technological progress and growth

Chapter 12: Technological Progress and Growth Slide #1Blanchard: Macroeconomics

Technological Progress and GrowthTechnological Progress and Growth

Technological Progress and the Production FunctionTechnological Progress and the Production Function

),( ANKFY 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)



Technological Progress and the Production FunctionTechnological Progress and the Production Function

f(K/AN)

Ou

tpu

t p

er

eff

ec

tiv

e w

ork

er,

Y/A

N

Capital per effective worker, K/AN


Investment sf(K/AN)


Investment, Capital, & Output per Effective WorkerInvestment, Capital, & Output per Effective Worker

Production f(K/AN)

Ou

tpu

t p

er e

ffec

tive

wo

rker

, Y

/AN




Determining the needed to maintain a givenDetermining the needed to maintain a given

AN

I

AN

K

Assume:

Then:

•A population growth rate/yr (gN)

•N grows at same rate as gN

•Rate of technological progress gA

Growth rate of effective labor (AN) = gA + gN

If: gA = 2% & gN = 1%, then AN growth = 3%




AN

I

AN

K

The level of investment needed to maintain :AN

K

KKgg NA ofondepreciati)(

KggK NA )( Or:

Therefore: K is needed to keep K constant




AN

I

AN

K

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

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




AN

I

AN

K

Amount of Investment Needed/Effective Worker to

maintain a constant AN

K

AN

Kgg NA )(



Dynamics of Capital & OutputDynamics of Capital & Output

Investment sf(K/AN)

Production f(K/AN)

Required investment ( + gA + gN)K/ANδ

Ou

tpu

t p

er

eff

ec

tiv

e w

ork

er,

Y/A

N


A

B

(K/AN)o

C

D Observe (K/AN)0:AC > AD

(K/AN)*

AN

Y *




Observations about the Steady State: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




The Characteristics of Balanced GrowthThe Characteristics of Balanced Growth

Growth: rate of

1.2.3.4.5.6.7.

Capital per effective worker 0Output per effective worker 0Capital per worker gA

Output per worker gA

Labor gN

Capital gA+gN

Output gA+gN



The Effects of the Savings RateThe Effects of the Savings Rate

f(K/AN)

Ou

tpu

t p

er

eff

ec

tiv

e w

ork

er,

Y/A

N


A

(K/AN)0

AN

Y

0

( + gA + gN)K/ANδ

s0f(K/AN)

Savings = s0

Steady-state = &

AN

Y

0

AN

Y

0

s1f(K/AN)

(K/AN)1

B

Savings increase to s1

S1f(K/AN)

Steady-state = &

AN

Y

1

AN

Y

1

AN

Y

1



The Effects of an Increase in the Savings RateThe Effects of an Increase in the Savings Rate

Ou

tpu

t, Y

(lo

g s

ca

le)

Time

t

Associated with s0

Associated with s1 > s0

B

slope (gA + gN)

B

A

A

Ca

pit

al,

K (

log

sc

ale

)

Time

t

Associated with s0

Associated with s1 > s0

B

slope (gN + gA)

B

A

A



The Facts of Growth RevisitedThe Facts of Growth Revisited

A ReviewA 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 furtherbehind have been growing faster



The Facts of Growth RevisitedThe Facts of Growth Revisited

Understanding These TrendsUnderstanding These Trends

Determinants of Fast Growth:•Higher rate of technological progress (gA)•Higher level of capital/effective worker (K/AN)

Capital Accumulation vs. Technological Progress



Capital Accumulation vs. Technological ProgressCapital 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

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



The FindingsThe Findings

•1950-1973 high growth of output per capita dueto 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 technologicalprogress

Capital Accumulation vs. Technological ProgressCapital Accumulation vs. Technological Progress



Measurement ErrorMeasurement Error

•Measuring productivity

•Quality changes and inflation

Why has technological progress slowed since themid 1970s?Why has technological progress slowed since themid 1970s?

What do you think…Has the measurement error increased?

What do you think…Has the measurement error increased?



The Rise of the Service SectorThe Rise of the Service Sector

•Limited technological progress in the service sector


The EvidenceThe Evidence




Decreased R&D Spending: The Evidence

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.”

Spending on R&D as a Percentage of GDP




The Findings: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?

What do you think…

Why has the fertility of R&D declined?

technological progress and growth

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