Transcript The Solow Model

Growth, Capital
Accumulation and the
Economics of Ideas:
Catching Up vs. The
Cutting Edge
Chapter 7
© 2010 WORTH PUBLISHERS MODERN PRINCIPLES: MACROECONOMICS COWEN AND TABARROK
Chapter Outline
• The Solow Model and Catch-Up Growth
• The Solow Model- Details and Further
Lessons (Optional Section)
• Growing on the Cutting Edge: the
Economics of Ideas
• The Future of Economic Growth
• Takeaway
• See the Invisible Hand Blog (click) for more
examples
2
Introduction
• In 2006 China: GDP per capita grew by
10%
– U.S: GDP per capita grew by 2.3 %
• United States has never grown as fast
as the Chinese economy is growing
today.
• Why is China growing more rapidly
than the U.S.?
– Is there something wrong with the U.S.
economy?
3
Introduction
• There are two types of growth
– Catch-up growth
• takes advantage of ideas, technologies, or
methods of management already in
existence
• focuses on capital accumulation
– Cutting-edge growth
• developing new ideas
• focuses on developing new technology for
resources.
4
The Solow Model and
Catch-Up Growth
• Robert Solow (Nobel Prize Laureate)
• Total Output, Y, of an economy depends
on:
– Physical capital: K
– Human capital: education x Labor = eL
– Ideas: A
• This can be expressed as the following
“production function”:
Y  F(A,K, eL)
The Solow Model and
Catch-Up Growth
• For now, ignore changes in ideas, education,
and labor so that A, e, and L are constant. The
production function becomes:
Y  F(K)
• If L is constant, then increases in K mean more
capital per worker
• MPK: marginal product of capital : The additional
output resulting from using an additional unit of
capital.
– MPK diminishes the more capital is added.
The Solow Model and
Catch-Up Growth
Assume a production function like Y 
Output, Y
Y K
5
5.0  4.7
MPK 
 0.3
10  9
4
3
2
K
MPK 
20
2
1 0
Conclusion: as more
capital is added,
MPK declines.
1
Capital, K
0 1 2 3 4 5 6 7 8 9 10 11 12
13
Growth in China and United States
• The “iron logic of diminishing returns” largely
explains why…
–The Chinese economy is able to grow so
rapidly.
»It turned toward markets which
increased incentives.
»The capital stock was low.
»The MPK was high.
–China will not be able to achieve these
high growth rates indefinitely.
8
The Solow Model and
Catch-Up Growth
• Why Bombing a Country Can Raise Its
Growth Rate:
– Much of the capital stock was destroyed
during WWII. Therefore the MPK was high.
– Following the war, both Germany and Japan
were able to achieve much higher growth
rates than the U.S. as they “caught-up.”
9
SEE THE INVISIBLE HAND
The first $500 spent on a computer for each of
these kids yields a lot. The second $500?
Not as big an increase.
10
The Solow Model and
Catch-Up Growth
• Capital Growth Equals Investment minus
Depreciation
– Capital is “output that is saved and
invested.”
– Let g be the fraction of output that is
invested in new capital.
• The next figure shows how output is divided
between consumption and investment
when g = 0.3. (30% of additional output is saved
and put into new capital)
12.11
The Solow Model and
Catch-Up Growth
Output, Y
Capital Growth Equals Investment Minus Depreciation
20
When K = 100, Output = 10
Y K
15
10
Consumption = (1- 0.3) x 10 = 7
5
Investment = 0.3∙Y
3
2
0
Investment = (0.3) x 10 = 3
Capital, K
0
100
200
300
400
12
The Solow Model and
Catch-Up Growth
• Capital Growth Equals Investment minus
Depreciation (cont.).
– Depreciation: amount of capital that wears out
each period
– Let d be the fraction of capital that wears out
each period. This is called the depreciation rate
so that:
depreciati on
δ
K
12.13
The Solow Model and
Catch-Up Growth
Capital Depreciation Depends on the Amount of Capital
Depreciation
Depreciation = 0.02∙K
8
6
4
42
Slope 
200  100
2
0
Capital, K
0
100
200
300
400
14
The Solow Model and
Catch-Up Growth
• Capital Alone Cannot be the Key to
Economic Growth
– As capital increases,
• depreciation increases at a constant rate of
d
• output increases at a diminishing rate.
• Because investment is a constant fraction of
output, at some point depreciation will
equal investment.
– The capital stock will stop growing.
– Output will stop growing.
15
The Solow Model and
Catch-Up Growth
Capital Increases or Decreases Until Investment = Depreciation
GDP, Y
Depreciation = 0.02∙K
8
At K = 400, Inv. < Dep. → ↓ K
6
Investment = 0.3∙Y
4.5
4
Result: equilibrium
at K = 225, Y = 4.5
investment =
depreciation =4.5
At K = 100,
Inv. > Dep.
→↑K
3
2
0
0
100
200 225
300
400
Capital, K
16
Capital Adjusts Until
Investment = Depreciation
Check the Math
• At K = 100, Y =√100 = 10
• Depreciation = 0.02∙100 = 2
• Investment = 0.3x10 = 3
• Investment > Depreciation
Result: K and Y grow.
Check the Math
• At K = 400, Y =√400 = 20
• Depreciation = 0.02x400 = 8
• Investment = 0.3x20 = 6
• Investment < Depreciation
Result: K and Y decrease.
Check the Math
•
•
•
•
At K = 225, Y =√225 =15
Depreciation = 0.02x225 = 4.5
Investment = 0.3x15 = 4.5
Investment = Depreciation
Result:
1. Investment = Depreciation
2. K and Y are constant.
This is steady state.
17
The Solow Model and
Catch-Up Growth
• The logic of diminishing returns means that
eventually capital and output will cease
growing.
• Therefore, other factors must be
responsible for long run economic growth.
• Consider:
– Human capital: knowledge, skills,
experience
– Technological knowledge: better ideas
18
Human Capital Investment
Pays Off
19
The Solow Model and
Catch-Up Growth
• Better Ideas Drive Long Run Economic Growth
– Human Capital
• Like capital, it is subject to diminishing
returns and it depreciates.
• Logic of diminishing returns also applies to
human capital.
• Conclusion: Human capital also cannot
drive long-run economic growth.
– (What about technological knowledge?)
20
The Solow Model and
Catch-Up Growth
• Better Ideas Drive Long Run Economic
Growth
– Technological knowledge
• A way of getting more output from the
same input (an increase in
productivity).
• We can include technological
knowledge in our model by letting A
stand for ideas that increase
productivity. Now the production
function is:
YA K
21
The Solow Model and
Catch-Up Growth
Increasing technology (even while holding K constant) creates a higher
growth rate.
22
The Solow Model and
Catch-Up Growth
• An Increase in A Increases Output Holding
K Constant
– Conclusion:
• Technological knowledge / better ideas
are the key to long run economic growth.
• Solow estimated that better ideas are
responsible for ¾ of our increased
standard of living.
23
Roman aquaducts: ushering in an era of economic growth…
Aquaducts were sophisticated feats of engineering that enabled
population and industry to thrive.
-Roman Aquaduct in Segovia, Spain, built in 2nd century A.D./C.E.
24
The Solow Model –
Details and Further Lessons
• What we know so far:
– If Investment > Depreciation → K and Y grow.
– If Investment < Depreciation → K and Y fall.
– If Investment = Depreciation → K and Y are
constant.
• Two important conclusions
– Steady state equilibrium occurs when
investment equals depreciation.
– When K is in steady state equilibrium, Y is in
steady state equilibrium.
25
The Solow Model –
Details and Further Lessons
When K is in steady state equilibrium, Y is in steady state equilibrium.
Output, Y
Depreciation = 0.02∙K
8
6
4.5
4
Investment = 0.3∙Y
3
The Steady State K is found where
2
Investment = Depreciation
0
Capital, K
0
100
200 225
300
400
26
The Solow Model –
Details and Further Lessons
When K is in steady state equilibrium, Y is in steady state equilibrium.
Output, Y
20
Y K
Steady state output
15
Depreciation = 0.02∙K
10
Investment  0.3 K
5
Steady state capital stock
0
100
200
225 300
400
Capital, K
27
The Solow Model –
Details and Further Lessons
• The Solow Model and an Increase in the
Investment Rate
– What happens when g, (the fraction of output
that is saved and invested) increases?
•↑ g  K  ↑ Y
– Conclusion: an increase in the investment
rate increases a country’s steady state level
of GDP.
• Countries with higher rates of investment will be
wealthier.
28
The Solow Model –
Details and Further Lessons
GDP per Capita is Higher in Countries with Higher Investment Rates
29
An Increase in the Investment Rate
Increases Steady State Output
Output, Y
Y K
20
15
Depreciation = 0.02∙K
10
Inv.  .4 K
5
Inv. 0.3 K
Capital, K
0
100
200 225
300
400
30
The Solow Model –
Details and Further Lessons
• Note:
– An increase in the investment rate = ↑ steady
state level of output.
– As the economy moves from the lower to the
higher steady state output = ↑ growth rate of
output.
– This higher growth rate is temporary.
• Conclusion: ↑ investment rate = ↑ steady
state level of output but not its long-run
growth rate.
31
The Solow Model –
Details and Further Lessons
• The Case of South Korea
– In 1950, South Korea was poorer than Nigeria.
– 1950s: the investment rate was < 10%.
– 1970s: Investment rate more than doubled.
– 1990s: Investment rate increased to over 35%.
– South Korea’s GDP increased rapidly.
–As GDP reached Western levels, the
growth rate has slowed…
32
What economic
growth looks like
at night
33
The Solow Model –
Details and Further Lessons
• The Solow Model and Conditional
Convergence
– Conditional Convergence: Among countries
with similar steady state levels of output,
poorer countries tend to grow faster than
richer countries, and so converge in income.
– The Solow model predicts that a country will
grow faster the farther its capital stock is
below its steady state value.
• Conditional convergence is a prediction of the
Solow model
34
The Solow Model –
Details and Further Lessons
The poorer the OECD country in 1960, the faster its growth
35
between 1960-2000
The Solow Model – Details and
Further Lessons
• Solow and the Economics of Ideas in one
diagram
– Generation of ideas results in long run
economic growth.
– Let’s see how this works:
• We begin at steady state equilibrium.
• New ideas → ↑A → ↑Output at every level of K
• ↑ Output → ↑Investment → Investment > Depreciation
→↑ K→ ↑ Output (movement along new production
function).
• As ideas continue to grow, output continues to grow.
36
Solow and the Economics
of Ideas in One Diagram
Output, Y
Effect of ↑A from 1 to 1.5
Y  1.5 K
c
33.7
Output ↑
b
Better
Ideas
15
Y 1 K
a
Depreciation = 0.02∙K
Investment  0.3(1.5) K
Investment  0.3(1) K
225
Old steady state
capital stock
506
New steady state
capital stock
Capital, K
37
The Solow Model –
Details and Further Lessons
• The Big Question: What Determines High
Investment Rates?
– Incentives which include
• Low real interest rates
• Low marginal tax rates
– Institutions which include
• Honest government
• Secure property rights
• Effective financial intermediaries (banks)
38
Growing on the Cutting Edge:
The Economics of Ideas
• The Economics of Ideas
1. Ideas for increasing output are primarily
researched, developed, and implemented by
profit-seeking firms.
2. Spillovers mean that ideas are underprovided.
3. Government has a role in improving the
production of ideas.
4. The larger the market, the greater the incentive
to research and develop new ideas.
39
Growing on the Cutting Edge:
The Economics of Ideas
1. Research and development is investment
for profit.
– keys to increasing technological knowledge:
• Incentives
• Institutions that encourage investment in
physical and human capital and R&D.
– 70% of scientists and engineers in the U.S. work
for private firms.
40
Growing on the Cutting Edge:
The Economics of Ideas
1. Research and development is investment
for profit
– All kinds of people come up with new ideas.
• Business culture and institutions are also important.
• Appreciation of entrepreneurs is a relatively recent
phenomenon.
– Institutions that are especially important:
• Commercial settings that help innovators to
connect with capitalists
• Intellectual property rights
• A high-quality education system
41
SEE THE INVISIBLE HAND
John Kay,
“destroyer of
jobs.”
John
Kay
(1704-1780)
invented the “flying shuttle” used
in cotton weaving, the single most
important invention launching the
industrial revolution.
Kay was rewarded for his
efforts by having his house
destroyed by “machine breakers,”
afraid of job loss. He died a poor
man.
42
Growing on the Cutting Edge:
The Economics of Ideas
• Institutions that increase R & D
– A commercial setting that helps
innovators connect with capitalists.
• Ideas without financial backers are dead.
• The U.S. is good at connecting innovators
with businessmen and venture capitalists.
• American culture supports entrepreneurs.
43
Growing on the Cutting Edge:
The Economics of Ideas
– Intellectual property rights
• New processes, products, and methods can
be copied by competitors.
• World’s first MP3 player was the Eiger Labs
MPMan introduced in 1998.
• Eiger Labs lost out to competition.
• Patents
• Grant temporary monopoly.
• But: can slow down the spread of
technology.
44
SEE THE INVISIBLE HAND
Profits provide incentive
to invest in R&D:
Property rights,
honest government,
political stability,
a dependable legal
system, and
competitive open
markets create profit
and so help drive the
generation of
“The patent system…added the fuel of
technological
interest to the fire of genius”
knowledge.
-Abraham Lincoln, 1859 (only U.S. President
45
to have been granted a patent)
Growing on the Cutting Edge:
The Economics of Ideas
– A high-quality education system
• Important at all levels of education.
• Creates necessary talent.
• Universities generate basic and applied
research.
46
Growing on the Cutting Edge:
The Economics of Ideas
2. Spillovers, and why there aren’t enough
good ideas
– Ideas are non-rivalrous.
– Ideas can be used simultaneously.
• Use of an idea by one individual does mean less of
the idea available to someone else.
– The spillover (or “diffusion”) of new ideas
generates widespread economic growth.
– Implication: Spillovers mean that the generator of
the idea doesn’t get all of the benefits.
• Result? Too few ideas are produced.
47
Growing on the Cutting Edge:
The Economics of Ideas
– Optimal social investment in R&D occurs where:
MSB = MSC (Marginal Social Benefit = Marginal
Social Cost)
– Optimal private investment occurs where:
MPB = MPC (Marginal Private Benefit = Marginal
Private Cost)
– With spillover benefits: MSB = MPB + spillovers
and MSC = MPC
– Conclusion:
Optimal Private
Investment in R&D
<
Optimal Social
Investment in R&D
– Implication: Spillovers result in too little investment
in research and development.
48
Spillovers Mean Too Little Investment
in Research and Development
$
Spillover benefits
IP = optimal private investment in R&D
IS =optimal social investment in R&D
MPB = MPC
MSB = MSC
MPC = MSC
MSB
Assumes there
are no spillover
costs
MPB
IP
IS
Quantity of R&D
49
Growing on the Cutting Edge:
The Economics of Ideas
3. Government’s Role in the Production of
New Ideas
– Ideas in mathematics, physics, and molecular
biology have many applications so spillovers
can be large.
• Problem: Even if the social benefits are large,
the private benefits can be small.
• Solution: Subsidize the production of new
ideas or give tax breaks for R&D expenditures.
– Both shift the MC of R&D curve down → ↑ R&D
investment.
50
Growing on the Cutting Edge:
The Economics of Ideas
– Large spillovers to basic science
suggest a role for government
subsidies to universities.
• Especially those parts of the universities
that produce innovations and the basic
science behind those innovations.
• Universities produce scientists.
– Most of the 1.3 million scientists were trained
in government-subsidized universities.
51
Growing on the Cutting Edge:
The Economics of Ideas
4. Market Size and Research and
Development
– Innovations like pharmaceuticals, new computer
–
–
–
–
chips, software, and chemicals require large R&D
expenditures.
Companies will avoid investing in innovations with
small potential markets.
Larger markets mean increased rewards (thus
incentives) for R&D.
As the world market grows some companies get
bigger and will increase their R&D investments.
Click here for Alex Tabarrok’s TED talk, “How Ideas
Trump Crises.”
52
The Future of Economic Growth
– Dawn of civilization to about 1500 A.D./C.E.:
growth = 0%
– AD 1500 – 1760: growth = 0.08%
– Growth doubled in next 100 years
– Increased even further during the 19th and 20th
centuries
– Today: world wide growth of per capital GDP =
2.2%
– Economic growth can be even faster. How?
53
The Future of Economic Growth
A (ideas) = Population x Incentives x Ideas/Hour
– Population
• ↑population → ↑ number of people with new ideas
– Much of the world is poor:
• thousands of potentially great scientists are laboring
in menial jobs.
– As the world gets richer → ↑ production of
ideas → everyone benefits
54
The Future of Economic Growth
• More Hopeful Signs:
• If A (ideas) = Population x Incentives x Ideas/Hour
– Incentives
• Appear to be increasing in many places:
–
–
–
–
–
–
–
Consumers are richer
Markets are expanding due to trade
World wide improvement in institutions
Property rights
Honest government
Political stability
Dependable legal system
55
The Future of Economic Growth
• More Hopeful Signs:
• If A (ideas) = Population x Incentives x Ideas/Hour
– Ideas per Hour
• New ideas do not experience diminishing
returns.
• Two reasons why:
1. Many ideas make creating new ideas easier.
2. The field of ideas that can be explored is so large
that diminishing returns may not set in for a very
long time.
56
The Future of Economic Growth
• Recap: Economic growth might be even
faster in the future than it has been in the
past…
– There are more scientists and engineers in the
world than ever before, and their numbers are
also increasing as percentage of the
population.
– Incentives are increasing due to growing
markets resulting from
• Increasing trade
• Increasing wealth in developing countries
– Better institutions and more secure property
rights are spreading throughout the world. 57
Key Concepts
•
•
•
•
Marginal Product of Capital
Steady State
Conditional Convergence
Non-Rivalrous
58
Try it!
In the Solow model, if the first unit of
capital increases output by one unit,
then the second unit of capital will
cause total output to
a) increase, but by less than one unit.
b) double.
c) remain the same as with one unit
of capital.
d) increase exponentially.
59
Try it!
In the Solow model, if the first unit of
capital increases output by one unit,
then the second unit of capital will
cause total output to
a) increase, but by less than one unit.
b) double.
c) remain the same as with one unit
of capital.
d) increase exponentially.
60
Try it!
The marginal product of capital
I. refers to the cost of purchasing one extra
unit of capital.
II. is expected to be higher for very poor
countries relative to wealthy countries.
III. increases as capital accumulation
occurs.
a) I only
b) II only
c) II and III only
d) III only
61
Try it!
The marginal product of capital
I. refers to the cost of purchasing one extra
unit of capital.
II. is expected to be higher for very poor
countries relative to wealthy countries.
III. increases as capital accumulation
occurs.
a) I only
b) II only
c) II and III only
d) III only
62
Try it!
Country
1950–1960
1980–1990
Germany
6.6%
1.9%
Japan
6.8%
3.4%
United States
1.2%
2.3%
Table: GDP Growth Average Annual Growth Rate of Per Capita GDP
Which of the following answers describes why Germany and
Japan experienced such high growth rates just after the Second
World War?
a) Trade agreements between Germany and Japan greatly
enhanced economic growth.
b) High MP K levels contributed to significant per capita output
growth.
c) Their technological advances at this time were higher than
those of the U.S.
d) All of the answers are correct.
63
Try it!
Country
1950–1960
1980–1990
Germany
6.6%
1.9%
Japan
6.8%
3.4%
United States
1.2%
2.3%
Table: GDP Growth Average Annual Growth Rate of Per Capita GDP
Which of the following answers describes why Germany and
Japan experienced such high growth rates just after the Second
World War?
a) Trade agreements between Germany and Japan greatly
enhanced economic growth.
b) High MP K levels contributed to significant per capita output
growth.
c) Their technological advances at this time were higher than
those of the U.S.
d) All of the answers are correct.
64
Try it!
If a country is at its steady state level of
capital, which of the following will not
result in economic growth in future
years ceteris paribus?
a) a technological advancement
b) producing capital at its current rate
c) an increase in the savings rate
d) a decrease in the depreciation rate
65
Try it!
If a country is at its steady state level of
capital, which of the following will not
result in economic growth in future
years ceteris paribus?
a) a technological advancement
b) producing capital at its current rate
c) an increase in the savings rate
d) a decrease in the depreciation rate
66
Try it!
Which of the following should lead to an
increased rate of economic growth due
to increased development of ideas?
a) increased population
b) increased consumer wealth and
larger markets
c) political stability and honest
governments
d) All of the answers are correct
67
Try it!
Which of the following should lead to an
increased rate of economic growth due
to increased development of ideas?
a) increased population
b) increased consumer wealth and
larger markets
c) political stability and honest
governments
d) All of the answers are correct
68
Appendix
• Excellent Growth
– Using a spreadsheet, you can easily explore
the Solow model and duplicate all the graphs.
First, calculate the
increasing capital stock
using the formula in A2 and
let the spreadsheet do
the rest.
Note: Clicking on the lower right
corner of a cell and dragging it
down will duplicate the formula
in the lower cells.
69
Appendix
• Excellent Growth (cont.)
Second, calculate output,
Y, using the formula:
Y K
12.70
Appendix
• Excellent Growth (cont.)
Fourth, graphs can be created using the data generated
In the steps one through three.
71
Appendix
• Excellent Growth (cont.)
Fifth, You can experiment with different investment shares
in
72
E2 or the depreciation rates in F2.
Appendix
• The Mathematics of Economic Growth
along the Transition Path
• Objective: To see how economic growth
varies along the transition path to a new
steady state equilibrium.
• We will do two things:
– Outline the mathematics
– Use a spreadsheet to visualize our
results.
73
Appendix
• The Mathematics
Recall
1
2
Investm ent  gY  γ K  γK (e.g., 0.3 K )
Depreciation  dK (e.g., 0.02 K )
thus
1
2
ΔK  Investm ent- Depreciation  gK  dK
T hegrowth rateof thecapitalstockis given by
By plotting these two
expressions
separately on a graph,
we can see how the
steady state changes
with the values of the
investment rate and
depreciation rate.
1
2
ΔK
gK
dK
g
 Growth rateof K 

 1 d
K
K
K
K2
Implication :
g
If
K
g
K
1
2
1
2
 d  Growth rateof K is positive
 d  Growth rateof K is negative
74
Appendix
• The Mathematics
d, g/K1/2
0.08
0.07
0.06
Difference is the growth rate of the
capital stock. The bigger the difference
the faster K grows.
0.05
0.04
0.03
0.02
d = 0.02
0.01
0.4/K1/2
400
Capital, K
75
Appendix
• The Spread Sheet
Plotting Y against time shows the transition to steady state
76
Appendix
• The Spread Sheet
Output, Y
16.00
14.00
12.00
10.00
8.00
Output, Y
6.00
4.00
2.00
0.00
0
100
200
300
400
500
600
Time
Result: The transition to steady state proceeds at a
decreasing rate. As K approaches 400 growth slows down.
77