CHAPTER
8
DYNAMIC P OWERP OINT™ S LIDES BY S OLINA L INDAHL
Growth, Capital Accumulation, and
the Economics of Ideas: Catching Up
vs. the Cutting Edge
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
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questions
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Video
Food for Thought….
Some good blogs and other sites to get the juices flowing:
Introduction
In 2010 China: GDP per capita grew by
10%
U.S: GDP per capita grew by 2.2 %
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?
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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.
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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)
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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.
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The Solow Model and
Catch-Up Growth
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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.
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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- so MPK was high.
After the war, Germany and Japan had much
higher growth rates than the U.S. as they
“caught-up.”
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Try it!
The adoption of computers in the workplace
has lead to a(n)
a) increase in the supply of labor because
people are needed to operate the
computers.
b) increase in labor productivity because
computers are a capital good.
c) decrease in labor productivity because
computers are a capital good.
d) decrease in human capital because
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computers are physical capital.
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.
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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)
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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
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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
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The Solow Model and
Catch-Up Growth
Capital Depreciation Depends on the Amount of Capital
Depreciation
Depreciation = 0.02∙K
6
4
Slope 
42
200  100
2
0
Capital, K
0
100
200
300
400
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The Solow Model and
Catch-Up Growth
Capital Alone Cannot be the Key to
Economic Growth. Why?
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 slows.
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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
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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 = 225, Y =√225 =15
• Depreciation = 0.02x225 =
4.5
• Investment = 0.3x15 = 4.5
• Investment = Depreciation
Check the Math
Result:
1. Investment = Depreciation
• At K = 400, Y =√400 = 20
• Depreciation = 0.02x400 = 8 2. K and Y are constant.
• Investment = 0.3x20 = 6
• Investment < Depreciation This is steady state.
Result: K and Y decrease.
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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
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Human Capital Investment
Pays Off
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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
alone drive long-run economic growth.
(What about technological knowledge?)
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The Solow Model and
Catch-Up Growth
Better Ideas Drive Long Run Economic
Growth
Technological knowledge:
Is a way of getting more output from
the same input (an increase in
productivity).
We represent this in our model by
letting A stand for ideas that increase
productivity. Now the production
function is:
YA K
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The Solow Model and
Catch-Up Growth
Increasing technology (even while holding K constant) creates a higher
growth rate.
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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.
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Click below for one of the authors’ TED talks….The "dismal science" truly shines
in this optimistic talk, as economist Alex Tabarrok argues free trade and
globalization are shaping our once-divided world into a community of ideasharing more healthy, happy and prosperous than anyone's predictions. (14:37
minutes)
SEE THE INVISIBLE HAND
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.
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:
1. Steady state equilibrium occurs when
investment equals depreciation.
2. When K is in steady state equilibrium, Y is in
steady state equilibrium.
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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
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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
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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.
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The Solow Model –
Details and Further Lessons
GDP per Capita is Higher in Countries with Higher Investment Rates
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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
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Try it!
In the Solow model, if the depreciation rate
increases, what happens to the steady state
capital level and output level?
a)
b)
c)
d)
they both increase
they both decrease
The steady state capital stock will
increase and the output will decrease.
The steady state capital stock will
decrease and the output will increase.
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Try it!
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.
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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…
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SEE THE INVISIBLE HAND
What economic
growth looks
like at night
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.
Solow predicts conditional convergence.
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The Solow Model –
Details and Further Lessons
The poorer the OECD country in 1960, the faster its growth.
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The Solow Model – Details and Further Lessons
Solow and the Economics of Ideas in one
diagram
New 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.
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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
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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)
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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.
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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.
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Growing on the Cutting Edge:
The Economics of Ideas
1. Research and development is investment
for profit (continued)
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
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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.
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.
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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 they can slow down the spread of
technology.
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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
technological
knowledge.
“The patent system…added the fuel of
interest to the fire of genius”
-Abraham Lincoln, 1859 (only U.S. President
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.
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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.
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Growing on the Cutting Edge:
The Economics of Ideas
Optimal social investment in R&D: MSB = MSC
(Marginal Social Benefit = Marginal Social Cost)
Optimal private investment: 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.
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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
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Growing on the Cutting Edge:
The Economics of Ideas
3. Government’s Role in the Production of
New Ideas
Ideas in science 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.
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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.
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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.
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When will people work harder to invent new
ideas?
a) When they can sell the new ideas to a
(relatively large) market of 1 billion people.
b) When they can sell the new ideas to a
(relatively small) market of 10,000 people.
c) When the government imposes high taxes
on R&D expenditures.
d) When the government lowers subsidies on
R&D expenditures.
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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?
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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
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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
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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.
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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.
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Try it!
Many people say that if people save too much,
the economy will be hurt. They often refer to the
fact that consumer spending is two-thirds of
GDP to make this point. This is sometimes called
the “paradox of thrift.”
Do you agree with the “paradox of thrift” for
long-run growth?
a) Yes, since a high savings rate makes a
country poorer in the long run.
b) No, since a high savings rate makes a
country richer in the long run.
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