Transcript Chapt7-8

Class Slides for EC 204
Spring 2006
To Accompany Chapters 7-8
The Solow Growth Model
The Supply of Goods and the Production Function:
Y = F(K, L)
(constant returns to scale)
Y/L = F(K/L, 1)
y = f(k) where y = Y/L and k = K/L
MPK = f(k +1) - f(k)
The Demand for Goods and the Consumption
Function:
y = c+ i
c = (1- s)y
y = (1- s)y + i
i = sy
Growth in the Capital Stock and
the Steady State:
i = sf(k)
Change in Capital Stock = Investment - Depreciation
k
=
i
-
k
k = sf(k) - k
At the Steady State : k = 0
This will happen at a particular value of k
= k*
The Golden Rule Steady State
Golden Rule Maximizes the Level of Consumption per Worker
We compare different Steady States to decide which
one achieves this.
y = c+ i
c = y-i
c* = f(k*) - k *
Take derivative w.r.t. k* : f' (k*) -  = 0
Implies that we choose the k * where MPK = 
Economy has Too Much Capital
Economy has Too Little Capital
Allowing for Population Growth
in the Solow Model
Growth Rate of Population : n = L/L
Roughly 0.01 for the United States (i.e., 1% a year)
Determining Steady State:
k = i - ( + n)k
Think of (  + n)k as the " break - even" level of investment
Thus,
k = sf(k) - ( + n)k
k = 0 when k = k *
What is the Golden Rule Steady State?
c = y-i
c* = f(k*) - ( + n)k *
MPK = ( + n) or MPK -  = n
Population Growth versus Labor Force
Growth
• Really should have growth of labor force in
model rather than population growth
• But if the labor force participation rate is
stable over time, then
• Population growth equals labor force
growth
• Take a look at the data:
Labor Force Participation
90
Percent of Population
80
Male
70
Total
60
50
Female
40
30
20
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Labor Force Participation
• Overall rate has increased steadily over the
past half century
• Men’s participation rate has dropped
sharply
• Women’s participation rate has increased
• What about older workers?
Labor Force Participation Age 65 and
Over
50
Percent of Population
45
40
35
Male
30
25
20
15
10
Female
5
0
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Per Capita Personal Income as a Percentage of
U.S. Average By Region
170
150
Far West
130
110
New
England
Southwest
Rocky Mt.
Mideast
90
Plains
70
Southeast
Great Lakes
50
1929 1934 1939 1944 1949 1954 1959 1964 1969 1974 1979 1984 1989 1994 1999
Allowing for Technological Progress
in the Solow Model
Production Function : Y = F(K, L  E)
where E is the " efficiency of labor."
We can view E as capturing the improvement in
labor productivity over time.
(L  E) measures the number of " effective workers."
Need to rewrite the production function in terms
of effective labor units :
Y/LE = F(K/LE, 1)
y = f(k) where y = Y/LE and k = K/LE
Assume that technological progress causes E to grow
at a constant rate per year : E/E = g
We call " g" the rate of labor - augmenting
technological progress.
Because the labor force (L) is growing at rate "
the number of " effective workers" (L  E)
is growing at rate n + g.
n,"
Determining Steady State:
k = i - ( + n + g)k
Think of (  + n + g)k as
the " break - even" level of investment.
Thus,
k = sf(k) - ( + n + g)k
k = 0 when k = k *
What is the Golden Rule Steady State?
c = y-i
c* = f(k*) - ( + n + g)k *
MPK = ( + n + g) or
MPK -  = n + g
Does the U.S. Have Too Much
or Too Little Capital?
Too Much Capital Implies : MPK -  < n + g
Too Little Capital Implies : MPK -  > n + g
Four Facts for U.S :
1. Real GDP grows an average of 3% per year
2. k = 2.5y
3. k = 0.1y
4. MPK  k = 0.3y
Thus,
(n +g) = 0.03
 = k/k = (0.1y)/(2.5y) = 0.04
MPK = (MPK  k)/k = (.03y)/(2.5y) = 0.12
Plug in to show that MPK -  = 8 percent per year
which is greater than (n +g) = 3 percent per year.
So, U.S. has too little capital and should save
more to reach Golden-Rule steady state
Policies to Promote Growth
According to Golden Rule the U.S. Capital Stock is too small.
1. Increase Saving Rate: Public and Private Saving
2. Allocate More Efficiently Economy’s Investment
3. Encourage Technological Progress
Worldwide Slowdown in Economic Growth
Growth rate fell sharply in early 1970s worldwide and remained low.
Slowdown in growth was due to a slowdown in total factor
productivity growth--closely related to the efficiency of labor
in Solow Model.
Real income in the United States today is about 20 percent lower
the it would have been if the slowdown had not occurred.
Recently, some economist believe that productivity growth has
picked up and that the long-run growth of the economy is now again
close to what it was before the slowdown.
Reasons for the Slowdown
1. Measurement Problems--but would have to have gotten worse
over time.
2. Oil Prices--timing is correct, yet magnitude and 1986 drop?
3. Worker Quality--demographics and social norms lead
to less experienced workforce. Also, educational attainment not
increasing as fast as in past and quality of education may be lower.
4. Depletion of Ideas--1950s and 1960s were unusual, had a
backlog of ideas that hadn’t been implemented fully due to
depression and war. Growth from 1870-1950 not much different!
Information Technology and the
“New Economy”
Took some time for computers to be used effectively
Similar to electric motor in late 19th-early 20th
centuries
Three channels:
1. Direct productivity gains in computer sector
2. Accumulation of “info-technology” capital
3. Indirect productivity gains in other sectors
Testing the Solow Model’s
Predictions
• Balanced growth: Y/L and K/L have grown at about 2
percent per year over last half century, so Y/K ratio
roughly constant; real wages grow at about 2 percent
rate while real rental approximately constant
• Convergence: Across regions of U.S.; Conditional
convergence across countries
• Factor Accumulation versus Production Efficiency:
Both matter for growth
Accounting for the Sources of Growth
Y = AF(K, L)
Y = A  F(K, L)  MPK  K  MPL  L
A
K
L
Y =
 AF(K, L)  MPK  K
 MPL  L
A
K
L
A
K
L
Y =
 Y  MPK  K
 MPL  L
A
K
L
Y A
MPK  K K MPL  L L
=




Y
A
Y
K
Y
L
Y A
K
L


 (1  )
Y
A
K
L
Table 1 Contributi ons to Growt h of Real Outp ut in Nonfarm B usiness Sector, 19741999 (annu al percent change)
Growth Rate of Output
Contribution from:
Capital
Info rmation Techno logy Capit al
Other Capit al
Labor Hou rs and Qu alit y
Multif actor Produc tivity
Multif actor Produc tivity in Comput er Sector plus
Computer-rela ted Semi conduc tor Sector
Multif actor Produc tivity in O ther Sectors
1974-90 1991-95 1996-99
3.06
2.75
4.82
1.35
0.49
0.86
1.38
0.33
0.17
1.01
0.57
0.44
1.26
0.48
0.23
1.85
1.10
0.75
1.81
1.16
0.49
0.16
0.25
0.67
Sour ce: Tables 1 and 4 in Stephen D. Oli ner and Dan iel E. Siche l, “The Resurgenc e of
Growth in the Late 1990s: Is Info rmation Techno logy the Story?” Journal of Economic
Perspectives, Volume 14, Number 4, Fal 2000.
Endogenous Growth Theory
Y = AK
K = sY - K
Y/Y = K/K = sA - 
If sA is greater than  , then economy
grows forever even without assuming
exogenous technological progress.