume constant rate of depreciation, d
Assume depreciation is fraction of capital stock, d*K
4-7
GDP per capita versus capital
stock per worker in 1990
4-8
Capital growth and GDP growth,
1965–90.
4-9
Diminishing Marginal Return
 Growth will be fast when level of capital is low
 Growth slows down as capital accumulates
 Eventually, firms won’t add new capital – firms
only replace depreciated capital
 Economy reaches a
Steady State
4-10
Optimal Investment
 Value of new capital is
(Marginal Product) x (Price of Output)
 Suppose 6 x $2 = $12
 Cost of new capital
 Denoted by “r”
 Suppose r = $12
 Purchase new capital if
 MP x Price of output= r

MP  Price of Output  r
4-11
Marginal product of capital
Decreasing Marginal Product of
Capital
Marginal Product = r/p
Cost of Capital, r/p
Marginal Product
Capital Stock
4-12
Firms will cease to add capital when marginal
return is less than the marginal cost…
Real GDP
(billions of 1996 $)
Stop here if r > 3.75%
$15
$12
$6
$80 $160
$240
Capital
(billions of 1996 $)
4-13
Comments on interest rates (R)
 What determines the interest rate?

Interaction of savings and investment
 Effect of changes in the interest rate


High interest rate economy is a low capital
economy
Low interest rate economy is a high capital
economy
4-14
Determination of R
Interest Rate
Savings
R0
Investment
I0
Output
4-15
Real GDP
(billions of 1996 $)
Effect of TFP growth
$20
$12
$6
$80 $160
$240
Capital
(billions of 1996 $)
4-16
Determination of R
Interest Rate
Savings
R1
R0
Investment
I0
I1
Output
4-17
Steady State
Real GDP
Output
C+G+X-M
Investment
Investment (20% of GDP)
Capital Stock
4-18
Steady State
Real GDP
Investment = Depreciation
Output
Depreciation
= d x Capital Stock
Investment
Capital Stock
4-19
Investment exceeds depreciation;
capital stock must decline
Output
Real GDP
Depreciation
Investment
KLow
Kss
KHigh
Capital Stock
4-20
Depreciation exceeds investment;
capital stock must increase
Output
Real GDP
Depreciation
Investment
KLow
Kss
KHigh
Capital Stock
4-21
Increase in Investment Rate
Output
Real GDP
Depreciation
Investment (30% of GDP)
Investment (20% of GDP)
K20%
K30%
Capital Stock
4-22
Investment Rate
The higher the investment rate of a country, the
greater the steady state capital stock and its
output level
4-23
The Golden Rule Level of Capital
 Depreciation = d x Capital Stock
 “d” is a technological parameter
 NIPA
 3% for structures
 8% for equipment
 New Capital = Investment – d x K
 Steady State
 Because of diminishing returns, will reach point where
increases in capital stock don’t pay off
 Investment = d*K
4-24
The Golden Rule
 Make consumption as high as possible

(ignore G and X-M for the moment)
Steady State Investment = d x K
Real GDP
Output
C
I
Ks
Capital Stock
4-25
The Golden Rule
 Make consumption as high as possible

(ignore G and X-M for the moment)
Steady State Investment = d x K
Real GDP
Output
Maximize this
C
I
Ks
Capital Stock
4-26
The Golden Rule
 Note: C is getting smaller as K increases to K1
Real GDP
Steady State Investment = d x K
Output
C
I
K0
K1
Capital Stock
4-27
The Golden Rule
 Note: C is getting smaller as K decreases to K2
Real GDP
Steady State Investment = d x K
Output
C
I
K2 K0
Capital Stock
4-28
Golden Rule
 Capital stock is too high


Output is used to maintain an overly-large
capital stock
Consumption is low
 Capital stock is too low


Output is used to support consumption
Capital is too low to produce sufficient output
4-29
Golden Rule
Marginal Product of Capital = Rate of Depreciation
Cobb – Douglas parameter (a) = Savings Rate
4-30
The Golden Rule
d = MPK
Steady State Investment = d x K
Real GDP
Output
C
I
Ks
Capital Stock
4-31
The Golden Rule
 What level of capital might a free market
choose?
 Are there forces that keep a country away
from the Golden Rule?
4-32
Investment & Depreciation
25%
Investment/GDP
Depreciation/GDP
20%
15%
10%
5%
0%
Canada
France Germany
Italy
Japan
UK
US
4-33
Convergence in real GDP per
capita in Europe, 1820–2010.
32000
France
16000
Germany
Italy
UK
8000
4000
2000
1000
4-34
Investment as a share of GDP
(1980-2009)
Country
Investment
Rate
Country
Investment
Rate
Country
Investment
Rate
Argentina
19.0
Germany
20.9
Spain
24.1
Australia
24.5
India
23.8
Sweden
18.8
Brazil
22.5
Israel
20.5
U.K.
17.4
Canada
20.6
Italy
21.1
U.S.
18.5
Chile
20.8
Japan
27.1
Zambia
15.4
China
33.7
Mexico
19.9
Low Income
17.9
Congo
11.3
Russia
20.5
Middle Income
24.0
Egypt
22.0
Singapore
33.9
High Income
21.2
France
19.9
S. Africa
19.0
World
21.7
4-35
The Demographic Transition
Child dependency ratio
Old Age dependency ratio
Death Rate
Birth Rate
Stage 1
Stage 2
Stage 3
Stage 4
Falling death rates and birth rates associated with
improved health can lead to a temporary fall in
the overall dependency ratio.
4-36
China and Europe, GDP per capita
51200
Western Europe
25600
China
GDP per capita
12800
6400
3200
1600
800
400
200
400
600
800
1000 1200 1400 1600 1800 2010
Year
4-37
Chinese Demographic Transition
90%
Old age dependency ratio
80%
Child dependency ratio
70%
Gross domestic savings % of GDP
60%
50%
40%
30%
20%
10%
0%
4-38
Chinese investment rate
50%
40%
30%
20%
10%
0%
4-39
Growth Accounting for China
4-40
Inequality in China
0.5
0.4
0.3
0.2
National pre 2002
0.1
National 2002 and after
Income inequality has risen in China
2007
2005
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
0
4-41
Regional Inequality in China
4-42
Summary
 Marginal Product of Capital
 Implications of decreasing MPK
 Role in determining Steady State
 Steady State Investment
 Investment = Depreciation
 Growth can no longer be achieved through investment
 Golden Rule
 Demographic Transition
 China’s Growth Miracle
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