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

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Technological progress and growth

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)


Technological progress and growth1

f(K/AN)

Output per effective worker, Y/AN

Capital per effective worker, K/AN

Technological Progress and Growth

Technological Progress and the Production Function


Technological progress and growth2

Production

f(K/AN)

Investment

sf(K/AN)

Technological Progress and Growth

Investment, Capital, & Output per Effective Worker

Output per effective worker, Y/AN

Capital per effective worker, K/AN


Technological progress and growth3

Determining the needed to maintain a given

Technological Progress and Growth

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%


Technological progress and growth4

Determining the needed to maintain a given

The level of investment needed to maintain :

Or:

is needed to keep K constant

Therefore:

Technological Progress and Growth


Technological progress and growth5

Determining the needed to maintain a given

If: , then investment = 10% of K to maintain K

Technological Progress and Growth

For Example:

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


Technological progress and growth6

Determining the needed to maintain a given

Amount of Investment Needed/Effective Worker tomaintain a constant

Technological Progress and Growth


Technological progress and growth7

Required investment

( + gA + gN)K/AN

Production

f(K/AN)

*

B

Investment

sf(K/AN)

C

Observe (K/AN)0:

AC > AD

D

A

(K/AN)o

(K/AN)*

Technological Progress and Growth

Dynamics of Capital & Output

Output per effective worker, Y/AN

Capital per effective worker, K/AN


Technological progress and growth8
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


Technological progress and growth9

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

Technological Progress and Growth

Dynamics of Capital & Output

The Characteristics of Balanced Growth


Technological progress and growth10

f(K/AN)

B

( + gA + gN)K/AN

0

A

Savings = s0

s1f(K/AN)

Output per effective worker, Y/AN

s0f(K/AN)

1

0

1

Savings increase to s1

S1f(K/AN)

Steady-state =

&

Steady-state =

&

(K/AN)0

(K/AN)1

1

0

Capital per effective worker, K/AN

Technological Progress and Growth

The Effects of the Savings Rate


Technological progress and growth11

Associated

with s1 > s0

Associated

with s1 > s0

B

B

Output, Y (log scale)

Capital, K (log scale)

B

B

A

A

Associated with s0

slope (gA + gN)

slope (gN + gA)

Associated with s0

A

A

t

t

Time

Time

Technological Progress and Growth

The Effects of an Increase in the Savings Rate


Technological progress and growth12
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


Technological progress and growth13
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)


Technological progress and growth14

Growth of Output per Capita Rate of Technological Progress

1950-73 1973-87 Change 1950-73 1973-87 Change (1) (2) (3) (4) (5) (6)

France 4.0 1.8 -2.2 4.9 2.3 -2.6

Germany 4.9 2.1 -2.8 5.6 1.9 -3.7

Japan 8.0 3.1 -4.9 6.4 1.7 -4.7

United Kingdom 2.5 1.8 -0.7 2.3 1.7 -0.6

United States 2.2 1.6 -0.6 2.6 0.6 -2.0

Average 4.3 2.1 -2.2 4.4 1.6 -2.8

Average is a simple average of the growth rates in each column. Germany refers to West Germany only.

Technological Progress and Growth

Capital Accumulation vs. Technological Progress


Technological progress and growth15
Technological Progress and Growth Progress

Capital Accumulation vs. Technological Progress

The Findings

  • 1950-1973 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


Technological progress and growth16
Technological Progress and Growth Progress

Why has technological progress slowed since themid 1970s?

Measurement Error

  • Measuring productivity

  • Quality changes and inflation

What do you think… Has the measurement error increased?


Technological progress and growth17
Technological Progress and Growth Progress

Why has technological progress slowed since themid 1970s?

The Rise of the Service Sector

  • Limited technological progress in the service sector

The Evidence


Technological progress and growth18

Spending on R&D as a Percentage of GDP Progress

1963 1975 1989

France 1.6 1.8 2.3

Germany 1.4 2.2 2.9

Japan 1.5 2.0 3.0

United Kingdom 2.3 2.0 2.3

United States 2.7 2.3 2.8

Source: Kumiharu Shigehara, “Causes of Declining Growth in Industrialized Countries.”

Technological Progress and Growth

Why has technological progress slowed since themid 1970s?

Decreased R&D Spending: The Evidence


Technological progress and growth19
Technological Progress and Growth Progress

Why has technological progress slowed since themid 1970s?

The Findings:

The proximate reason for the decline in the rate oftechnological progress is a decline in fertility ofR&D

What do you think…

Why has the fertility of R&D declined?


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