Transcript 7. Long Run Growthx - Ohio Wesleyan University

National Income &
Business Cycles
Ohio Wesleyan University
Goran Skosples
7. Long-Run Growth
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Objectives
 Why growth matters?
 Learn the closed economy Solow model
 See how a country’s standard of living depends
on its saving and population growth rates
 Importance of productivity growth
 Policies to promote growth
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Key Concepts






Solow growth model
Steady state
Break-even investment
Rule of 70
Depreciation
Dilution
 Productivity
 Sustainable growth
rate
 Capital flows
 Foreign Direct
Investment (FDI)
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Question
Shall we play a game?
• Life expectancy is less than 50 years
• 1 out every 10 infants dies before the age of one
• More than 90% of households have no electricity,
refrigerator, telephone, or car
• Fewer than 10% of adults have completed high
school.
 What country is it?
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Why growth matters
…for poor countries
 Data on infant mortality rates:
• 20% in the poorest 1/5 of all countries
• 0.4% in the richest 1/5
 In Bangladesh, about 80% of people live on less
than $2/day.
 One-fourth of the poorest countries have had
famines during the past 3 decades.
 Poverty is associated with oppression of women
and minorities.
Economic growth raises living standards and
reduces poverty….
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Income and poverty in the world
selected countries, 2000
100
Madagascar
% of population
living on $2 per day or less
90
India
Nepal
Bangladesh
80
70
60
Botswana
Kenya
50
China
40
Peru
30
Mexico
Thailand
20
Brazil
10
0
$0
Chile
Russian
Federation
$5,000
$10,000
S. Korea
$15,000
Income per capita in dollars
$20,000
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Why growth matters
…for rich countries
 Anything that effects the long-run rate of economic
growth – even by a tiny amount – will have huge
effects on living standards in the long run.
annual
growth rate of
income per
capita
…25 years
…50 years
…100 years
2.0%
64.0%
169.2%
624.5%
2.5%
85.4%
243.7%
1,081.4%
percentage increase in
standard of living after…
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The lessons of growth theory
…can make a positive difference in the lives of
hundreds of millions of people.
These lessons help us
 understand why poor
countries are poor
 design policies that
can help them grow
 learn how our own
growth rate is affected by
shocks and our
government’s policies
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Int’l Differences in the Standard of Living
Country
Qatar
Singapore
Norway
United States
Hong Kong
Australia
Netherlands
Canada
Sweden
Germany
United Kingdom
Japan
data is in PPP
GDP
per capita
$179,000
$62,100
$54,600
$47,200
$45,900
$41,000
$40,300
$39,400
$39,100
$35,700
$34,800
$34,000
Country
France
Israel
Argentina
Brazil
China
India
Nigeria
Ghana
Bangladesh
Somalia
Zimbabwe
Congo, DR
GDP
per capita
$33,100
$29,800
$14,700
$10,800
$7,600
$3,500
$2,500
$2,500
$1,700
$600
$500
$300
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Historical GDP per capita
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US GDP per capita
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Growth of US GDP per capita
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Sources of Economic Growth
 Given what you have learned so far, what causes
differences in incomes?


1
Y=AK L
1.
2.
3.
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The Solow Model
 due to Robert Solow,
won Nobel Prize for contributions to
the study of economic growth
 a major paradigm:
• widely used in policy making
• benchmark against which most
recent growth theories are compared
 looks at the determinants of economic growth and
the standard of living in the long run
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How Solow model is different from
Chapter 3’s model
1. K is no longer fixed:
investment causes it to grow,
depreciation causes it to shrink.
2. L is no longer fixed:
population growth causes it to grow.
3. The consumption function is simpler.
4. No G or T
(only to simplify presentation;
we can still do fiscal policy experiments)
5. Cosmetic differences.
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The production function
 In aggregate terms: Y = F (K, L )
 Define: _______ = ______________
_______ = ______________
 Assume constant returns to scale
 Divide through by L:
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The production function
Output per
worker, y
f(k)
MPK
1
Note: this production function
exhibits ___________MPK.
Capital per
worker, k
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The national income identity
 Y = _______ (remember, no G )
 In “per worker” terms:
y = _____ , where c = _____ and i =_____
The consumption function
 s = the saving rate (an exogenous parameter)
Note: s is the only lowercase variable that is not
equal to its uppercase version divided by L
 Consumption function:
(per worker)
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Saving and investment
 saving (per worker) =
=
=
 National income identity is
Rearrange to get:
(investment = saving, like in chap. 3!)
 Using the results above,
i =
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Output, consumption, and investment
Output per
worker, y
f(k)
sf(k)
k1
Capital per
worker, k
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Population Growth
 Assume that the population--and labor force-grow at rate n.
(n is exogenous)
L
L
 n
 EX: Suppose L = 1000 in year 1 and the
population is growing at 2%/year ( ________ ).
 Then L = n L
so L =
in year 2.
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Capital accumulation
The basic idea: _________ increases the capital
stock, ___________ and_______ reduces it.
Change in
capital stock = investment – depreciation – dilution
k
Since _________ , this becomes:
k = s f(k) – (+n )k
The equation of motion for k
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Break-even investment
 ( + n)k =
,
the amount of investment necessary
to keep ___ constant.
 Break-even investment includes:
• ____ to replace capital as it wears out
•

____ to equip new workers with capital
(otherwise, k would fall as the existing capital
stock would be spread more thinly over a
larger population of workers)

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Break-even investment
Break-even
investment,
(+n)k
δ = the rate of depreciation
n = population growth rate
Capital per
worker, k
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The steady state
k = s f(k) – (+n)k
If investment is just enough to cover depreciation (s f(k)
– (+n)k ) then capital per worker will remain ________:
k = ____.
This constant value, denoted k*, is called the _______
______________________.
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The steady state
Investment
and
depreciation
(+n)k
sf(k)
Capital per
worker, k
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Moving toward the steady state
Investment
and
depreciation
k = sf(k)  (+n)k
(+n)k
sf(k)
k1
k*
Capital per
worker, k
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An increase in the saving rate
An increase in the saving rate ______ investment …
…causing k to ____________________________:
Investment
and
depreciation
(+n)k
s1 f(k)
k 1*
k
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Prediction:
 Higher s  _______ k*.
 And since y = _____ ,
______ k*  _______ y* .
 Thus, the Solow model predicts that countries
with higher rates of saving and investment will
have _________ levels of capital and income per
worker in the long run.
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International Evidence on Investment Rates
and Income per Person
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The impact of population growth
Investment,
break-even
investment
An increase in n
causes an
_______ in breakeven investment,
leading to a ____
steady-state level
of k.
( +n1) k
sf(k)
k1* Capital per
worker, k
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Prediction:
 Higher n  _______ k*.
 And since y = f(k) ,
_______ k*  _______ y* .
 Thus, the Solow model predicts that countries
with higher population growth rates will have
_________ levels of capital and income per
worker in the long run.
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Income per person in 2000 (log scale)
International Evidence on Population
Growth and Income per Person
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The impact of population growth
Determine what happens to each variable when population
growth is 0 and when it is n? Fill in whether at the steadystate the variable is constant or whether it grows or declines
and at which rate:
Population growth = 0
Population growth = n
L:
L:
K:
K:
Y:
Y:
k:
k:
y:
y:
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Productivity Growth
Output and
Investment
f1(k)
Productivity
growth _______
investment
which leads to a
_____ steadystate level of
income per
capita
(+n)k
s1 f(k)
k 1*
k
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Implications of the Solow Model
 Countries below the steady-state level of capital
per worker will _____ and countries above the
steady-state level of capital per worker will _____
 The further below its steady-state level of capital
per worker a country is, the _______ it will grow
• After a war or a natural disaster, a country will
grow _______
 Capital should flow from rich to poor countries
• Why?
• Is that happening?
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Growth Rates in the OECD
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Growth Rates Around the World
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Implications of the Solow Model
 What can cause growth in the Solow model?
•
•
•
•
 However, in a new steady-state:
 Can the above sources of growth continuously

rise?
In the long run, the rate of ______________
_____________ is the dominant factor
determining how quickly living standards rise
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Examples of technological progress
 From 1950 to 2000, U.S. farm sector productivity
nearly tripled.
 The real price of computer power has fallen an
average of 30% per year over the past three
decades.
 Percentage of U.S. households with ≥ 1 computers:
8% in 1984, 62% in 2003
 2000: 361m Internet users, 740m cell phone users
2011: 2.4b Internet users, 5.9b cell phone users
 2001: iPod capacity = 5gb, 1000 songs. Not capable
of playing episodes of Entourage.
2009: iPod capacity = 120gb, 30,000 songs. Can
play episodes of Entourage.
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Total Factor Productivity
 Differences in income per capita: y = Ak
 Both capital per worker (k) and total factor
productivity (A) explain differences in incomes per
capita around the world
 Richer countries have both more capital per
worker and higher total factor productivity
• capital per worker explains about ____ of the
difference in incomes per capita
• TFP explain about ____ of the difference in
incomes per capita
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The US and China
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Policies to Raise Living Standards
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Measures of Living Standards
 Is GDP per capita a good measure of the living
standards?
 What are some other measures?
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Happiness and GDP per capita
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Summary
1. The Solow growth model shows that, in the long
run, a country’s standard of living depends
• positively on its saving rate.
• negatively on its population growth rate.
• positively on total factor productivity
2. An increase in the saving rate leads to
• higher output in the long run
• faster growth temporarily
• but not faster steady state growth.
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Summary
3. In the long run, only a continuous increase in
productivity growth can lead to sustained
increase in the standard of living
4. Both capital per worker and total factor
productivity explain income differences around
the world
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