Economic Growth II: Technology, Empirics, and Policy - PowerPoint Presentation

Slide1

Economic Growth II: Technology, Empirics, and Policy

Chapter

9

of

Macroeconomics

,

8

th

edition, by N. Gregory

Mankiw

ECO62

Udayan

Roy

Slide2

Recap: Solow-Swan, Ch. 7

L

and

K

are used to produce a final good

Y

=

F

(

K

,

L

)

k

=

K

/

L

and

y

=

Y

/

L

=

f

(

k

) are

per worker

capital and output

The population is

P

, but a fraction

u

is not engaged in the production of the final good. Therefore,

L

= (1 –

u

)

P

.

Both

P

and

L

grow at the rate

n

.

A fraction

s

of

Y

is saved and added to capital

A fraction

δ

of

K

depreciates (wears out)

Slide3

Recap: Solow-Swan, Ch. 8

In the long run, the economy reaches a steady state, with constant k and y

Slide4

Recap: Solow-Swan, Ch. 8

In the long run, the economy reaches a steady state, with constant

k

and

y

Like

the

per-worker

variables,

k

and

y

,

per-capita

capital and output are also constant in the long run

Total capital (

K

) and total output (

Y

)

both increase at the rate

n

,

which is the rate of growth of both the number of workers (

L

)

and

the population (

P

)

Slide5

Recap: Solow-Swan, Ch. 8

Variable

Symbol

Steady state behavior

Capital per worker

k

Constant

Income per worker

y

=

f

(

k

)

Constant

Saving and investment per worker

sy

Constant

Consumption per worker

c

= (1

–

s

)

y

Constant

Labor

L

Grows at rate

n

Capital

K

Grows at rate

n

Income

Y

=

F

(

K

,

L

)

Grows at rate

n

Saving and investment

sY

Grows at rate

n

Population

P

Grows at rate

n

Capital per capita

(1 –

u

)

k

Constant

Income per capita

(1 –

u

)

y

Constant

Saving and investment per capita

(1 –

u

)

sy

Constant

Consumption per capita

(1 –

u

)

c

Constant

Slide6

The sad lesson of Solow-Swan

It is an undeniable fact that our standards of living increase over time

Yet, Solow-Swan cannot explain this! Why?

Solow-Swan relies on capital accumulation as the only means of progress

Therefore, the model’s failure to show economic progress indicates that we must introduce some means of progress

other than

capital accumulation

Slide7

Technological Progress

Maybe Solow-Swan fails to show economic progress because there is no technological progress in it

We need to create a theory with technological progress

But how?

Slide8

Technological Progress

A simple way to introduce technological progress into the Solow-Swan model is to

think of

technological progress

as increases in our ability to

multitask

Slide9

Technological Progress

Imagine that both population and the number of workers are constant but that steady increases in the workers’ ability to multitask creates an economy that is

equivalent

to the Solow-Swan economy with steadily increasing population

Slide10

Technological Progress

In such an economy, total output would be increasing—exactly as in the Solow-Swan economy with steady population growth—but

without population growth

That is, under multitasking technological progress, per capita and per worker output would be steadily increasing

In this way, a simple re-interpretation of the Solow-Swan economy gives us what we were looking for—steadily increasing income per worker

Slide11

Efficiency of Labor

Specifically, section

9

−

1 defines a new variable

E

is the

efficiency of labor

Specify some date in the past, say

1984, and arbitrarily set

E

= 1 for 1984.

Let’s say that

technological progress has enabled each worker of 2011 to do the work of 10 workers of 1984.

This implies that

E

= 10 in 2011.

Slide12

Efficiency of Labor

The old production function

F

(

K

,

L

)

no longer applies

to

both

1984 and 2011

Suppose

K

= 4 in both 1984 and 2011

Suppose

L

= 10 in 1984 and

L

= 1 in 2011

The old production function

F

(

K

,

L

) will say that output is larger in 1984

But we know that output is the same in both years because just one worker in 2011 can do the work of 10 workers of 1984

We need a new production function:

F

(

K

,

E

✕

L

)

Slide13

Y = F(K, E ✕ L)

In other words, although the number of human workers is 10 in

1984 and

1 in

2011,

the

effective number of workers

is 10 in both

years,

and that’s what matters in determining the level of output

The effective number of workers is

E

✕

L

Slide14

Efficiency of Labor

Assumption

:

the efficiency of labor grows at the constant and exogenous rate

g

Slide15

Production

As the production of the final good no longer depends only on the number of workers, but instead depends on the effective number of workers, …

… we replace the production function

Y

=

F

(

K

,

L

) by the

new

production function

Y

=

F

(

K

,

E

✕

L

)

Slide16

From “per worker” to “per effective worker”

Similarly, we will now redefine

k

, which used to be capital per worker (

K

/

L

), as

capital per

effective

worker:

k

=

K

/(

E

✕

L

)

Likewise,

we will now redefine

y

,

which used to be

output per

worker

(

Y

/

L

), as

output per

effective

worker:

y

=

Y

/(

E

✕

L

)

Slide17

From “per worker” to “per effective worker”

As

a result of the redefinition of

k

and

y

,

we still have

y

=

f

(

k

)

, except that the definitions of

y

and

k

are now in “per

effective

worker” form

sy

=

sf

(

k

)

, is now saving (and investment) per

effective

worker

Only the growth rate of effective labor is slightly different

Slide18

From “per worker” to “per effective worker”

In Chapter 8, what mattered in production was

L

, the number of workers, and the growth rate of

L

was

n

Now, however,

what

matters

in production

is

E

✕

L

,

the

effective number

of workers, and the

growth rate of

E

✕

L

=

growth rate of

E

+

growth rate of

L

=

g

+

n

Slide19

From “per worker” to “per effective worker”

Recall from Chapter 8 that the break-even investment per worker was (

δ

+

n

)

k

This will have to be replaced by

the break-even investment per

effective

worker

We can do this by redefining

k

as capital per effective worker (which we have already done) and by replacing

n

by

g

+

n

Therefore,

break-even investment per

effective

worker

is now

(

δ

+

n

+

g

)

k

Slide20

Dynamics: algebra

Ch. 8 No technological change

Ch. 9 Technological Progress

Slide21

Dynamics: graph

As in Ch. 8, in the long run, k and y reach a steady state at k = k* and y = y* = f(k*)

Slide22

Describing the Steady State

We just saw that

k

is constant in the steady state

That is,

k

=

K

/(

E

✕

L

) is constant

Therefore, in terms of growth rates,

k

g

=

K

g

– (

E

g

+

L

g

) =

K

g

–

(

g

+

n

) = 0

Therefore,

the economy’s

total

stock of capital grows at the rate

K

g

=

g

+

n

Slide23

Describing the Steady State

Capital per worker (

K

/

L

) grows at the rate

K

g

–

L

g

=

g

+

n

–

n

=

g

Therefore,

the per-worker capital stock, which was constant in Chapter 8, grows at the rate

g

As each worker’s ability to multitask increases at the rate

g

, the capital used by a worker also increases at that rate

Slide24

Describing the Steady State

y

=

f

(

k

) is constant in the steady state

That is,

y

=

Y

/(

E

✕

L

) is constant

Therefore, in terms of growth rates,

y

g

=

Y

g

– (

E

g

+

L

g

) =

Y

g

–

(

g

+

n

) = 0

Therefore,

the economy’s total output grows at the rate

Y

g

=

g

+

n

Recall that this is also the growth rate of the total stock of capital,

K

.

Slide25

Describing the Steady State

Output per worker (

Y

/

L

) grows at the rate

Y

g

–

L

g

=

g

+

n

–

n

=

g

Therefore,

the per-worker output, which was constant in Chapter 8, grows at the rate

g

Recall that this is also the growth rate of per-worker capital,

K

/

L

.

Slide26

Progress, finally!

We have just seen that if we introduce technological progress in the Solow-Swan theory of long-run growth, then in the economy’s steady statePer-worker output (Y/L) increases at the rate g, which is the rate of technological progressThis is a major triumph for the Solow-Swan theory

Slide27

Solow-Swan Steady State

Table 9.1 Steady-State Growth Rates in the Solow Model With Technological Progress

Slide28

Solow-Swan Steady State

Remember from Chapter 8 that, when the production function follows the Cobb-Douglas form, the steady state value of k = k* was given by the formulaNow the formula changes to

Slide29

Technological Progress: where does it come from????

But a puzzle remains …

So far, the rate of technological progress,

g

, has been exogenous

We need to ask, What does

g

depend on?

We need to make

g

endogenous

Slide30

Endogenous Technological Progress

Remember that in Chapter 8 we had distinguished between the population (

P

) and the number of workers (

L

)

We had defined the exogenous variable

u

as the fraction of the population that does not produce the final good

Therefore, we had

L

= (1 –

u

)

P

or

L

/

P

=

1

–

u

In

C

h. 8 we had interpreted

u

as the long-run unemployment rate

Now,

we’ll reinterpret

u

as the fraction of the population that does scientific research

Slide31

Endogenous Technological Progress

Once

u

is seen as the fraction of the population that is engaged in scientific research, it makes sense to assume that …

Assumption

:

the rate of technological progress increases if and only if

u

increases

This assumption is represented by

the technology function

g

(

u

)

Example:

g

(

u

) =

g

0

+

g

u

u

Slide32

Endogenous Technological Progress

We now have a theory that gives an answer to the following question: Why is growth in living standards slow in some cases and fast in others?

Growth in per-worker output is fast when

u

is high.

That is, our standards of living grow rapidly when we invest more heavily in scientific research

Slide33

Productivity Slowdown

There was a worldwide slowdown in economic growth during 1972-1995. Why?

Slide34

Growth Accounting

Table 9.3 Accounting for Economic Growth in the United States