1. Technological Progress and Growth
Technological Progress and the Production Function
AN = Effective Labor. Assuming:
Constant returns to scale
Given state of technology
2Y = F(2K,2AN)
xY = F(xK,xAN)
Y/AN = f(K/AN)

2. Technological Progress and Growth
Technological Progress and the Production Function
f(K/AN)
Output per effective worker, Y/AN
Capital per effective worker, K/AN

3. Technological Progress and Growth
Investment, Capital, & Output per Effective Worker
Production
f(K/AN)
Investment
sf(K/AN)
Output per effective worker, Y/AN
Capital per effective worker, K/AN

4. Technological Progress and Growth
Determining the needed to maintain a given
Assume:
A population growth rate/yr (gN)
N grows at same rate as gN
Rate of technological progress gA
Then:
Growth rate of effective labor (AN) = gA + gN
If: gA = 2% & gN = 1%, then AN growth = 3%

5. Technological Progress and Growth
Determining the needed to maintain a given
The level of investment needed to maintain :
Or:
Therefore:
is needed to keep K constant

6. Technological Progress and Growth
Determining the needed to maintain a given
For Example:
If: , then investment = 10% of K to maintain K
And: (gA + gN)K is needed to ensure K increases at the same rate as AN
Required Investment to maintain K/AN = (d + gA + gN)K

7. Technological Progress and Growth
Determining the needed to maintain a given
Amount of Investment Needed/Effective Worker to maintain a constant

8. Technological Progress and Growth
Dynamics of Capital & Output
Production
f(K/AN)
Required investment
( + gA + gN)K/AN
(K/AN)* *
Investment
sf(K/AN) A B
(K/AN)o
Output per effective worker, Y/AN C D
Observe (K/AN)0:
AC > AD
Capital per effective worker, K/AN

9. Technological Progress and Growth
Dynamics of Capital & Output
Observations about the Steady State:
Growth rate of Y = growth rate of AN
AN growth rate = (gA + gN)
Y growth rate = (gA + gN) independent of s
K growth rate = (gA + gN)
Y/N growth rate = gA

10. Technological Progress and Growth
Dynamics of Capital & Output
The Characteristics of Balanced Growth
Growth: rate of 1. 2. 3. 4. 5. 6. 7.
Capital per effective worker 0
Output per effective worker 0
Capital per worker gA
Output per worker gA
Labor gN
Capital gA+gN
Output gA+gN

11. Technological Progress and Growth
The Effects of the Savings Rate
f(K/AN)
Output per effective worker, Y/AN
Capital per effective worker, K/AN A
(K/AN)0
( + gA + gN)K/AN
s0f(K/AN)
Savings = s0
Steady-state =
&
s1f(K/AN)
(K/AN)1 B
Savings increase to s1
S1f(K/AN)
Steady-state =
& 1

12. Technological Progress and Growth
The Effects of an Increase in the Savings Rate
Capital, K (log scale)
Time t
Associated with s0
Associated
with s1 > s0 B
slope (gN + gA) A
Output, Y (log scale)
Time t
Associated with s0
Associated
with s1 > s0 B
slope (gA + gN) A

13. Technological Progress and Growth
The Facts of Growth Revisited
A Review
Observations on growth in developed countries since 1950:
Sustained growth 1950-mid 1970s
Slowdown in growth since the mid 1970s
Convergence: countries that were further behind have been growing faster

14. Technological Progress and Growth
The Facts of Growth Revisited
Understanding These Trends
Capital Accumulation vs. Technological Progress
Determinants of Fast Growth:
Higher rate of technological progress (gA)
Higher level of capital/effective worker (K/AN)

15. Technological Progress and Growth
Capital Accumulation vs. Technological Progress
Average is a simple average of the growth rates in each column. Germany refers to West Germany only.
Growth of Output per Capita Rate of Technological Progress
Change Change (1) (2) (3) (4) (5) (6)
France
Germany
Japan
United Kingdom
United States
Average

16. Technological Progress and Growth
Capital Accumulation vs. Technological Progress
The Findings
high growth of output per capita due to technological progress
Since 1973 slowdown in growth of output per capita due to a decrease in the rate of technological progress
Convergence is the result of technological progress

17. Technological Progress and Growth
Why has technological progress slowed since the mid 1970s?
Measurement Error
Measuring productivity
Quality changes and inflation
What do you think… Has the measurement error increased?

18. Technological Progress and Growth
Why has technological progress slowed since the mid 1970s?
The Rise of the Service Sector
Limited technological progress in the service sector
The Evidence

19. Technological Progress and Growth
Why has technological progress slowed since the mid 1970s?
Decreased R&D Spending: The Evidence
France
Germany
Japan
United Kingdom
United States
Source: Kumiharu Shigehara, “Causes of Declining Growth in Industrialized Countries.”
Spending on R&D as a Percentage of GDP

20. Technological Progress and Growth
Why has technological progress slowed since the mid 1970s?
The Findings:
The proximate reason for the decline in the rate of technological progress is a decline in fertility of R&D
What do you think…
Why has the fertility of R&D declined?