Download Capital per effective worker

CHAPTER 12
CHAPTER12
Technological
Progress
and Growth
Prepared by:
Fernando Quijano and Yvonn Quijano
© 2006 Prentice Hall Business Publishing
Macroeconomics, 4/e
Olivier Blanchard
Chapter 12: Technological
Progress and Growth
12-1
Technological Progress
and the Rate of 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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Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Technological Progress
and the Production Function
Let’s denote the state of technology by A and
rewrite the production function as:
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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Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Technological Progress
and the Production Function
 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 (2 K,2 AN )
More generally,
xY  F ( xK , xAN )
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Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Technological Progress
and the Production Function
The relation between output per effective worker
and capital per effective worker is:
Y
 K 
 F
,1

AN
AN 
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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Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Technological Progress
and the Production Function
Figure 12 - 1
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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Interactions Between
Output and Capital
The dynamics of output and capital per worker
involve:
 The relation between output per worker and
capital per worker.
I  S  sY
Dividing both sides by AN, we get
© 2006 Prentice Hall Business Publishing
I
 Y 
 s


AN
AN 
Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Interactions Between
Output and Capital
The dynamics of output and capital per worker
involve:
 The relation between investment per worker
and capital per worker.
Y
I
 K 
 K 
Given that
 f
 sf 
 then

 AN 
 AN 
AN
AN
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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Interactions Between
Output and Capital
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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Interactions Between
Output and Capital
Figure 12 - 2
Dynamics of Capital
per 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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Dynamics of Capital and Output
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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Dynamics of Capital and Output
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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Dynamics of Capital and Output
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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Dynamics of Capital and Output
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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Macroeconomics, 4/e
Olivier Blanchard
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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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Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Dynamics of Capital and Output
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
gA
4
Output per worker
gA
5
Labor
gN
6
Capital
gA + gN
7
Output
gA + gN
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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Dynamics of Capital and Output
On the balanced growth path (equivalently, in
steady state; equivalently, 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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
The Effects of the Saving Rate
Figure 12 - 3
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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Macroeconomics, 4/e
Olivier Blanchard
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The Effects of the Saving Rate
Chapter 12: Technological
Progress and Growth
Figure 12 - 4
The Effects of an
Increase in the
Saving Rate: II
The increase in the
saving rate leads to
higher output growth
until the economy
reaches its new,
higher, balanced
growth path.
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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
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.
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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Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
The Fertility of the Research Process
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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
The Appropriability
of Research Results
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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Olivier Blanchard
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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, 1932-1956
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Chapter 12: Technological
Progress and Growth
12-3
The Facts of
Growth Revisited
Recall from Chapter 10 that we looked at growth
in rich countries since 1950, and we identified
three main facts:
 Sustained growth, especially from 1950 to the
mid-1970’s
 A slowdown in growth starting in the mid1970’s
 Convergence: Countries that were further
behind have been growing faster
Keep this in mind as we look ahead.
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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Capital Accumulation Versus
Technological Progress
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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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Capital Accumulation Versus
Technological Progress
Table 12-2
Average Annual Rates of Growth of Output per Capita
and of Technological Progress in Five Rich
Countries, 1950-2000
Rate of Growth of Output per
Worker (%)
Rate of Technological Progress
(%)
1950-1973
(1)
1973-2000
(2)
Change
(3)
1950-1973
(4)
1973-2000
(5)
Change
(6)
France
4.8
2.1
-2.7
5.3
1.6
-3.7
Japan
7.1
2.1
-5.0
7.0
1.4
-5.6
United Kingdom
3.4
1.7
-1.7
3.7
1.9
-1.8
United States
2.7
1.2
-1.5
2.9
1.4
-1.5
Average
4.5
1.8
-2.7
4.7
1.6
-3.1
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Macroeconomics, 4/e
Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Capital Accumulation Versus
Technological Progress
Table 12-2 illustrates three main facts:
1. The period of high growth of output per
capita, from 1950 to 1973, was due to rapid
technological progress, not to unusually high
capital accumulation.
2. The slowdown in growth of output per capita
since 1973 has come from a decrease in the
rate of technological growth, not from
unusually low capital accumulation.
3. Convergence of output per capita across
countries has come from higher technological
progress rather than from faster capital
accumulation.
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Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
Fluctuation in the Pace of
Technological Progress
Why did technological progress slow down in the
mid-1970s? The truth is that, despite a large
amount of research, this slowdown remains
largely a mystery.
One hypothesis is that there was a general
decline in R&D, which led to lower technological
progress.
Another hypothesis is that the decline was not in
the amount but in the fertility of R&D.
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Olivier Blanchard
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Chapter 12: Technological
Progress and Growth
12-4
Institutions and Growth
Figure 12 - 5
Protection from
Expropriation and
GDP per Capita
There is a strong
positive relation
between the degree
of protection from
expropriation and the
level of GDP per
capita.
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Chapter 12: Technological
Progress and Growth
The New Economy and
Productivity Growth
Figure 1
Moore’s Law, Number
of Transistors per
Chip, 1970-2000
Moore’s Law
predicts that the
number of
transistors in a
chip would
double every 1824 months.
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Chapter 12: Technological
Progress and Growth
The Importance of
Institutions: North and South
Korea
Figure 1
PPP GDP per
Capita, North and
South Korea,
1950-1998
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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
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 appropriability
 patents
 Moore’s Law
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