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.

 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, and on the state of technology.

 Technological progress reduces the number of workers needed to achieve a given amount of output.
 Technological progress increases AN , which we can define as the amount of effective labor in the economy.
 With constant returns to scale,

)

 As in the previous framework, the relation between output per effective worker and capital per effective worker is:
Y
AN
 f


K
AN



Output per
Effective
Worker
Versus
Capital per
Effective
Worker

 We now relax the two assumptions we used before (in Chapter 11):
1. The number of workers (the population) is growing at a constant (exogenous) rate.
2. Technology is improving at a constant
(exogenous) rate.

Interactions Between
Output and Capital In a Steady State
 The amount of investment per effective worker needed to maintain a constant level of capital per effective worker is
(
  g
A
 g
N
)
K
AN
As before, in the steady state, this expression will equal investment
(per effective worker)

Dynamics of Capital per
Worker and
Output per
Effective
Worker

In the steady state:
 Output per effective worker is constant.
 Output per worker grows at a rate (
N
).
g
A
).
 Output growth equals ( g
A
+ g
 The growth rate of output in the steady state is independent of the saving rate.
 Capital and effective labor also grows at a rate equal to ( g
A
+ g
N
).
 Because output, capital, and effective labor all grow at the same rate, ( g
A
+ g
N
), the steady state of the economy is also called a state of balanced growth .

The Characteristics of the Steady State
Rate of growth of:
1 Capital per effective worker
2 Output per effective worker
3 Capital per worker
4 Output per worker
5 Labor
6 Capital
7 Output
Chap. 12
0
0 g
A g
A g
N g
A
+ g
N g
A
+ g
N
Chap. 11
0
0
0
0
0

The Determinants of
Technological Progress
 Technological progress in modern economies is the result of research and development (R&D) activities.
 Private 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.

The Fertility of Research
 The determinants of fertility include:
– The interaction between basic research and applied research.
– The institutional environment: education levels, firms characteristics, legal frameworks, etc.
– Time: It might take many years for the full potential of major discoveries to be realized.

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?
– 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.

Capital Accumulation Versus
Technological Progress
Average Annual Rates of Growth of Output per Capita and of Technological Progress
Growth of Output per Capita
1950-73
(1)
1973-87
(2)
Change
(3)
Rate of Technological
Progress
1950-73
(4)
1973-87
(5)
Change
(6)
France
Germany
Japan
United
Kingdom
United States
4.0
4.9
8.0
2.5
2.2
1.8
2.1
3.1
1.8
1.6

2.2

2.8

4.9

0.7

0.6
4.9
5.6
6.4
2.3
2.6
2.3
1.9
1.7
1.7
0.6

2.6

3.7

4.7

0.6

2.0

Capital Accumulation Versus
Technological Progress
 The table illustrates three main facts:
1. The earlier period of high growth of output per capita was due to rapid technological progress.
2. The slowdown in growth of output per capita since 1973 has come from a decrease in the rate of technological progress.
3. Convergence of output per capita across the rich countries has come from higher technological progress rather than from faster capital accumulation.

France
Spending on R&D as a Percentage of GDP
Germany
Japan
United Kingdom
United States
1963
1.6
1.4
1.5
2.3
2.7
1975
1.8
2.2
2.0
2.0
2.3
1989
2.3
2.9
3.0
2.3
2.8

 We still cannot explain well enough why some countries grow more than others.
 There seem to be many different reasons for the vastly different growth performances across countries (and to a lesser extent across time).