Download Capital per effective worker

12-1 Technological Progress
and the Rate of Growth
Technological Progress and the Production Function
Chapter 12: Technological Progress and Growth
Technological progress has many dimensions. It may mean:

Larger quantities of output

Better products

New products

A larger variety of products
Technological progress leads to increases in output for given
amounts of capital and labor.
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12-1 Technological Progress
and the Rate of Growth
Technological Progress and the Production Function
Let’s denote the state of technology by A and rewrite
the production function as:
Chapter 12: Technological Progress and Growth
Y  F ( K, N , A)
(+ + +)
A more restrictive but more convenient form is
Y  F ( K, AN )
Output depends on both capital and labor (K and N),
and on the state of technology (A).
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12-1 Technological Progress
and the Rate of Growth
Technological Progress and the Production Function
Chapter 12: Technological Progress and Growth
 Technological progress reduces the number of workers needed
to achieve a given amount of output.
 Technological progress increases AN, which we can think of as
the amount of effective labor, or labor in “efficiency units” in
the economy.
With constant returns to scale,
2Y  F (2K , 2 AN )
More generally,
xY  F ( xK , xAN )
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12-1 Technological Progress
and the Rate of Growth
Technological Progress and the Production Function
Chapter 12: Technological Progress and Growth
The relation between output per effective worker and
capital per effective worker is:
Y
 K
 F
,
AN
 AN

1

which we can redefine as
Y
 K 
 f

AN
 AN 
In words: Output per effective worker is a function of
capital per effective worker.
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12-1 Technological Progress
and the Rate of Growth
Technological Progress and the Production Function
Figure 12 - 1
Chapter 12: Technological Progress and Growth
Output per Effective
Worker versus Capital
per Effective Worker
Because of decreasing returns
to capital, increases in capital
per effective worker lead to
smaller and smaller increases
in output per effective worker.
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12-1 Technological Progress
and the Rate of Growth
Interactions between Output and Capital
The dynamics of output and capital per worker involve:
Chapter 12: Technological Progress and Growth
 The relation between output per worker and capital per worker.
I  S  sY
Dividing both sides by AN, we get
I
 Y 
 s


AN
AN 
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12-1 Technological Progress
and the Rate of Growth
Interactions between Output and Capital
The dynamics of output and capital per worker involve:
Chapter 12: Technological Progress and Growth
 The relation between investment per worker and capital per
worker.
Given that
Y
 K  then, I
 K 
 f
 sf 


 AN 
 AN 
AN
AN
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12-1 Technological Progress
and the Rate of Growth
Interactions between Output and Capital
Chapter 12: Technological Progress and Growth
The dynamics of output and capital per worker involve:
 The relation between depreciation per worker—equivalently, the
investment per worker needed to maintain a constant level of
capital per worker—and capital per worker.
K  ( g A  g N ) K
or equivalently
(  g A  g N ) K
The amount of investment per effective worker needed to
maintain a constant level of capital per effective worker is
K
(  g A  g N )
AN
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12-1 Technological Progress
and the Rate of Growth
Interactions between Output and Capital
Chapter 12: Technological Progress and Growth
Figure 12 - 2
The Dynamics of Capital
per Effective Worker and
Output per Effective
Worker
Capital per effective worker
and output per effective worker
converge to constant values in
the long run.
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12-1 Technological Progress
and the Rate of Growth
Chapter 12: Technological Progress and Growth
Interactions between Output and Capital
This figure focuses on
output, capital, and
investment per effective
worker, rather than per
worker:
 Output per effective
worker increases with
capital per effective
worker, but at a
decreasing rate.
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12-1 Technological Progress
and the Rate of Growth
Chapter 12: Technological Progress and Growth
Interactions between Output and Capital
This figure focuses on
output, capital, and
investment per effective
worker, rather than per
worker:
 The relation between
investment per
effective worker and
capital per effective
worker is drawn as
the upper curve,
multiplied by the
saving rate, s.
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12-1 Technological Progress
and the Rate of Growth
Chapter 12: Technological Progress and Growth
Interactions between Output and Capital
This figure focuses on
output, capital, and
investment per effective
worker, rather than per
worker:
 Finally, now that we
allow for technological
progress (so A
increases over time),
the number of
effective workers (AN)
increases over time.
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12-1 Technological Progress
and the Rate of Growth
Dynamics of Capital and Output
Chapter 12: Technological Progress and Growth
We can now give a graphical description of the dynamics of capital
per effective worker and output per effective worker:
Because actual investment exceeds the investment level
required to maintain the existing level of capital per effective
worker, K/AN increases.
Starting from (K/AN)0, the economy moves to the right, with
the level of capital per effective worker increasing over time.
In the long run, capital per effective worker reaches a constant
level, and so does output per effective worker.
This implies that output (Y) is growing at the same rate as
effective labor (AN).
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12-1 Technological Progress
and the Rate of Growth
Chapter 12: Technological Progress and Growth
Dynamics of Capital and Output
In steady state, output (Y) grows at the same rate as
effective labor (AN); effective labor grows at a rate (gA+gN);
therefore, output growth in steady state equals (gA+gN).
Capital per effective worker also grows at a rate equal to
(gA+gN).
The growth rate of output is independent of the saving rate.
Because output, capital, and effective labor all grow at the
same rate, (gA+gN), the steady state of the economy is also
called a state of balanced growth.
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12-1 Technological Progress
and the Rate of Growth
Dynamics of Capital and Output
Table 12-1
The Characteristics of Balanced Growth
Chapter 12: Technological Progress and Growth
Rate of growth of:
1
Capital per effective worker
0
2
Output per effective worker
0
3
Capital per worker
gA
4
Output per worker
gA
5
Labor
gN
6
Capital
gA + gN
7
Output
gAW + gN
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12-1 Technological Progress
and the Rate of Growth
Dynamics of Capital and Output
Chapter 12: Technological Progress and Growth
On the balanced growth path (equivalently: in steady state,
or in the long run):
 Capital per effective worker and output per effective
worker are constant.
 Equivalently, capital per worker and output per worker
are growing at the rate of technological progress, gA.
 Or, in terms of labor, capital, and output: Labor is
growing at the rate of population growth, gN; capital
and output are growing at a rate equal to the sum of
population growth and the rate of technological
progress, (gA + gN).
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12-1 Technological Progress
and the Rate of Growth
The Effects of the Saving Rate
Figure 12 - 3
Chapter 12: Technological Progress and Growth
The Effects of an
Increase in the Saving
Rate: I
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.
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12-1 Technological Progress
and the Rate of Growth
The Effects of the Saving Rate
Figure 12 - 4
Chapter 12: Technological Progress and Growth
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.
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12-2 The Determinants of Technological
Progress
“Technological progress” in modern economies is the result
of firms’ research and development (R&D) activities. The
outcome of R&D is fundamentally ideas.
Chapter 12: Technological Progress and Growth
Spending on R&D depends on:
The fertility of the research process, or how spending
on R&D translates into new ideas and new products,
and
the appropriability of research results, or the extent to
which firms benefit from the results of their own R&D.
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12-2 The Determinants of Technological
Progress
The Fertility of the Research Process
Chapter 12: Technological Progress and Growth
The determinants of fertility include:
The interaction between basic research (the search for
general principles and results) and applied research (the
application of results to specific uses).
The country: some countries are more successful at basic
research; others are more successful at applied research
and development.
Time: It takes many years, and often many decades, for
the full potential of major discoveries to be realized.
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Chapter 12: Technological Progress and Growth
Information Technology, the New Economy,
and Productivity Growth
Figure 1 Moore’s Law: Number of Transistors per Chip, 1970 to 2000
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12-2 The Determinants of Technological
Progress
The Appropriability of Research Results
Chapter 12: Technological Progress and Growth
If firms cannot appropriate the profits from the development
of new products, they will not engage in R&D. Factors at
work include:
The nature of the research process. Is there a payoff
in being first at developing a new product?
Legal protection. Patents give a firm that has
discovered a new product the right to exclude anyone
else from the production or use of the new product for
a period of time.
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Chapter 12: Technological Progress and Growth
The Diffusion of New Technology: Hybrid Corn
Figure 1 Percentage of Total Corn Acreage Planted with
Hybrid Seed, Selected U.S. States, 1932 to 1956
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12-3 The Facts of Growth Revisited
Capital Accumulation versus Technological Progress
in Rich Countries since 1950
Chapter 12: Technological Progress and Growth
Fast growth may come from two sources:
 A higher rate of technological progress. If gA is higher,
balanced output growth (gY=gA+gN) will also be higher. In
this case, the rate of output growth equals the rate of
technological progress.
 Adjustment of capital per effective worker, K/AN, to a higher
level. In this case, the growth rate of output exceeds the
rate of technological progress.
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12-3 The Facts of Growth Revisited
Capital Accumulation versus Technological Progress
in Rich Countries since 1950
Chapter 12: Technological Progress and Growth
Table 12-2
Average Annual Rates of Growth of Output per Capita and
Technological Progress in Four Rich Countries since 1950
Rate of Growth of Output per Worker (%)
1950 to 2004
Rate of Technological
Progress (%) 1950 to 2004
France
3.2
3.1
Japan
4.2
3.8
United Kingdom
2.4
2.6
United States
1.8
2.0
Average
2.9
2.9
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12-3 The Facts of Growth Revisited
Capital Accumulation versus Technological Progress
in Rich Countries since 1950
Chapter 12: Technological Progress and Growth
Table 12-2 illustrates two main facts:
First, growth since 1950 has been a result of rapid
technological progress, not unusually high capital
accumulation.
Second, convergence of output per worker across
countries has come from higher technological
progress, rather than from faster capital
accumulation, in the countries that started behind.
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12-3 The Facts of Growth Revisited
Chapter 12: Technological Progress and Growth
Capital Accumulation versus Technological
Progress in China since 1980
Going beyond growth in OECD countries, one of the
striking facts in Chapter 10 was the high growth rates
achieved by a number of Asian countries. This raises
again the same questions we just discussed: Do these
high growth rates reflect fast technological progress, or do
they reflect unusually high capital accumulation?
To answer the questions, I shall focus on China because of
its size and because of the astonishingly high output
growth rate, nearly 10%, it has achieved since the early
1980s.
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12-3 The Facts of Growth Revisited
Capital Accumulation versus Technological
Progress in China since 1980
Chapter 12: Technological Progress and Growth
Table 12-3
Average Annual Rate of Growth of Output per Worker and
Technological Progress in China, 1983 to 2003
Rate of Growth
of Output (%)
9.7
Rate of Growth of
Output per Worker (%)
8.0
Rate of Technological
Progress (%)
8.2
The nature of technological progress is likely to be different in more
and less advanced economies. The more advanced economies,
being by definition at the technological frontier, need to develop
new ideas, new processes, and new products.
It is easier for the less advanced economies to imitate rather than
innovate new technologies. This can explain why convergence,
both within the OECD and in the case of China and other countries,
typically takes the form of technological catch-up.
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Chapter 12: Technological Progress and Growth
Key Terms
 effective labor, or labor in
efficiency units
 balanced growth
 research and development
(R&D)
 fertility of research
 appropriability of research






Information technology revolution
New Economy
Moore’s law
patent
technology frontier
technological catch-up
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