ECONOMIC GROWTH

& THE SOLOW GROWTH MODEL

CHAPTER 6

GOALS OF CHAPTER 6

Answer the following questions:

ï‚¡ What factors effect Economic Growth?

ï‚¡ Does the standard of living necessary rise over time?

ï‚¡ What policy can be used to alter economic growth?

ï‚¡ Do all countries converge or diverge in terms of economic

growth? Why?

We develop a growth model to answer these questions.

Table 6.3 Sources of Economic Growth in the United States (Percent per

Year) â€“ productivity slowdown

Productivity Slowdown

MOTIVATION

Labor Productivity (Y/N) Growth:

mid 70â€™s to mid 90â€™s: 1.5%

mid 97 to end 2003: 3.6%

2004 to 2015: 1.6%

ACROSS COUNTRY COMPARISONS OF GDP/N

As you look at the WORLD DATA at the link below, keep in mind:

ï‚¡ The higher the GDP per person, the higher the consumption per

person, and hence the higher the standard of living

ï‚¡ Economies that are growing over time, typically see their standard of living rise.

ï‚¡ Countries with high income per capita (like US, Canada, and other western

economies), continue to have rising income per capita over time & hence rising

standards of living.

LINK: Growth in Standard of Living across the World

SOLOW GROWTH MODEL

PART I

THE SOLOW GROWTH MODEL

ï‚¡ Basic questions about growth

ï‚¡ Whatâ€™s the relationship between the long-run standard of

living and the saving rate, rate of technical progress,

and population growth rate?

ï‚¡ How does economic growth change over time? Will it

speed up, slow down, or stabilize?

THE SOLOW GROWTH MODEL â€“ SET UP

ï‚¡ Basic assumptions and variables

ï‚¡ Economy is closed and G = 0

Ct

= Yt

â€“ I

t

(6.4)

This is because Yt=Ct +It

;

It is also the case that St = It over time

ï‚¡ Population and work force grow at same rate = n

ï‚¡ Rewrite all variables in per-worker terms:

y

t = Yt

/Nt

; c

t = Ct

/Nt

; kt = Kt

/Nt

c

t measures standard of living â€“ ct

is consumption per worker

ï‚¡ kt

is the capital-labor ratio

THE SOLOW GROWTH MODEL â€“ SET UP

ï‚¡ The per-worker production function

y

t = f(kt

) (6.5)

Same shape as

aggregate

production

function in ch.3!

NOTE: Assume no productivity growth for now (to be discussed later)

THE SOLOW GROWTH MODEL â€“ SET UP

ï‚¡ STEADY STATE (definition)

ï‚¡ Steady state: y, c, and k are constant over time

ïƒž BUT Yt

, Ct

, and Kt grow over time!!!

ï‚¡ Gross investment AT STEADY STATE (ss) is given by:

I

t = (n + d)Kt

(6.6)

ï‚¡ Replace worn out capital, dKt

ï‚¡ Expand so the capital stock grows as the population grows, nKt

ïƒž these two ensure that kt

remains constant over time

NOTE: steady state investment is not always equal to actual investment in

the economy!

INVESTMENT PER WORKER AT STEADY STATE

ï‚¡ Since I

t = (n + d)Kt

per worker steady state investment = (n + d)k

ï‚¡ PLOT:

(n + d)k

capital-labor ratio = k

Steady

state

investment

per

worker

(n+d)k

CONSUMPTION AT STEADY STATE

ï‚¡ Use the Yt=Ct +It

and the definition of ss I (6.6) to get:

Ct = Yt

â€“ I

t

Ct = Yt

â€“ (n + d)Kt

(6.7)

ï‚¡ Hence, steady state per-capita consumption:

c = f(k) – (n + d)k at steady state (6.8)

ï‚¡ Plot of c, f(k), and (n + d)k (Fig. 6.4)

FIGURE 6.4 THE RELATIONSHIP OF

CONSUMPTION PER WORKER TO THE CAPITALâ€“

LABOR RATIO

DISCUSSION FIGURE 6.4

ï‚¡ Difference between the production

function and the (n+d)k line is â€œcâ€

ï‚¡ Increasing k will increase c up to a

point

ï‚¡ kG

is the level of k that maximizes c:

ï‚¡ it is called â€œthe Golden Rule

capital-labor ratioâ€

ï‚¡ For k beyond this point, c will decline

ï‚¡ To simplify, we assume henceforth that

k is less than kG

ï‚¡ Hence c always rises as k rises

f(k)=(n+d)k

c=0!!!!

THE SOLOW GROWTH MODEL â€“ HOW DOES

THE ECONOMY GET TO SS?

ï‚¡ REACHING the steady state

ï‚¡ Suppose saving is proportional to current income:

St = sYt

, (6.9)

where s is the saving rate, which is between 0 and 1

Recall: savings always equals investment. However, it

may not always equal ss level of investment!

ï‚¡ Equating saving to ss investment gives

sYt = (n + d)Kt

(6.10)

THE SOLOW GROWTH MODEL â€“ STEADY STATE

ï‚¡ Putting this in per-worker terms gives

sf(k) = (n + d)k – this must hold in steady state

ï‚¡ Plot:

THE SOLOW GROWTH MODEL â€“ STEADY STATE

ï‚¡ The only possible steady-state capital-labor ratio is k*

ï‚¡ Hence at steady state, output at that point is y* = f(k*);

ï‚¡ consumption is c* = f(k*) â€“ (n + d)k*

ï‚¡ If k begins at some level other than k*, it will move toward

k*

ï‚¡ For k below k*, saving > the amount of investment needed to keep k

constant, so k rises

ï‚¡ For k above k*, saving < the amount of investment needed to keep k

constant, so k falls

CONCLUSION: SOLOW GROWTH MODEL

With no productivity growth (i.e. unless there is productivity

growth), the economy reaches a steady state, with constant

capital-labor ratio, constant output per worker, and

constant consumption per worker

SOURCES OF GROWTH IN THE MODEL

ï‚¡ The fundamental determinants of long-run living

standards according to the Solow Growth Model are:

ï‚¡ The saving rate

ï‚¡ Productivity growth

ï‚¡ Population growth

THE SOLOW GROWTH MODEL

1. The saving rate

Higher saving rate

means higher capitallabor ratio, higher

output per worker, and

higher consumption

per worker

THE SOLOW GROWTH MODEL

2. Productivity growth

ï‚¡ The key factor in economic growth is productivity improvement

ï‚¡ Productivity improvement raises output per worker for a given level of the

capital-labor ratio – since savings depends on y, more is saved!

FIGURE 6.9 THE EFFECT OF A PRODUCTIVITY

IMPROVEMENT ON THE STEADY-STATE CAPITALâ€“

LABOR RATIO

Higher productivity means higher capital-labor ratio, higher output per

worker, and higher consumption per worker

The increase in

output per

worker

increases the

supply of saving,

causing the

long-run

capital-labor

ratio to rise

THE SOLOW MODEL

3. Population growth

Higher population growth means a lower capital-labor ratio, lower output per

worker, and lower consumption per worker

SOLOW GROWTH MODEL

PART II

POLICY IN THE SOLOW GROWTH MODEL

Should a policy goal be to raise the saving rate?

ï‚¡ Not necessarily, since the cost is lower consumption in the short

run

ï‚¡ If the private market is efficient, the government shouldnâ€™t try to

change the saving rate

ï‚¡ The private marketâ€™s saving rate represents its trade-off of

present for future consumption

ï‚¡ But if tax laws or myopia cause an inefficiently low level of

saving, government policy to raise the saving rate may be

justified

ï‚¡ One way is to raise the real interest rate to encourage saving;

but the response of saving to changes in the real interest rate

seems to be small

GOVERNMENT POLICIES TO RAISE LONG-RUN

LIVING STANDARDS

Policies to raise the rate of productivity growth

ï‚¡ Improving infrastructure

ï‚¡ Infrastructure examples: highways, bridges, utilities, dams, airports

ï‚¡ Empirical studies suggest a link between infrastructure and

productivity

ï‚¡ There might be reverse causation: Richer countries with higher

productivity spend more on infrastructure, rather than vice versa

ï‚¡ U.S. infrastructure spending has declined in the last two decades

ï‚¡ Would increased infrastructure spending increase productivity?

ï‚¡ Infrastructure investments by government may be inefficient, since

politics, not economic efficiency, is often the main determinant

GOVERNMENT POLICIES TO RAISE LONG-RUN

LIVING STANDARDS

Policies to raise the rate of productivity growth

ï‚¡ Building human capital

ï‚¡ Thereâ€™s a strong connection between productivity and human capital

ï‚¡ Government can encourage human capital formation through educational

policies, worker training and relocation programs, and health programs

ï‚¡ Another form of human capital is entrepreneurial skill

ï‚¡ Government could help by removing barriers like red tape

ï‚¡ Encouraging research and development

ï‚¡ Government can encourage R and D through direct aid to research

THE SOLOW MODEL

ï‚¡ Population growth

ï‚¡ Should a policy goal be to reduce population growth?

ï‚¡ Doing so will raise consumption per worker

ï‚¡ But it will reduce total output and consumption, affecting a nationâ€™s

ability to defend itself or influence world events

ï‚¡ The Solow model assumes that the proportion of the population

of working age is fixed

ï‚¡ But when population growth changes dramatically this may not be true

ï‚¡ Changes in cohort sizes may cause problems for social security

systems and areas like health care

THE SOLOW MODEL

Last question:

ï‚¡ Can consumption per worker grow indefinitely?

ï‚¡ The saving rate canâ€™t rise forever (it peaks at 100%) and the population

growth rate canâ€™t fall forever

ï‚¡ But productivity and innovation can always occur, so living standards

can rise continuously

ï‚¡ Summary: The rate of productivity improvement is

the dominant factor determining how quickly living

standards rise

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